a scalable correlation aware aggregation strategy for...

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Information Fusion 9 (2008) 354–369

A scalable correlation aware aggregation strategyfor wireless sensor networks

Yujie Zhu a,*, Ramanuja Vedantham a, Seung-Jong Park b, Raghupathy Sivakumar a

a School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, Georgia 30332, USAb Department of Computer Science Louisiana State University, Baton Rouge, LA 70803, USA

Received 8 September 2005; received in revised form 4 September 2006; accepted 23 September 2006Available online 13 November 2006

Abstract

Sensors-to-sink data in wireless sensor networks (WSNs) are typically characterized by correlation along the spatial, semantic, and/ortemporal dimensions. Exploiting such correlation when performing data aggregation can result in considerable improvements in thebandwidth and energy performance of WSNs. In this paper, we first identify that most of the existing upstream routing approachesin WSNs can be translated to a correlation-unaware data aggregation structure – the shortest-path tree. Although by using a short-est-path tree, some implicit benefits due to correlation are possible, we show that explicitly constructing a correlation-aware structurecan result in considerable performance improvement. Toward this end, we present a simple, scalable and distributed correlation-awareaggregation structure that addresses the practical challenges in the context of aggregation in WSNs. Through simulations and analysis,we evaluate the performance of the proposed approach with centralized and distributed correlation-aware and -unaware structures.� 2006 Elsevier B.V. All rights reserved.

Keywords: Sensor networks; Data aggregation; Information fusion; Correlation; Data gathering

1. Introduction

Wireless sensor networks (WSNs) have gained tremen-dous importance in recent years because of their potentialuse in various fields. However, the devices used for sensingand communication in these networks are usually small,cheap and low-powered and hence, have limited resourcesfor computation as well as for communication. This hasspurred a need for efficient protocols tailored specificallytowards sensor network environments.

One of the key tasks performed by any WSN is the col-lection of sensor data from the sensors in the field to thesink for processing. This task is also referred to as data

gathering. An important challenge associated with data

1566-2535/$ - see front matter � 2006 Elsevier B.V. All rights reserved.

doi:10.1016/j.inffus.2006.09.002

* Corresponding author.E-mail addresses: [email protected] (Y. Zhu), [email protected]

ch.edu (R. Vedantham), [email protected] (S.-J. Park), [email protected] (R. Sivakumar).

gathering is to reduce the message cost to minimize thebandwidth usage of the network and the energy consump-tion of the sensor nodes. In this paper, we consider theproblem of efficient data gathering in environments wherethe data from the different sensors are correlated. Such cor-relation of data being collected can be leveraged by appro-priately fusing the data in the network to the best extentpossible. Hence, the specific problem addressed in thiswork can be stated as: How should an energy-efficient data

gathering structure be constructed to leverage any existingcorrelation between data reported by the sensors?

Many research work have proposed solutions to con-struct correlation-aware structures [1–3]. However, theseapproaches are either centralized and require completeknowledge regarding the number and location of sources,or do not address several important practical challengesfor WSNs, such as ease of construction, maintenanceand synchronization requirements. Therefore, thoseapproaches are not suitable for a real-life sensor networkenvironment.

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Y. Zhu et al. / Information Fusion 9 (2008) 354–369 355

In this context, we present a simple, scalable, and dis-tributed approach called SCT (semantic/spatial correla-tion-aware tree) that does not require any centralizedcoordination while still achieving potential cost benefitsdue to efficient aggregation. The SCT structure is instanta-neously constructed during the course of a single querydelivery and does not require any knowledge of the numberof sources or their locations. The SCT approach, with itshighly manageable structure, ensures low maintenanceoverhead of the aggregation structure, eliminates the needfor global synchronization among sensors for aggregationof sensor-data, while also addressing the other challengesdescribed in Section 4 including load balancing and nodefailures. Through simulations and analysis, we establishthe message costs incurred by SCT for a variety of networkconditions, and compare them with an ideal correlation-aware and a correlation unaware approach. We show thatSCT, though simple in its realization, can achieve substan-tial performance benefits.

The rest of the paper is organized as follows: Section 2defines the problem and Section 3 discusses existing datagathering structures and analyzes their characteristics.Section 4 identifies the different challenges in designing apractical, efficient correlation-aware structure. Section 5presents the key design principles in the SCT approachand describes how it addresses the corresponding chal-lenges. Section 6 explains the SCT approach in detail.Section 7 evaluates the performance of SCT in comparisonto ideal structures and practical implementation of shortestpath tree (SPT). Section 8 discusses the issues pertaining tothe SCT approach while Section 9 concludes the paper.

2. Problem definition

We consider a multi-hop WSN with one sink at the cen-ter and n sensors distributed randomly in a circular fieldaccording to a Poisson process.1 The sink sends a queryand k of the n sensors respond to the query. We refer tothese sensors that have information to send as sources inthe rest of the paper. We assume that all the sensors havethe same fixed transmission range equal to cr0, where c isa small constant (c > 1) and r0 is the minimum connectivitytransmission range [4].

As a measure of the energy efficiency of a data gatheringstructure, we define its message cost as the total number oftransmissions required for responses from all k sources toreach the sink. Our primary goal is to minimize messagecost when there is correlation present between data fromdifferent sources.

The following two types of correlations are consideredin this paper:

1 Note that the assumptions about the shape of the sensor field and thelocation of the sink are made for better illustration of the proposedapproach and are not essential to the solution. We will discuss theimplications of different network shapes and sink locations in Section 8.

• Spatial correlation: This refers to the correlation of thedata reported by multiple sensors sensing the same eventor phenomenon. For example, consider the query: whatis the temperature in the region defined by the rectangle(x1,y1,x2,y2)? Given the typical dense deployments ofsensors in WSNs, it is likely that the sensing regions oftwo different sensors within the rectangular region over-lap. Consequently, the data reported by these sensorsare spatially correlated. If the two sensors are very closeto each other, the data reported by both sensors is prac-tically the same, which implies that the sensors are per-fectly correlated.

• Semantic correlation: This refers to the correlation ofdata reported by multiple sensors due to the semanticsof the query. The messages from different sensors report-ing different events or phenomena and hence the contentof these messages may not be spatially correlated. How-ever, if the query imposed is not about the specificdetails of each event, but about certain statistics overthe entire event region, it is likely that the messages gen-erated by each source can still be aggregated. For exam-ple, consider the query: Is the total number of cars in therectangular region (x1,y1,x2,y2) greater than K? In thiscase, even if the sensors are reporting data about differ-

ent cars, the information reported is correlated as it isonly required to find the total number of cars and con-sequently determine if it is greater than K. Responses tostatistical queries such as min, avg, max, usually fallunder this category.

Characterizing the correlation existing between sensordata is a fairly complicated task, since the nature of corre-lation differs with the type of applications considered. Evenfor a simple correlation model, the mathematical represen-tation becomes difficult when multiple distributed sourcesare involved. For simplicity, we adopt the same correlationmodel used in reference [1], where each raw data packet isassumed to bring a fixed amount of new information intothe aggregated data packet. Specifically, if q is defined tobe the correlation degree, and m to be the sizes of raw datapackets generated by sensor nodes, then after aggregationof two data packets, the message size becomesm + (1 � q)m. Similarly, for n sources, the aggregated datapacket has a size of m + (n � 1)(1 � q)m. Correlationdegree q = 1 means that two messages are perfectly corre-lated (i.e. semantic correlation) therefore can be reducedto one message of the same size. Correlation degree0 < q < 1 indicates that two messages are partially corre-lated (i.e. spatial correlation), while q = 0 implies thattwo messages are independent of each other.

3. Related work

3.1. Correlation unaware approaches

We now consider two of the popular choices used in thedesign of routing protocols in sensor networks: (i) using the

356 Y. Zhu et al. / Information Fusion 9 (2008) 354–369

query paths to construct the sensors-to-sink routes and (ii)using the location information of sensors and the sink toforward messages to the sink. Most of the contemporaryrouting approaches [5–7] fall under one of the two catego-ries in terms of basic routing design principle. We considerdirected diffusion [5] and GPSR [6] as representative exam-ples of (i) and (ii), respectively, and show that the structuregenerated by these approaches can be translated to a Short-est Path Tree (SPT).

In directed diffusion [5], sink requests data by sendinginterests for named data. The interests are propagatedthrough the network wherein every node delivers the inter-est to all its neighbors through a local broadcast. Duringthe diffusion process, all nodes set up gradients towardstheir neighbors from which the interest was received. Whilethere are different possible criteria for the reinforcement ofthe gradient, the most common practice results in a short-est path tree rooted at the sink [1,8].

GPSR is a geographic routing protocol that eliminatesthe need to maintain states while performing routing. Inthis approach, every source in the sensor field knows thegeographical location of the sink, and addresses the mes-sage for sink with the specific location. For each hop alongthe path to sink, a node chooses the node closest in geom-etric distance to the sink as the next hop destination andforwards the message to it. Since GPSR delivers a vastmajority of packets in the optimal number of hops [6],the data gathering tree again approximates shortest pathtree.

From the previous discussion we establish that two ofthe representative routing schemes in sensor networks areapproximations of shortest path trees. Since the primarygoal of this structure is to minimize delay, shortest pathtree is not a correlation-aware data gathering structure.Even though opportunistic aggregation may still occurwhen different paths overlap with each other, this structuredoes not maximize the aggregations possible in the net-work. A correlation-aware structure, on the other-hand,would be able to cut down message cost by explicitly facil-itating data aggregation in the network.

3.2. Correlation-aware approaches

Several related work have been proposed in the contextof explicit aggregation [1–3,8]. We categorize them into twogeneral classes: correlation-aware structures assumingcomplete global source knowledge and incomplete sourceknowledge.

3.2.1. Structures built with complete source knowledge

When the full knowledge about source location isknown, the Steiner tree over all sources, sink and non-source nodes gives the optimal message cost when thedegree of correlation is close to 1. However, the computa-tion of Steiner tree is an NP-hard problem [9].

In [1,8], the authors propose simple heuristics thatapproximate the Steiner tree to perform efficient aggrega-

tion when messages are correlated. For any given correla-tion factor 0 < q 6 1, the authors describe (i) leavesdeletion heuristic and (ii) balanced SPT/multiple TravelingSalesman Problem (TSP) tree as simple alternatives of theSteiner tree.

In [10], the authors first identify that the message costcan be modeled as a concave-cost function for any correla-tion factor 0 < q < 1, and propose an algorithm that con-structs approximation trees simultaneously good for allconcave cost functions.

However, these approaches require complete informa-tion regarding the number of sources and their locationto be available at the sink and cannot work for the caseswhen the information is incomplete. While such informa-tion can be made available via queries and responses, theoverheads involved in acquiring such information both interms of message cost and delay could be potentially pro-hibitive. Moreover, they are centralized approaches hencedo not scale well with increasing node densities typical toWSN environments. Finally, these approaches try to solvethe problem of efficient aggregation from a theoretical per-spective and do not consider the practical challenges thatwe identify in Section 4.

3.2.2. Structures built with incomplete source knowledge

[2,3] address the more general problem of buildingaggregation structure with optimal expected cost whenthe knowledge of sources is incomplete.

The problem considered by both work is a network witha root node and a collection of N client nodes in the net-work. Each client, i, may choose to contact the root inde-pendently from others with some probability pi along apath from itself to the root. If a client chooses to contactthe root, the edges on this path become active. The goalis to minimize the expected number (or cost) of active net-work edges over a random choices of the clients. This prob-lem is a stochastic version of the deterministic Steiner treeproblem.

The stochastic Steiner tree problem is an NP-completeproblem. Therefore, the focus of this work is on developingconstant-factor approximation algorithms. In [2], theauthors observe that the optimum solution is invariably atree, and the optimum tree consists of a central ‘‘hub’’ areawithin which all edges are almost certainly used, togetherwith a fringe of ‘‘spokes’’ in which multiple clients contrib-ute independently to the cost of the solution. To set up agood approximation structure, their solution leverages afacility location algorithm to identify a good set of ‘‘hubs’’to which clients route messages at independent costs, andthe set of hubs are connected using a Steiner tree algorithm.In [3], the authors design a similar structure constructed intwo stages: during the first stage, a subset of nodes D ischosen by picking each node independently from the net-work with probability proportional to pi, then a minimumspanning tree is built over D; later revealed clients request-ing services are connected to the existing structure with anaugmentation algorithm. Using the above principle, the


authors propose a two-approximate algorithm for the sto-chastic Steiner tree problem.

Both papers propose good constant-factor approx-imation algorithms. However, they are not distributedsolutions and are not tailored for sensor network environ-ments. For example, [2] requires building a Steiner treeover ‘‘hubs’’, and [3] requires building a minimum span-ning tree to form a first-stage backbone. Both need central-ized computation with high complexity. Also, they assumea fixed probability for nodes responding to a query and donot handle the situation where the source density is vari-able. Finally, they do not address all the practical chal-lenges we identified in Section 4.

4. Challenges

The main goal of this work is to design an efficientaggregation structure that minimizes the message cost. Torealize this goal, we first identify the following importantchallenges and list the desirable properties of a solutionthat addresses the challenges.

4.1. Construction

The foremost consideration in building an aggregationstructure is the manner in which the aggregation structureis constructed. We have already seen that existingapproaches in WSNs are correlation unaware and approx-imate a shortest path tree (SPT). In a SPT, aggregation isnot efficient even if the data from the sources are highlycorrelated because the primary concern is to minimize thedelay. The ideal solution for the aggregation structurewould be a Steiner tree or a stochastic Steiner tree [2],which depends on whether complete source knowledge isavailable at the time of construction. However, both prob-lems are NP-hard.

Even the approximation algorithms for constructing aSteiner tree impose requirements such as the informationregarding the number of sources and the location of themto be available at the sink a priori. This information couldbe obtained if the sink adopts a two-phase querying proce-dure, where the query is sent in the first phase and theresponses collected reveal the location of the sources inter-ested in responding to that query. In the second phase, thesink initiates the construction of the approximation of aSteiner tree to optimize the message cost of the data trans-mitted. However, the overhead involved is O(k), where k isthe number of sources. This overhead might be comparableor even exceed the message cost of the aggregated mes-sages. Another drawback of such a two-phase approachis the delay incurred in determining required information.

Moreover, the types of queries and responses sent mayinfluence the nature of the ideal solution required foraggregation. The queries and responses can be categorizedas (1) single query and one-time responses from thesources, (2) single query and multiple continuous responsesfrom the same set of sources and (3) single query and multi-

ple responses from a varying set of sources. We will explaineach of these classifications briefly and present the idealsolution for each classification:

• One-shot queries and responses: In this category, the sen-sors send a one-time query and the correspondingresponses from the sources are also one-time responses.In this case, the two-phase procedure that we had dis-cussed above will be clearly infeasible both in terms ofdelay and message cost, since the message cost of thefirst phase will be comparable to the message cost ofthe aggregated responses. If the probability distributionof sources is given, the stochastic Steiner tree is the opti-mal aggregation structure.

• Single queries and multiple responses from the same set of

sources: Here, the sink sends one-time queries but theresponses from each sensor may comprise multiplepackets. However, the set of sensors responding to thequery remains the same over all the packets. If the num-ber of continuous responses is large, the cost incurred indetermining the number of sources in a two-phaseapproach could be amortized over the message costsinvolved in aggregation. In this case, the network Steinertree is the optimal aggregation solution.

• Single query and multiple responses from a varying set of

sources: Here, the responses to the one-time queries maycomprise multiple messages but the responding sourcesets may vary with time. For this case, it is desirableto have a solution that is independent of the locationof sources or the number of sources. Therefore, the opti-mal solution is neither a network Steiner tree nor a Sto-chastic Steiner tree problem as the set of sources andtheir probability can vary for different packets. Wedefine this problem as a generalized Stochastic Steiner

tree problem.

In summary, a desirable practical solution should con-sider the tradeoffs between the overhead involved in theconstruction process itself on the one hand, and the mes-sage cost of the aggregation structure on the other hand,and ensure that it is reasonably efficient across all queryand response paradigms.

4.2. Maintenance

An aggregation structure may be modified or recon-structed after a certain period of time to accommodate loadbalancing, node failures or for any other reasons.

Load balancing is to ensure that the energy consumedby all the nodes is fairly even over a certain period of time.In an aggregation structure, aggregation nodes take theresponsibility of receiving, computing and transmitting ofaggregated messages, hence consume more energy thannon-aggregation nodes. If the role of aggregation node isperformed by a certain node for a long time, this nodemay fail much earlier than other nodes, impacting the con-nectivity of the network. To address this issue, we would

2 Ratio of the number of sensors that send data packets to the sink to thetotal number of sensor nodes in the network.


like to spread the roles of aggregation nodes among allnodes so that the network does not become disconnectedprematurely.

The aggregation structure should also be resilient tonode failure, which is very common in sensor networks.Otherwise, it is likely that some messages will never reachthe sink even though there may be alternate paths avail-able. Therefore, when node failure occurs, the structureshould have the ability to adapt and form a different,near-efficient structure.

One way to reconstruct the structure is where the nodessend explicit beacons to the central coordinator requestinga structure modification, and the coordinator reconstructsthe structure partially or globally according to the numberof nodes requesting such changes. However, this approachrequires central coordination and may incur large over-heads. In a more desirable approach, nodes should be ableto reconstruct the aggregation structure in a distributedfashion with low overheads and delay.

4.3. Synchronization requirements

One of the main considerations for any aggregationscheme is the time each node has to wait before it aggre-gates the messages received from all sources downstreamof it. We refer to these timing requirements as synchroniza-tion requirements. In the absence of such timing require-ments, messages from some downstream sources mayarrive after aggregation at a particular aggregation nodeand hence need to be transmitted separately. This willincrease the message cost despite the existence of an effi-cient aggregation structure.

Ideally, a scheme should enable an aggregation node towait until the arrival of messages from all sources down-stream before aggregation is performed. One way to do thisis by having a timer at every node and wait for the expira-tion of the timer based on a waiting function, similar to theone described in [11], before performing aggregation. Inthis approach, each node waits for a time correspondingto MAX � i · D after the reception of the first response,where MAX is the maximum wait time proportional tothe depth of the aggregation tree constructed, i is the hopcount of the node from the sink and D is the average degreeof a sensor node. When the timer expires, it is assumed thatall the messages from sources downstream have arrived atthis node and the messages are aggregated. One of theobvious problems of this approach is that the nodes usethe average degree of the network as opposed to the degreeof that particular node. This makes the timer value notaccurate and may cause imperfections in aggregation. Onthe other hand, the problem with incorporating a fine-grained timer is the higher message overhead of time syn-chronization, and complicated computation at each sensornode.

In order to address this problem, an ideal aggregationstructure should facilitate event-driven aggregation andshould rely on timing requirements only sparingly. In this

case, the timers can be made coarse as they will not be usedoften.

4.4. Other considerations

An aggregation approach should also be reasonably effi-cient in terms of message cost when the degree of correla-tion varies (0 < q 6 1). In addition, it should be able toperform efficient aggregation irrespective of the distribu-tion of sources. As we will see in Section 7, the proposedapproach takes into account these considerations andperforms reasonably well for a wide range of networkscenarios.

5. The SCT design basis

The design of SCT is predicated on two importantelements:

• An aggregation backbone facilitating the generation ofefficient aggregation trees

• A fixed structure independent of source distribution anddensity.2

These two design elements address the challenge of effi-cient construction, and incorporate the characteristics andrequirements of sensor networks. In this section, we estab-lish and justify these two design elements. The details ofSCT approach will be present in Section 6.

5.1. Motivation for a ring-and-sector division

Our target problem of data collection with variablesource distributions and densities can be thought of as ageneralized version of the stochastic Steiner tree problem.The stochastic Steiner tree gives the optimal message costwhen there is a given source probability while our goal isto find the efficient aggregation tree for variable sourceprobabilities. In [2,3], the authors have presented central-ized constant-factor approximations to the stochastic Stei-ner tree problem. In this subsection, we will providemotivation of the structure we used to approximate thegeneralized stochastic Steiner tree, adopting similar argu-ments provided by the above two related work.

Consider the network model in which each sensor, i, hasa probability, pi, to report data to sink. If an edge e

between two sensor nodes is used by a set of source nodeD to transmit data to sink, then the cost of this edge canbe defined as:

ce ¼ Pr½e is active� ¼ 1�Yi2D

ð1� piÞ ð1Þ

Fig. 1. SCT structure: rings, sectors and aggregation nodes.


This cost function captures the tradeoffs in the characteris-tics of data transmission and correlation in sensor net-works as follows: when more sources use one particularedge, the total communication cost for this edge increases;on the other hand, the cost per message decreases due tothe correlation between multiple messages. Since the ce isa concave function, if the number of sources using one edgeis beyond a certain value, adding more sources causes onlya minimal increase in the total cost. Therefore, it pays toplace a certain number of aggregation nodes in the networkwith the property that all the edges between those aggrega-tion nodes are highly utilized. The sources can then connectopportunistically to closest aggregation nodes using edgeswith a higher cost. With this structure, the total expectedcost of the aggregation tree for a certain source probabilitydistribution can be minimized.

Based on these observations, a good aggregation struc-ture should have the following features: (i) A subset ofnodes is chosen as aggregation nodes and a spanning treeis built on top of these nodes to form a ‘‘backbone’’ foraggregation; (ii) Each node in the backbone is responsiblefor aggregating messages from sources within a certainsub-area.

There are many ways to construct the aggregation back-bone. In this paper, we design a uniform division of the net-work to assist in the construction of the backbone, basedon the following criteria:

• The division of the network should facilitate the distrib-uted selection of aggregation nodes within the networkwith no additional message overhead.

• The division should result in energy-efficient data aggre-gation irrespective of distribution of sources.

• The interconnection of aggregation nodes to form thebackbone should be achieved in a distributed fashionwith low overhead.

• The division of the network should ensure easy connec-tivity of all non-backbone nodes to the aggregationbackbone.

In SCT, one such efficient division of the network isadopted, where the network is divided into rings and sec-tors. The division not only addresses all of the above desiredcriteria, but is also characterized by several impressivepractical benefits, including lack of global synchronization

requirement for aggregation of sensor-data, ability to per-form load balancing with no additional message overhead,ability to address node failures, etc. The ring-sector division

is also characterized by the unique invariant that a message

sent by any source always propagates towards the sink at

each hop, because of the symmetrical structure of the divi-

sion. We elaborate more on the motivations of ring-sectordivision in SCT later in this section and in Section 6.

As illustrated in Fig. 1, the network is divided into mconcentric rings with the same width (R/m). Each ring isin turn divided into sectors of the same size such that onaverage each sector contains about n0 nodes. For each sec-

tor, an aggregation node is chosen as a member of theaggregation backbone, and each aggregation node in ithring is connected to it’s upstream aggregation node in (i-1)th ring via shortest path. The collection of all aggregationnodes and shortest paths form the backbone aggregationtree. Each aggregation node is responsible for collectingmessages from all sources in the sector it belongs to.

As we will see in the Section 6, this structure can facili-tate the realization of a desirable aggregation backbone ina distributed fashion. But the problem is only partiallyaddressed because our goal is an optimal aggregation struc-ture for variable source densities. Therefore, the next ques-tion is what is the optimal number of the aggregationnodes. An immediate observation is that with increasingnumber of sources, the number of optimal backbone aggre-gation nodes increases. This can be explained intuitively asfollows: when the number of sources is small, probabilityof aggregating two or more messages from different sourcesat an aggregation node is relatively small. Moreover, hav-ing more aggregation nodes translates to a backbone withhigher cost, because of the additional transmissionsrequired by the aggregation nodes. Therefore, fewer aggre-gation nodes are more desirable.

However, as source number increases, the probabilitythat two or more messages from sources being aggregatedat each aggregation node increases. Therefore, addition ofaggregation nodes helps in aggregating the messages fromdifferent sources as early as possible. In this case, the addi-tional cost incurred by introducing extra aggregation nodescan be offset by the reduced high-transmission cost edgesused due to early aggregations. Hence, as source densityincreases, more aggregation nodes are desirable.

As we identified above, a good approximation of opti-mal structure should adapt with different source densities:the higher the source density, the more nodes are involvedin the backbone. This indicates that the proposed ring-sec-tor structure should also adapt to source densities in orderto approximate the optimal solution. However, in the nextsubsection, we will show that a fixed structure satisfyingcertain properties is reasonably efficient for a wide range

Fig. 2. The optimal structures when n = 2000.


of source densities, and hence motivate a relatively stableaggregation structure with low maintenance overhead.

5.2. Motivation for a source-independent aggregation

structure

In the previous sub-section we pointed out that for thering-sector structure proposed, the optimal number ofaggregation nodes increases with the source density. In thissub-section, we will show that when the source density isbeyond a certain point, the optimal structure stays thesame because of a ‘‘saturation’’ phenomenon. Thus, bychoosing a fixed aggregation structure, we are able to doefficient aggregation for a large range of source densitieswhile incurring very little construction overhead.

The optimal sector size generally reduces with increasingsource density. But this reduction is not always desirable.Consider a certain threshold source number k0 at whichthe optimal sector size is small enough such that aggrega-tion node just falls into transmission range of every othernode in the sector. We call the size of the sectors at thispoint the saturation size. In this case, every source messagecan reach aggregation node with 1-hop transmission.Reducing sector beyond the saturation size will not helpincreasing aggregation efficiency. Furthermore, the intro-duction of additional aggregation nodes increases the mes-

1700

1900

2100

2300

2500

2700

2900

10 15 20 25 30 35

Sector Size (n0)

Nu

mb

er

of

Tra

nsm

issi

on

s

n=6000, k=1500 n=8000, k=2000

Fig. 3. Find the opt

sage cost. Thus, when the number of sources, k, isincreased beyond k0, decreasing the sector size results inincreased message cost. Therefore, when k > k0, the opti-mal aggregation structure should remain the same.Fig. 2(a) and (b) are visualizations of the aggregation treeswhen each sector reaches saturation size. These figuresshow the SCT aggregation tree constructed over all sourcenodes and aggregation nodes. The scattered points on thebackground are non-source, non-aggregation nodes.Fig. 2(a) is the optimal aggregation tree when n = 2000and k = 250, and Fig. 2(b) is the optimal structure whenn = 2000, and k = 500. From the two figures we canobserve that the ‘‘backbone’’ of the aggregation trees arethe same, only the sources increase in the latter case. Thisis because saturation is already achieved when k = 250.Therefore, even if k increases, the optimal structureremains the same. Notice that the above ‘‘saturation’’ phe-nomenon is not specific to the ring-sector structure we pro-posed, but is true for the optimal aggregation structure ingeneral due to the fixed transmission ranges of all sensornodes.

The effect of saturation on message cost is also substan-tiated by other simulation results. Fig. 3(a) shows for a cer-tain n and k how the message cost of aggregation treevaries with varying sector size n0. When n0 is small, themessage costs of the aggregation trees decrease as n0

Optimal n0 vs. k (n=4000)

0

10

20

30

40

50

60

70

0 500 1000 1500 2000 2500 3000 3500

Source number (k)

Op

tima

l se

cto

r si

ze (

n0)

imal sector size.

Table 1Comparison of computed and experimental m* and n�0

Nodedensity

Computedm*

Experimentalm*

Computedn�0

Experimentaln�0

n = 2000 8.54 9 13.9 16n = 4000 11.6 12 14.9 16n = 6000 14.1 15 15.5 16n = 8000 16.1 17 16.0 16

Fig. 4. Maximum travel distance within a sector.


increase. However, after n0 = 16, costs increase withincreasing n0, indicating saturation for both cases.

Fig. 3(b) shows how the optimal n0 varies with k/n. Fora wide range of source densities, the optimal structure is thesame. This implies that a fixed aggregation structure isgood enough most of the time in our application.Simulation results for other node densities give similarresults.

We now describe how the optimal values for m3 and n04

can be estimated at the sink. Both parameters are chosensuch that each sector in the network reaches the saturationsize. The choice of m and n0 is explained next.

The choice of m determines the depth of the aggregationtree. Since the downstream aggregation nodes are sourcesfor the aggregation nodes one ring closer to the sink, toachieve saturation size, level-i aggregation nodes shouldbe within 1-hop distance to level-i + 1 aggregationnodes. Therefore, m can be determined by the followingformula:

m� ¼ Rr

b ð2Þ

where R is the radius of the network, r is the transmissionrange of the nodes, and b is a constant used to accommo-date the fact that aggregation nodes are not distrubted on astraight line. We choose a empirical value of 1.32 for bbased on experimental results.

Determination of n0 is based on the requirement thatevery node within this sector is less than 1-hop away fromthe aggregation node. Refer to Fig. 4, the furthermost pos-sible node within this sector is located at the corner of thissector, we indicate the distance of this node to aggregationpoint as b. The distance b is calculated in the right-angledtriangle as follows:

3 The total number of rings in network, or the aggregation levels.4 The average number of sensor nodes in each sector, determines the

sector size.

z ¼ ði� 1ÞR sin am

ð3Þ

y ¼ iRm� ði� 1ÞR cos a

mð4Þ

b ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiz2 þ y2

pð5Þ

¼ Rm

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið4iði� 1Þ sin2 a

2Þ þ 1

rð6Þ

The angle a for the ith ring is given by:

a ¼ m2n0p2ð2i� 1Þn ð7Þ

When a! 0, sin a2! a

2, and Eq. (6) reduces to

b ¼ Rm

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1

2ðm

2n0p2nÞ2 þ 1

rð8Þ

To make sure b is less than transmission range, we let b = rr, where r < 1 is a constant. From Eqs. (8) and (2), and wecan derive the optimal n�0 for large k as:

n�0 ¼ 0:428rR

� �2ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffirb2 � 1

qð9Þ

Through empirical studies, we determine r = 0.836. Toverify the accuracy of the choice of constants, we compareoptimal m and n0 derived from Eqs. (2) and (9) and thoseobtained from simulations. Table 1 shows that the theoret-ical values match experimental optimums closely.

6. The SCT approach

In this section, we explain the SCT approach in detail.We present the different phases of the data aggregationprocess as well as provide insights for the design choices.

6.1. Division of the network

During the setup phase, the sink propagates the follow-ing information to the entire network: (i) location of itself,(Xs,Ys), (ii) the total number of nodes, n (iii) the radius ofthe network, R and (iv) the computed values for m and n0

to all the nodes in the network. Each node in the network isassumed to know it’s own geographical location. When anode receives the packet, it first computes the distancebetween itself and the sink. This determines the ring, i, towhich it belongs to. For example, any node at a distanced from the sink, such that ði� 1Þ R

m < d 6 i Rm, belongs to

the ith ring. Each node can calculate the number of sectors

Fig. 5. A Subsection of the SCT aggregation structure.


per ring s(i) as: sðiÞ ¼ d2ði�1Þnn0m2 e. Given the locations of the

node with respect to the sink and the number of sectorswithin the ring, any node can determine the sector numberto which it belongs.

6.2. Determination of aggregation nodes

Once the network has been divided into sectors andrings, the aggregation node for each sector has to beselected. In the SCT approach, the aggregation nodes areselected by leveraging the fixed, geometric division of thesensor field.

For each sector in a given ring, the geometric center ofthe lower arc bounding the sector is defined as the ideallocation of the aggregation node for this sector. The nodeclosest to this ideal location is chosen as the aggregationnode. Given the value of m and n0, each source not onlyknows the sector and ring numbers to which it belongsbut can also determine the boundaries of the sector. If weare to adopt polar coordinates and if a and b are thebounding angles of a sector corresponding to the ith ring,the location of the aggregation node is given byði� 1Þ R

m ;aþb

2

� �.

Each source within this sector routes messages to thislocation of the aggregation point. During the query for-warding phase, each node piggybacks the coordinates ofitself along with the query and other information sent bythe sink. In this fashion, a node can learn the locationsof its immediate neighbors during the query delivery phase.When a source wants to send it’s message to the ideal loca-tion of the aggregation point, it sends the packet to thenode closest to the ideal location. Once a node receives thispacket, it then does a local broadcast declaring itself as theaggregation node. Since most of the nodes within any sec-tor are in a one-hop region of the aggregation node, theother source nodes will then forward their packets to thisaggregation node. In this way, the node closest to this ideallocation becomes the aggregation node where messages areaggregated. In a few cases, it is possible that two sourcesmay elect two different nodes as aggregation nodes simulta-neously. However, such instances are rare and do notincrease the message cost considerably because of the fol-lowing two reasons: (i) most of the nodes in a sector arewithin a 1-hop region of each other, and (ii) once a nodeis elected as the aggregation node, the local broadcast willenable other sources to identify this node as the aggrega-tion node.

Thereafter, these aggregation nodes act as sources forthe sectors in the next ring closer to the sink, and sendaggregated messages to aggregation nodes of those sectors.With this approach messages are combined step by step asthey progress towards the sink, until the last ring isreached, for which the sink is the aggregation node.Fig. 5 is a illustration of this aggregation process.

The aggregation nodes are implicitly elected by the rout-ing protocol when the sources first send their data to thelocation of the aggregation nodes. To ensure that an aggre-

gation nodes is elected at every sector irrespective of thepresence or absence of sources in that sector, we adoptthe following procedure in the last ring: (i) During thequery forwarding phase, some nodes in the last ring iden-tify themselves as a corner nodes within each sector. Thecorner nodes are located at the periphery of the upperarc bounding a sector and farthest from the ideal locationof the aggregation node. (ii) These corner nodes take on theresponsibility to identify the physical aggregation node forthis sector by forwarding a dummy packet to the geograph-ical location of the aggregation node. Note that this proce-dure needs to be done only for sectors in the last ring asthese aggregation nodes act as sources when communicat-ing to the upstream aggregation nodes.

This geometric election of the aggregation nodes facili-tates independent and distributed computation of aggrega-tion point locations by each node. It also enables a locationbased routing approach to be used to send packets fromthe sources to the aggregation nodes or between aggrega-tion nodes. The geometric structure construction andaggregation nodes election allow each node to have a con-sistent view of the entire network to help set up the SCTstructure in a distributed fashion.

6.3. Event-driven data collection

To achieve maximum aggregation of the source data atthe aggregation nodes, it is also necessary to ensure thatthese nodes wait for an optimum delay value. In Section4, we identified the drawbacks of using a fine-grainedaggregation timer to trigger the aggregation process. InSCT we use a more desirable alternative where there areonly coarse-grained timers and the aggregation process ismainly event-driven. This approach is motivated by thefact that each aggregation node knows the exact numberof children that are also aggregation nodes. When anaggregation node receives information from all childrenthat are aggregation nodes, it is assured that the data fromall sources within the sector are also received by an aggre-gation node. This is because the sources transmit their dataat the beginning of each message collection round while theaggregation nodes wait for the notifications from all the


downstream aggregation nodes. The arrival of messagesfrom all downstream aggregation nodes is used as the trig-ger to merge and propagate the information collected,upstream towards the sink. Thus, synchronization isachieved in an event-driven fashion without the need forexplicit delay timers at each aggregation node.

The aggregation node identification procedure in the lastring also helps in determining the time to aggregate andforward messages to the upstream aggregation node. Evenif there are no sources within a sector, the aggregation nodesends out a small message to the upstream sector indicatingthe absence of sources. The arrival of messages from all thedownstream aggregation nodes is used to trigger the aggre-gation process in that aggregation node. In this way, theaggregation process is mainly event driven. For the casewhen there are no nodes in a downstream sector, there willnot be any downstream aggregation node in that sector. Inthese rare cases, the aggregation nodes use the coarse-grained aggregation timer before aggregating the messagesfrom other downstream aggregation nodes and sources.Note that the probability of occurrence of such empty sec-tors is extremely low as we will discuss in Section 8.

6.4. Load balancing

Load balancing schemes, as we have identified in Section4, are important to ensure that the resources of all non-source nodes are utilized to roughly the same extent overa period of time. We propose two simple schemes to dis-tribute the roles of aggregation nodes to different sets ofnodes over a certain period of time:

(1) Location of the rings: In the current SCT description,the different rings are of width R

m, where R is the radiusof the network and m is number of rings. To do loadbalancing, the location of the first ring can be shiftedby a distance R

m� rc, where r is the one-hop transmis-sion range and c is a small integer that is varied from0 � � � R

mr. The same offset is applied to every ring so thatthe width of the ring is still maintained to be R

m for allrings except the first and last.

2) Orientation of the sectors: In a similar way, we canchoose the offset angle for a sector to be differentacross multiple queries. The offset angle, h, can beincremented according to the relation, h ¼ c

sðiÞ wheres(i) is the number of sectors in the ith ring and c isa small integer dependent on the query identifier. Thisagain assures that different nodes are chosen as aggre-gation nodes over several query floods.

6.5. Aggregation reliability and node mobility

The failure of any non-aggregation node will not impactthe correctness or efficiency of the SCT approach. There-fore, here we only discuss how the aggregation node failuresare addressed in SCT. Recall that we require an aggregationnode to announce itself to its neighbors once it receives the

first message from a source. In this way, aggregation nodefailures before the setup of the SCT structure can be identi-fied by the lack of announcement from the particular node,and another node closet to the ideal location can announceitself as the aggregation node of this sector. If an aggrega-tion node fails during the information collection phase,the lack of ACK messages from this node to sources caninform them of its failure. In this case, the retransmissionof the first packet enables the election of a new aggregationnode, which in turn broadcasts an announcement uponreceiving the retransmitted message. After the re-election,aggregation proceeds as usual. Notice that the election ofa new aggregation node may delay the entire aggregationprocess due to the retransmissions and announcement nec-essary, but the correctness and efficiency of the aggregationprocess will not change since it is event-driven.

In the case of node mobility, the proposed solutionneeds to be modified to accommodate mobility in (i)sources, (ii) aggregation nodes and (iii) other nodes. Ifthe sources are mobile but the aggregation nodes are fixed,sources will forward to the closest aggregation node givenits current location. If aggregation nodes are mobile, thenode failure handling mechanism can be leveraged to electa new aggregation node for that sector. Mobility of othernodes does not affect the SCT approach.

7. Performance evaluation

In this section we evaluate the performance of the SCTapproach under different network configurations and com-pare it with two centralized schemes: minimum SteinerTree, SPT, and one decentralized scheme: DSPT (Decen-tralized Shortest Path Tree). We vary the node density,source density, source distribution, as well as correlationcoefficient (q) and evaluate the message cost of the fourstructures under different scenarios.

7.1. Simulation environment

• We use a discrete event simulator based on the LECSsimulator for all evaluations. The simulation topologiesare largely similar to those used in general sensor net-works: 2000–8000 nodes are uniformly distributedwithin a circular field of radius 400 m. The number ofsources that generate messages for one specific queryvaries from 1

10, 1

6, 1

4to 1

2of the total number of nodes in

the network.• We evaluate the SCT approach using two metrics: mes-

sage cost and data gathering latency. For message cost,we measure the total number of transmissions requiredfor all responses to reach the sink for one round of datacollection, and for data gathering latency, we measurethe time interval from the time when all sources startto send messages, to the last message reaches the sink.

• To focus on the comparison of aggregation efficiency ofdifferent structures, we assume a perfect MAC layer thatavoid collisions of data packets.


• All the simulation results are derived after averagingresults over 10 random seeds and are presented within95% confidence intervals.

• Since minimum Steiner tree is the optimal solution whensources are fixed, we compare SCT with an approxima-tion of minimum Steiner tree (MST) generated usingPrim’s algorithm. We also compare the SCT with SPTgenerated by Dijkstra’s algorithm because it is represen-tative of correlation-unaware structures. To highlight thebenefit of SCT as a distributed solution, a decentralizedversion of the shortest path tree (DSPT) is also includedin the evaluation. In DSPT, GPSR routing protocol isused to approximate SPT in a distributed fashionbecause the routes generated by GPSR closely approxi-mate SPT, especially when node density is high [6].

7.2. Perfect correlation (q = 1) scenarios

7.2.1. Different node densities

We first compare the performance of the decentralizedSCT with that of the DSPT. In this scenario, we assumethat data from all sources are correlated perfectly (q = 1).We will address the (q < 1) case later in this section.

Fig. 6(a)–(c) show the cost of two decentralized schemesas a function of the number of nodes for different numbersof sources k. In these simulations, we choose the totalnumber of nodes n as 2000, 4000, 6000, and 8000, andthe number of sources k as n

10, n

4, and n

2, respectively. To

ensure fair comparison, we assume DSPT uses an explicitmechanism to achieve perfect aggregation, therefore themessage cost is a measure of the aggregation structure effi-ciency only (we will present results related to delay perfor-mance of both schemes later). It can be seen that SCToutperforms DSPT scheme under all situations. Interest-ingly, we observe that the cost of DSPT is up to 200% ofthe SCT cost as the number of nodes increases. The DSPTcost also increases faster than the SCT cost as node num-ber increases. This is expected since more nodes reducesthe efficiency of aggregation in DSPT as the paths chosenby different sources are less likely to overlap. Therefore,SCT can be considered a more scalable approach. Further-more, it is observed that the difference between the two

0.0

0.5

1.0

1.5

2.0

2.5

3.0

0 2000 4000 6000 8000 10000

Number of nodes (k=n/10)

Nu

mb

er

of

tra

ns

mis

sio

ns

[ X

10

3 ]

DSPT SCT

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

5.0

0 2000 4000

Number o

Nu

mb

er

of

tra

ns

mis

sio

ns

[ X

10

3 ]

DSPT

Fig. 6. Performance comparison between SCT, and DSPT: Figure (a), (b), anddifferent source densities k.

schemes increases as the ratio of the number of sourcesto the number of nodes, k

n, decreases because more sourcesincrease the probability of aggregation for DSPT. As theratio k

n approaches 1, both schemes converge into n

transmissions.

7.2.2. Decentralized vs. centralized schemes

We compare the performance of the decentralized SCTand DSPT schemes with the centralized schemes theyapproximate. Fig. 7 shows the cost of the proposed schemeand the centralized schemes as a function of the nodenumber. To evaluate the cost of the centralized schemes,we assume perfect aggregation for both SPT and MST.From the figures we can see that DSPT’s message costapproaches closely that of SPT while SCT’s message costapproaches closely the cost of MST. Furthermore,although SCT is a decentralized scheme without perfectaggregation, it still outperforms the centralized SPT, sinceSCT explicitly aggregates sensor data, while SPT just lever-ages aggregation opportunistically. We also observe that asthe k/n ratio increases, the difference between both decen-tralized schemes and their approximated centralizedschemes decreases, because as k increases, both schemescan achieve better aggregation and approach the perfor-mance of an ideal structure.

7.3. Different correlations (0 < q < 1)

In the extreme case of q = 1, minimum Steiner tree is theoptimal aggregation structure, while for q = 0 (no correla-tion), SPT is the optimal aggregation structure. For thegeneral case 0 < q < 1, no optimal solution exists. Andthe problem is classified as NP-complete in [1].

In Fig. 8, we characterize the message complexity ofSCT when the correlation coefficient varies from 0.2 to0.9. Notice that in this graph, the number of transmissionsis normalized to a unit message size. For example, if afteraggregation, a node transmits a message of size 1.5 timesthe unit message size, it is counted as 1.5 transmissions.From this figure, we can see that for both DSPT andSCT, message cost reduces as q increases, since the twoschemes have either implicit or explicit mechanisms to

6000 8000 10000

f nodes (k=n/4)

SCT

0.0

1.0

2.0

3.0

4.0

5.0

6.0

7.0

0 2000 4000 6000 8000 10000

Number of nodes (k=n/2)

Num

ber

of tr

ansm

issi

ons

[ X10

3 ]

DSPT SCT

(c) show the number of transmissions as a function of number of nodes for

0.0

0.5

1.0

1.5

2.0

2.5

0 0.2 0.4 0.6 0.8 1

Correlation coefficient

Nu

mb

er o

f tr

ansm

issi

on

s [

X 1

03 ]

DSPT SCT

0

2

4

6

8

10

12

14

0 0.2 0.4 0.6 0.8 1

Correlation coefficient

Nu

mb

er o

f tr

ansm

issi

on

s [

X 1

03]

DSPT SCT

Fig. 8. Performance comparison between SCT and DSPT in case of different correlation factor q.

Fig. 7. Performance comparison between SCT and centralized schemes, SPT and MST: Figure (a) and (b) show the number of transmissions as a functionof number of nodes for different number of sources k.


leverage the correlation. However, the message cost of SCTreduces faster than DSPT because it facilitates aggregationat an earlier stage of packet forwarding, hence can reducepacket transmission cost more effectively. Since DSPT isthe optimal structure when q = 0, we expect that the twocurves will cross each other at a certain small correlationfactor. For n = 8000, the cross point occurs at q = 0.2,while for n = 2000, the cross point is expected to occur atq < 0.2. As we analyzed earlier, DSPT aggregates less effi-ciently when n becomes large, hence it does not lose muchwhen q decrease, therefore it performs relatively better fora smaller q when n is large.

7.4. Delay sensitivity

To evaluate a data gathering scheme, latency is anotherimportant metric besides the message cost. In this part, westudy the data gathering latency of SCT and at the sametime characterize the message cost-latency trade off forSPT.

Since SCT is an event-driven approach, none of theaggregation nodes on the tree needs a timer, and eachaggregation node can forward messages as soon as itreceives responses from downstream aggregation nodes.Therefore, there is very little overhead for perfect aggrega-tion. While for SPT, in order to achieve perfect aggrega-tion, each node on the tree has to set a timer and waitfor a certain amount of time before aggregation.

Since SPT itself does not include any mechanism foraggregation timing, we implement a simple scheme [11] thatsets aggregation timer for each node based on its hop dis-tance to the sink. Each node on the tree knows its distance(in hop count) as well as the maximum distance D amongall nodes on the tree to the sink (depth of the tree). Givena maximum delay MAX_DELAY, per-hop delay D is calcu-lated as MAX_DELAY/D. A node that is i hops away fromthe sink will wait for MAX_DELAY-i * D time beforeaggregating and forwarding data it has received. In thisway, if D is large enough to accommodate transmissionand contention delay at each hop, perfect aggregationcan be achieved.

Fig. 9 shows the number of transmissions as a functionof maximum delay MAX_DELAY for n = 2000 andn = 4000 cases. It is shown that SPT achieves perfect aggre-gation when MAX_DELAY is more than 8.0 s. However,the cost of SPT increases as MAX_DELAY approaches5.0 s since smaller MAX_DELAY increases the possibilityof late arrivals of data before aggregation. Once a packetmisses its aggregation deadline at one of the intermediatehops, the probability of it missing deadlines at later hopsbecomes higher, which explains why SPT performanceaggravates quickly as MAX_DELAY decreases. On theother hand, since SCT is an event driven data aggregationstructure, its message cost remains the same irrespective ofdifferent delays, which explains the flat curves in bothfigures.

0.5

0.7

0.9

1.1

1.3

1.5

1.7

1.9

4 5 6 7 8 9Delay (second)

Nu

mb

er o

f tr

ansm

issi

on

s (x

103 )

DSPT SCT

0.5

0.7

0.9

1.1

1.3

1.5

1.7

1.9

4 5 6 7 8 9Delay (second)

Nu

mb

er o

f tr

ansm

issi

on

s (x

103 )

DSPT SCT

Fig. 9. Performance comparison between SCT and SPT in case of different delays.


7.5. Localized events

Until now, we have assumed that sources are deployedindependently in a sensor field. This is typical when consid-ering semantic correlation, where each source reports infor-mation about a discrete event. However, spatial correlationusually generates non-uniformly distributed sources, wheremultiple sources are reporting the same event. In this case,sources are clustered around one or more spots in the net-work. In this section, we investigate how SCT performswhen sources are distributed in such a fashion.

In the simulation, we consider n = 2000 and n = 8000scenarios, each has a total of k ¼ n

4sources in the network.

The number of events (spots) in the network is varied fromk

100, k

50� � � to k

5. With this configuration, the total number of

sources does not change, but the distribution varies from ahighly concentrated scenario to close to uniformdistribution.

Fig. 10(a) and (b) show the simulation results for suchspot topologies. When there are very few events and sourcedistributions are highly concentrated, DSPT achieves goodaggregation at early stage and aggregated messages reachthe sink along only a few paths. But SCT also performswell because SCT does explicit aggregation within each sec-tor that contains sources, while other sectors withoutsources or not on the aggregation paths to the sink donot take part in the aggregation process, therefore doesnot incur any extra cost. From the figure, we can see thatat n = 2000, when the number of events is small, DSPT

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0 20 40 60 80 100 120

Number of events

Nu

mb

er o

f tr

ansm

issi

on

s [

X 1

03

]

DSPT SCT

Fig. 10. Performance comparison between SCT and DSPT for Different nu

and SCT have similar cost. But as the number of eventsincreases, sources are less concentrated as in the previouscase, and the probability of DSPT paths overlappingreduces, hence the higher message cost. However, forSCT the only extra cost is the introduction of more aggre-gation nodes into the aggregation tree, which is limited bythe total number of sectors in the network. Therefore, theincrease of message cost is much less compared with DSPT.For n = 8000 case we observe a similar trend, and even forthe least event number, SCT outperforms DSPT, becauseas we analyzed earlier, the chance of DSPT paths overlap-ping decreases as node density increases.

8. Issues and discussions

8.1. Empty sectors

In Section 6, we assumed that each sector contains atleast one node which can serve as an aggregation pointand ensure that the tree is connected. However, due tothe irregularity of Poisson node distribution, it is possiblethat some of the sectors may not contain any node. Here,we investigate the implications of having an empty sector.In this case, downstream aggregation nodes of the emptysector won’t find a path to aggregate, and hence will notbe able to forward the aggregated information. The designof SCT has a simple back up strategy in this case: if anaggregation node is not able to find an aggregation nodeupstream, it will simply forward the aggregation message

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 100 200 300 400 500Number of events

Nu

mb

er o

f tr

ansm

issi

on

s [

X 1

03

]

DSPT SC T

mbers of localized events in case of 2000 and 8000 nodes, respectively.


to a neighbor in the adjacent sector. After that, the aggre-gated message will be delivered via a connected aggregationpath.

Although this is a less efficient aggregation path, weargue that the probability of empty sectors is extremelylow for the target environment.

Consider a network with n nodes and S total number ofsectors of the same size, the probability that no empty sec-tor exists in the network is:

P ¼Sn �

PS�1

i¼1

s

i

� �ðS � iÞnð�1Þiþ1

Sn

¼ 1�XS�1

i¼1

s

i

� �1� i

S

� �n

ð�1Þiþ1

where

S ¼Xm

i¼1

sðiÞ ¼Xm

i¼1

ð2i� 1Þnmn0

ð10Þ

For the n�0 and m* we chose for the fixed structure, theprobabilities of non-empty sectors for various node densi-ties are shown in Table 2.

8.2. Comparison with clustering approaches

Structure-wise, SCT approach bears a few similaritieswith clustering algorithms proposed for ad-hoc and sensornetworks [12,13]. In a clustering approach, the entire net-work is partitioned into clusters of similar size, with a headnode elected in each cluster. Non-cluster nodes report mes-sages via a short path to their corresponding cluster heads,where messages are aggregated and transmitted to the sink,and the total transmission cost is reduced through thedecreased total transmission distance and smaller messagesize. With this analogy, a natural question to ask is: How

is SCT different from these clustering algorithms?

In terms of cluster construction, there are two differentsolutions from existing works. One approach is for eachnode to broadcast in a certain area its properties (id, nodedegree, residual energy etc.), following which an electionprocess is executed to choose the cluster head [13,14]. Thisapproach generally assures regular cluster size and fullnode coverage, but at the cost of high communication over-head. Using the approach proposed in [13], the clusteringalgorithm is triggered at periodic intervals to select newcluster heads. At each interval, the clustering processrequires a certain number of iterations to finally select

Table 2The probability of non-empty sectors

Node density Probability (%)

n = 2000 99.97n = 4000 99.99n = 6000 99.94n = 8000 99.89

the desired cluster head. If the minimum probability ofa node becoming a cluster head is p, it takes N 6dlog2

1pe þ 1 steps for the election algorithm to terminate

(N = 6 � 15 iterations for average scenarios). During eachiteration, a tentative cluster head generates broadcastingmessages, resulting in a total message cost (for setting upthe cluster structure) to be of order N*n, where n is thetotal number of nodes in the network. This translates tosignificant energy consumption, given that the election pro-cess is invoked repeatedly to achieve load balancing. Incontrast SCT does not require the overhead of messageexchange in either the initial set up phase or in the latermaintenance phase, where structure modifications areperformed.

Another approach, such as the one used in [12], is tospecify a certain probability for each node to become acluster head, and the node which turns out to be clusterhead announces itself through a limited-scope flooding.This approach incurs lower message overhead, but cannotguarantee a uniform cluster head distribution and full cov-erage of all non-cluster nodes. Therefore, the orphan nodesnot covered by any cluster heads have to transmit theirmessages directly to the sink, significantly increasing thetotal message cost. On the contrary, in SCT, aggregationnodes are chosen implicitly without any message exchange,since the location of the node is the criteria for head selec-tion. Therefore, in terms of clustering forming overhead, itis comparable to the probability-based approach. On theother hand, the clustering structure formed in SCT is orga-nized such that each node is guaranteed to be covered byan aggregation node, and every cluster has similar size.In this sense, a low message cost is achieved without incur-ring any overhead for additional message exchanges.

In terms of cluster manageability, SCT benefits from itshighly regular structure. Since cluster heads consume moreenergy in terms of communication and computation, clus-ter head rotation is a essential part of any clusteringscheme. For most of the clustering schemes, rotationinvolves re-election of cluster heads, which incurs a lot ofoverhead. While with SCT, since the structure is symmetricalong all radii, a simple rotation of the SCT rings and sec-tors moves the roles of cluster heads to a different set ofnodes in the network. With carefully designed rotationsequence, the role of cluster heads can be evenly distributedto all sensors in the network.

8.3. Impact of network shape and sink location

In the previous sections, we assume that the sensor net-work has a circular shape and the sink is located at the cen-ter of the network. These assumptions are made for ease ofdiscussion and presentation of SCT. The approach itselfdoes not impose any constraint on the shape of the net-work and the location of the sink. For example, considera network with rectangular shape and the sink located atone of the four corners of the rectangle. In this case, theSCT structure can still be constructed by fitting the entire


network into a polar coordinate, with sink being the rootof the SCT and the diagonal of the rectangle being theradius. Load balancing can be achieved as well by shiftingthe rings and sectors periodically as described before.Although the efficiency of the SCT structure for irregularnetwork shapes may not be as high as that of circular net-work shape, the correctness of SCT is not compromised.

8.4. Other related work

In [15], a TTDD approach is proposed to provide scal-able and efficient data delivery to multiple mobile sinksin sensor fields. Each data source in TTDD pro-activelybuilds a grid structure which enables mobile sinks to con-tinuously receive data on the move by flooding querieswithin a local cell only. This approach is similar to SCTin that they both construct virtual geometric structures (agrid structure in TTDD and a ring-sector structure inSCT) to facilitate data delivery. However, TTDD addressesthe problem of communication between sensors and mobilesinks in the sensor field. The focus of TTDD is point-to-point communication in wireless sensor networks, whileour work focuses on data collection in many-to-onecommunication (i.e. data aggregation). Furthermore, theprimary challenge addressed in [15] is to maintain connec-tivity between senders and receivers when one of them ismobile, while we consider mainly static sensor networksand focus on the energy-efficiency of the data aggregationprocess.

EWSN [16] proposes combining passive clusteringscheme with directed diffusion to restrict the flooding ofinterests and exploratory data at the initial stage of directdiffusion. Passive clustering is proposed in [17] to controlthe exchange of flooded messages in sensor networks.Instead of constructing a cluster structure pro-actively, thisscheme piggybacks all control information on data mes-sages to save the cost required for setting up clusters, atthe cost of less up-to-date clustering structures. A simplecluster-head selection approach, where the first sensornodes declaring itself as cluster-head wins, is used to reducethe overhead of complicated clustering approach. Theapplication of passive clustering to directed diffusion caneffectively reduce the flooding overhead of interest andexploratory message propagation. However, it does notaddress the problem of improving the aggregation effi-ciency of directed diffusion, which is the problem consid-ered in this work.

In [18], the authors describe an approach to set up con-nections among a given set of cluster heads to ensure a con-nected backbone among cluster heads. In this approach, arandom distributed algorithm is proposed to provide con-nectivity with high probability. The focus of this work isensuring connectivity of cluster heads (aggregation nodesin our context), while our focus is to select a subset ofnodes as aggregation nodes to minimize the total messagecost of data gathering. Therefore, the contributions ofthese two works are orthogonal to each other.

9. Conclusions

In this paper, we propose a novel solution to aggregatecorrelated information from a subset of sensors to the sink.The proposed scheme is scalable, distributed, requires min-imal computation and is highly-manageable compared withexisting solutions. The proposed scheme is assessed bothintuitively and analytically. Through simulations, we com-pared the proposed scheme with ideal, centralized datastructures as well as a distributed structure. Simulationresults show that as a correlation-aware structure, SCTperforms significantly better than correlation-unawarestructures in terms of message cost and data gatheringlatency.

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