active nearest n eighbor queries for moving objects

24.11.2002 The Fourth WIM Meeting 1

Active Nearest Neighbor Queries

for Moving Objects

Jan Kolar, Igor Timko


Outline

Problem StatementSystem Architecture Data ModelTracking Moving Objects NNC Search & Active Result Distance between Moving Points Conclusions Proposals for Bachelor Projects


Problem Statement Road Network

Copenhagen Moving Data Points

Cars, pedestrians, cyclists, ... Distance along the roads Query Point

A shop assistant Active K-Nearest Neighbor

Query

Monitor 2 nearest shoppers

that need

a nice and cheap dress Active Query Result

T1 : <A, B>

T2 : <B, C>






Query


that need


T1 : <A, B>

T2 : <B, C>




Cars, pedestrians, cyclists, ...

Query Point


Query


that need


T1 : <A, B>

T2 : <B, C>

Distance along the roads






Query


that need


T1 : <A, B>

T2 : <B, C>

?

A

B

C






Query


that need


T1 : <A, B>

T2 : <B, C>

?

Time T1

A

B

C






Query


that need


T1 : <A, B>

T2 : <B, C>

?

Time T2

AB

C


System Architecture

Active Result

Positioning Unit

Client Position

Visualization

DB of Distances

Road Network

User Query

Result

NNC Search

DB of Moving Points

Road Network

NNC Request

NNC ReplyNNC Refresh

RN Input

Position Update

RN Update

SERVER CLIENT


System Architecture

Active Result

Positioning Unit

Client Position

Visualization

DB of Distances

Road Network

User Query

Result

NNC Search

DB of Moving Points

Road Network

NNC Request


RN Input

Position Update

RN Update

SERVER CLIENT


Outline



Data Model : Overview

Problem Data Road Network (RN) Data Points (DPs)

2D Representation Captures data in native form Supports positioning and visualization Source for graph representation

Graph Representation Captures data in simpler and more ”compact” form Supports algorithms for NN search


Data Model : Road Network

2D

Graph

Real-World RN Road segments

2D RN Lines approximate road segments Lines start and end at vertices Vertices have coordinates

Graph RN Edges are obtained from paths Edges start and end at nodes Nodes have no coordinates

RoadNetwork



2D

Graph




RoadNetwork



Graph




2D

RoadNetwork



Graph

2D




RoadNetwork


Data Model : RN Characteristics

Graph

2D

Real-World RN Road segments have length, maximum

speed, and width

2D RN Lines approximate road segments Lines have length and maximum speed Lines have no width

Graph RN Edges are obtained from paths Edges have edge weight Edge weight is minimal travel time along the

edge – distance in graph Edge weight is calculated by combining line

length and maximum speed

RoadNetwork


Data Model : RN Characteristics Real-World RN

Road segments have length, maximum speed, and width





RoadNetwork

Graph

2D








RoadNetwork

Graph

2D

L=10 MS=2

L=12 MS=4

L=10 MS=5








RoadNetwork

Graph

2D

W=2+3+5=10

L=10 MS=2

L=12 MS=4

L=10 MS=5


Data Model : Data Points Real-World DPs

Movement of a DP is a continuous function of time

2D Road DPs A DP at a reference time is given by DP

characteristics (DPC): reference timecoordinatespeed

RoadNetwork

2D






RoadNetwork

2D

C(12)=(33,60)






RoadNetwork

C(12)=(33,60)

2D

T=11 C=(34,56) S=3


Data Model : Data Points 2D Road DPs

A DP at the reference time is given by DP characteristics (DPC):

reference timecoordinatespeed

Graph DPs Movement of a DP is a function of time

(positioning function) Positioning function is a combination of DPC:

reference timeedge initial positiongraph speed

2D

T=11 C=(34,56) S=3

Graph

T=11 E=3 IP=3 GS=3


Data Model : Data Points 2D Road DPs

A DP at the reference time is given by DP characteristics (DPC):

reference timecoordinatespeed

Graph DPs Movement of a DP is a function of time

(positioning function) Positioning function is a combination of DPC:

reference timeedge initial positiongraph speed

2D

T=11 C=(34,56) S=3

Graph

T=11 E=3 IP=3 GS=3

P(12)=3+3 = 6


Outline

Problem StatementSystem ArchitectureData ModelTracking Moving Objects NNC Search & Active Result Distance between Moving Points Conclusions Proposals for Bachelor Projects


System Architecture

Active Result

Positioning Unit

Client Position

Visualization

DB of Distances

Road Network

User Query

Result

NNC Search

DB of Moving Points

Road Network

NNC Request


RN Input

Position Update

RN Update

SERVER CLIENT


For a DP, its Client DPC are obtained from the Positioning Unit on the Client

For a DP, its Server DPC reside in the DB of Moving Points on the Server

Update Policy Threshold is a maximum allowed deviation between the positions

given by the Client DPC and by the Server DPC

Start

Node Node

End

Deviation

P(S)

Th Th

P(C)

Tracking Moving Points

P(C)=P(S)

Th Th

P(S)

Th Th

P(C)

Deviation

P(C)=P(S)

Th Th


Outline

Problem Statement Data ModelSystem ArchitectureTracking Moving ObjectsNNC Search & Active Result Distance between Moving Points Conclusions Proposals for Bachelor Projects


System Architecture

Active Result

Positioning Unit

Client Position

Visualization

DB of Distances

Road Network

User Query

Result

NNC Search

DB of Moving Points

Road Network

NNC Request


RN Input

Position Update

RN Update

SERVER CLIENT


NNC Search

Searches for some number of DPs that are nearest to the QP

Application of the Best First Search in graphs Extended with “reading” DPs from edges

During the search, all the DPs are fixed at the time when the search starts


NNC Search





Active Result

Distance between QP and NNCs Sorting NNCs with respect to the distance Estimate of imprecision of NNCs

Expiration Number Distance Limit


Active Result




Active Result: Procedure

Distance from QP 1 3 5 8 9

Expired DP false false false false false

Distance Limit = 10

Expiration Number = 2

Number of Expired DP = 0

NNC is Valid: YES

1 2 3 4 52 1 4 3 5Time = 1


Time = 2

1371112Distance from QP

falsefalsetruefalsefalseExpired DP

NNC is Valid: NO

15121613Distance from QP

truetruetruefalsefalseExpired DP

Time = 3


2 1 4 3 5

New NNC Request


Outline



Definition Distance between two DPs is the shortest path

between the DPs

Difficulty The shortest path between two DPs changes as

the DPs move

Distance between Moving Points



between the DPs


the DPs move



5

1

13

2

3

6

1

4

6

7


QD

QD

Q

D



Requirement Find the shortest path quickly

Idea DB of Distances: pre-compute shortest distances

between each pair of nodes Reduces the distance calculation to several

arithmetic operations


Distance between moving DP: Procedure

5

1

2 1

6

4

6

Q

D

A B

X

Y

|AX|

|AY|

|BX|

|BY|Aq

Aq

Aq

Bq

Bq

Bq

Xd

Xd

Xd

Yd

Yd

Yd

D = min


Outline

Problem StatementSystem Architecture Data ModelTracking Moving ObjectsNNC Search & Active Result Distance between Moving PointsConclusions Proposals for Bachelor Projects


Conclusions

Reusable data model Applicable for other NN, and non-NN problems

Classical algorithm for the NNC search An extension of the Best First Search

Simple idea for maintaining the active result Sort NNCs with respect to the distance to the QP Ask for new NNCs, if the current ones get too far from the QP

Efficient algorithm for the distance calculation Uses the pre-computed shortest distances between each pair of

nodes Reduces the distance calculation to several arithmetic operations


Conclusions







Conclusions

Reasonable system architecture Based on the client-server architecture Distributes the tasks in an efficient way

“Balanced” handling of position updates Updates are not performed continuously Threshold controls precision

Prototype Single-process system that simulates the real application Experiment results show that the solutions are

reasonable


Conclusions




reasonable


Outline

Problem Statement Data ModelNNC Search & Active Result Distance between Moving PointsSystem Architecture Conclusions Proposals for Bachelor Projects


Proposals for Bachelor Projects

Implementation, experiments, and improvements NNC search Active result Distance calculation Complete architecture

Extending the settings: influence on the algorithms,

the architecture, and the data model “Richer” model Uncertainty of Query Results Pre-Defined Routes Dynamic Weights


Active Nearest Neighbor Queries

for Moving Objects

Jan Kolar, Igor Timko


Uncertainty in the NN problem

Igor Timko


Outline

UncertaintyHandling Location UncertaintyConclusions


Uncertainty

Sources of the uncertainty Location of DPs NNCs Dynamic weights Partial NNC search Partial DB of distances Communication network

Problem with the uncertainty Imprecise query result

Handling the uncertainty Calculate the probabilistic NN neighbor


Uncertainty





Outline



Handling Location Uncertainty Old active result procedure

Obtain NNCs Calculate distances between the NNCs and the QP Sort the NNCs

Identifying the uncertainty Calculated distances are uncertain, because locations of NNCs are uncertain


Measuring the Uncertainty

Bounded normal distribution• Mean is at the distance value• Deviation is the update threshhold

D1 D2 D3

Th Th


New Active Result Procedure New active result procedure

Obtain NNCs For each NNC

• calculate distances between it and the QP• construct the probability distribution• calculate the probability of being NN


Conclusions

There are many sources of the uncertainty in the NN problem

The uncertainty makes the NN query result imprecise

The uncertainty is handled by the probabilistic NN queries


Conclusions






Igor Timko


Outline



Uncertainty





Outline





D1 D2 D3

Th Th


Conclusions





Outline



Conclusions






Igor Timko

active nearest n eighbor queries for moving objects

Documents

nearest neighbor querymonitor

data pointscars

shoppersthat needa nice