efficient algorithms to monitor continuous constrained k nearest neighbor queries

Efficient Algorithms to Monitor Continuous Constrained k Nearest Neighbor Queries

Presented by: Mahady Hasan

Joint work withMuhammad Aamir Cheema, Wenyu Qu, Xuemin Lin

University of New South Wales, Australia

Wednesday, April 19, 2023 Presented by: Mahady Hasan2

Outline of the Presentation

• Introduction

• Related Work (Motivation)

• GridTree Approach

• ArcTrip Approach

• Continuous monitoring

• Experiments

• Conclusion


What is NN?

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Finding kNN objects. Let k=3Finding contrained kNN objects. Let k=3

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What is Constrained NN?



• Introduction





• Experiments

• Conclusion


Related works

• Constrained kNN queries:– H. Ferhatosmanoglu et al. first introduce the

constrained kNN queries (SSTD 2001). – Gao et. al find k-nearest trajectories in a

constrained region. (DASFAA 2008)

• Continuous k NN queries:– YPK-CNN( Yu et al. ICDE 2005)– SEA-CNN (Xiong et al. ICDE 2005)– CPM (Mouratidis et al. SIGMOD 2005)


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Related work: CPM

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Heap

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Finding one Nearest Neighbor

We check an cell or entry before we insert in the heap that it intersects with the given constrained region or not.


Motivation

We have observed that in case of our problem setting CPM needs to check lots of cells before it inserts the cell in the cellin the heap.

So CPM becomes expensive in terms of computational time.

At the same time CPM needs more space to store the heap and visit lists to updatethe data efficiently.

So we use some other access methods that are more naturalwith our problem setting



• Introduction





• Experiments

• Conclusion


Concept of Grid-Tree Structure

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Intermediate Entries

Grid Cells


Grid-Tree based NN search algorithm

Heap

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q

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R3R4c11c13 c14c21 c22 c23c24 o9o8 o6

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R1c44

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Grid-Tree Based constrained NN Algorithm

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q

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• Introduction





• Experiments

• Conclusion


Concept of ArcTrip

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Output:•cells that intersect the arc with in θstart and θend

with radius r from the query point q

Input:•Radius r•Angle range θstart , θendθstart θend

r

Returned values are c22, c32, c33


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ArcTrip Based contained NN Algorithm

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Heap

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Finding 1 constrained NN



• Introduction





• Experiments

• Conclusion


Continuous monitoring

• Phase 1: receive object and query updates.– Find affected queries.– Change in the queries based on the update below.

• Internal update (dist(oold,q)≤q.distk Λ dist(onew,q)≤q.distk)

– Arrange the order in q.CkNN

• Incoming update (dist(oold,q)>q.distk Λ dist(onew,q)<q.distk)

– Insert object in q.CkNN

• Outgoing update (dist(oold,q)≤q.distk Λ dist(onew,q)>q.distk)

– Remove object from q.CkNN


Continuous monitoring …

• Phase 2: Check the status of each query one by one– If query moved then

• Execute the initial algorithm.

– If q.CkNN > k then • Keep top k objects and remove rest of the objects.

– If q.CkNN < k then • Expand the search area by visiting more cells



• Introduction





• Experiments

• Conclusion


Experiment Setup

Parameter Range

Grid size 162, 322, 642, 1282, 2562, 5122

Object cardinality 20k , 40k, 60k, 80k, 100k

Query cardinality 100, 200, 500, 1000, 2500, 5000

Values of k 2, 4, 8, 16, 32, 64, 128

Object/query speed Slow, Medium, Fast

Object/query agility 10%, 30%, 50%, 70%, 90%

Brinkhoff data generator; Oldenburg city (Germany).


Grid cardinality effect

16 3.5480.0003.5483.54803.5483.5480.2293.778 .1323.5500.0003.5503.55003.5503.5500.2973.847 .6643.5580.0003.5583.55803.5583.5580.7164.274 1.11283.5730.0003.5733.57303.5733.5732.2275.800 1.62563.6190.0003.6193.61903.6193.6198.17111.790 2.15123.7430.0003.7433.74303.7433.74330.72934.472 2.6

Need to check too many objects.

Need to check many empty cells.


Grid Memory Effect

CPM stores the heap and the visit list.


Effect of k size


Cardinality Effect

Updating in CPM become expensive


Speed Effect

In CPM paper it was showed that speed has no affect.


Agility effect

With increase in query agility CPM needsto compute the results from the scratch.

Object agility results more updates so the computation cost increases.



• Introduction





• Experiments

• Conclusion


Conclusion

• We proposed two novel Grid access methods.

• We devise two algorithms to compute the constrained k nearest neighbors.

• Our experimental results show our algorithms performs much better than the existing algorithm in terms of memory space and run time.

Thank you…

Questions??


Some changes to calculate distance

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Cell 1Cell 2

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mindist(q,Cell1)maxdist(q,Cell2)mincdist(q, Cell1)maxcdist(q, Cell2)

efficient algorithms to monitor continuous constrained k nearest neighbor queries

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mahady hasanoutline

mahady hasanarctrip

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mahady hasanmotivationwe

mahady hasangridtree

mahady hasanconcept

constrained knn queries

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