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The Threshold Join Algorithm for Top-k Queries in Distributed

Sensor NetworksD. Zeinalipour-Yazti , Z. Vagena,

D. Gunopulos, V. Kalogeraki,V. Tsotras

Proceedings of the 2nd international workshop on Data Management for sensor networks (DMSN’05)

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Introduction

• Let R be a relation with n attributes s1,s2,…,sn, each featuring m objects o1,o2,…om.

• Oij: The jth attribute of the ith object.• qj: The jth attribute.

• 1>=sim(qj,oij)>=0 ; wj > 0

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Introduction

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Threshold Join Algorithm• Lower Bound: the querying node finds a

lower bound on the lists by probing the nodes in a network.

• Hierarchical Joining: each node uses the lower bound for eliminating the objects that are below this bound and join the qualifying the objects that are below this bound and join the qualifying objects with results coming from children nodes.

• Clean-Up: the actual top-k results are identified.

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Lower Bound (LB) Phase

• list(Vi) : each node Vi sort in descending similarity order the elements in list(Vi).

• listk(Vi) : the objectIDs of the k local highest ranked objects.

• listk(Vj) : listk(Vi) include all its children Vj.

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Hierarchical Join (HJ) Phase

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Clean-Up (CL) Phase

• Computing the complete score or an upper bound of this score.

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Threshold Join Algorithm(Example)

O3:0.67O4:0.67O1:0.58

O3:0.74O1:0.56

O1:0.92O3:0.75

O1:0.91O3:0.90

O3:0.9901:0.66

Find the time moment with the highest average temperature.

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Threshold Join Algorithm(Example)

V5 V4 V3 V2 V1

O4=0.67+0.56+0.75+0.90+0.66=3.54O3=0.67+0.74+0.75+0.90+0.99=4.05O1=0.58+0.56+0.92+0.91+0.66=3.63

The Querying node has calculated an upper bound of 3.54 for O4, which is less than the score of O3 (i.e. 4.05), and so the querying node does not have to execute the CL phase.

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Experimental Evaluation

• CJA: Centralized Join Algorithm• SJA: Staged Join Algorithm• TJA: Threshold Join Algorithm• penalty(Oi)=realrank(Oi)-rank(Oi)• Average error function

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Experimental Evaluation

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Experimental Evaluation

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Conclusion

• Hierarchical Join

• Experimentation under Failures