1. 1 The Threshold Join Algorithm for Top-k Queries in Distributed Sensor Networks D. Zeinalipour-Yazti, Z. Vagena, D. Gunopulos, V. Kalogeraki, V. Tsotras Proceedings of the 2nd international workshop on Data Management for sensor networks (DMSN’05)

2. 2 Introduction Let R be a relation with n attributes s 1,s 2,…,s n, each featuring m objects o 1,o 2,…o m. O ij : The j th attribute of the i th object. q j : The j th attribute. 1>=sim(q j,o ij )>=0 ; w j > 0

3. 3 Introduction

4. 4 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.

5. 5 Lower Bound (LB) Phase list(V i ) : each node V i sort in descending similarity order the elements in list(V i ). list k (V i ) : the objectIDs of the k local highest ranked objects. list k (V j ) : listk(V i ) include all its children V j.

6. 6 Hierarchical Join (HJ) Phase

7. 7 Clean-Up (CL) Phase Computing the complete score or an upper bound of this score.

8. 8 Threshold Join Algorithm(Example) O 3 :0.67 O 4 :0.67 O 1 :0.58 O 3 :0.74 O 1 :0.56 O 1 :0.9 2 O 3 :0.7 5 O 1 :0.91 O 3 :0.90 O 3 :0.99 0 1 :0.66 Find the time moment with the highest average temperature.

9. 9 Threshold Join Algorithm(Example) V 5 V 4 V 3 V 2 V 1 O 4 =0.67+0.56+0.75+0.90+0.66=3.54 O 3 =0.67+0.74+0.75+0.90+0.99=4.05 O 1 =0.58+0.56+0.92+0.91+0.66=3.63 The Querying node has calculated an upper bound of 3.54 for O 4, which is less than the score of O 3 (i.e. 4.05), and so the querying node does not have to execute the CL phase.

10. 10 Experimental Evaluation CJA: Centralized Join Algorithm SJA: Staged Join Algorithm TJA: Threshold Join Algorithm penalty(Oi)=realrank(Oi)-rank(Oi) Average error function

11. 11 Experimental Evaluation

12. 12 Experimental Evaluation

13. 13 Conclusion Hierarchical Join Experimentation under Failures