Data Gathering Tours in Sensor Networks

1. Data Gathering Tours in Sensor Networks Alexandra Meliou, David Chu, Carlos Guestrin, Joe Hellerstein, Wei Hong

2. Fundamental Task Basic Task: Data gathering Challenge: Limited Resources Goal: Minimize energy consumption

3. Focus: Selective Data Gathering • Motivating examples: • Specified area of interest • Model driven data acquisition (BBQ) [Deshpande et al, VLDB’04] • Standard approach: Flooding, tree-based

4. Selective data gathering with flooding More nodes participate in communication than necessary Flooding-based methods are good when we are interested in a large portion of the nodes For more selective queries, we need more specialized retrieval mechanisms

5. A better alternative Less nodes participate in communication

6. 1 2 2 2 1 1 1 1 2 2 1 2 2 3 Problem Statement • Given: • a network graph • link qualities for every edge (represented by cost function c(.)) • a data gathering query • Find: • Least expensive communication strategy, which: • Propagates the query to all nodes of interest • Retrieves all required measurements

7. Assumptions • Centralized knowledge of the network topology • Nodes do not maintain neighbor tables Semi-static Number of links Success probability variance

8. Query Propagation & Data Gathering • In previous work treated as 2 separate phases • But: Can be done simultaneously packet

9. Simple Solution: A simple tour Optimal Solution: A splitting tour

10. Minimum Splitting Tour Problem • The splitting tour with the minimum cost is optimal • Properties: • Spans all nodes of interest (red nodes) • Is strongly connected • For every node, there needs to be a path from the basestation to that node, and a path from the node to the basestation.

11. Problems with Splitting Tours • Theorem: Solving the problem is NP-hard • Tricky to implement: • Merges require complicated waiting rules

12. Simplifying the problem • Relevance to a familiar problem • Traveling Salesman Problem (TSP)!!! • Advantages: • Simpler • Easy to implement • Well studied • Problem: • CostST ≤ CostTSP Cost of the optimal TSP Solution Cost of the optimal Splitting Tour

13. TSP vs Splitting Tour • So… TSP is always worse than the optimal Splitting Tour: CostST ≤ CostTSP • But never too much worse: Theorem: CostTSP ≤ 1.5CostST • Constant factor approximation! but… • TSP still NP-hard…

14. TSP TSP TSP TSP A Polynomial Algorithm • Christofides approximation algorithm gives a tour with cost Cost ≤1.5 CostTSP • A naïve bound would be: Cost ≤ 1.5*1.5 CostST= 2.25 CostST • But we can get an even better bound of: Cost ≤ 1.75CostST • Constant factor approximation and polynomial!

15. Practical Issue I • Packets are finite • Cannot fit all the information • Heuristics: • Using multiple packets • Cutting tours into smaller ones • Cutting is performed with dynamic programming • Hybrid: using both the above approaches

16. Simulations: Big Tours cutting multiple packets hybrid infinite packet Using hybrid achieves performance very close to optimal with reasonably small packet size

17. Practical Issue II • Assumed semi-static topology • But node and link failures will still occur • Recovery algorithms: • Backtracking • Local flooding

18. Backtracking Nodes need to maintain the ID of the previous hop for the query duration Cannot deal with disconnected components in the path caused by multiple failures

19. Local Flooding Worst case is full flood Performance depends on exact protocol (see paper for details)

20. TOSSIM: Recovery Simple backtracking surprisingly effective Backtracking (5% failures) Backtracking (5% failures) Flooding (5% failures) Flooding (5% failures) Backtracking (10% failures) Backtracking (10% failures) Flooding (10% failures) Flooding (10% failures) Backtracking (15% failures) Backtracking (15% failures) Flooding (15% failures) Flooding (15% failures)

21. Conclusions • Combined the tasks of query propagation and data gathering • Suggested splitting tours as a communication strategy • Proved hardness • Provided polynomial constant factor approximations • Addressed practical issues (oversize tours, reliability)