Data gathering tours in sensor networks
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Data Gathering Tours in Sensor Networks. Alexandra Meliou, David Chu, Carlos Guestrin, Joe Hellerstein, Wei Hong. Fundamental Task. Basic Task: Data gathering. Challenge: Limited Resources. Goal: Minimize energy consumption. Focus: Selective Data Gathering. Motivating examples:

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Data Gathering Tours in Sensor Networks

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Data Gathering Tours in Sensor Networks

Alexandra Meliou, David Chu, Carlos Guestrin, Joe Hellerstein, Wei Hong


Fundamental Task

Basic Task: Data gathering

Challenge: Limited Resources

Goal: Minimize energy consumption


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


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


A better alternative

Less nodes participate in communication


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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


Assumptions

  • Centralized knowledge of the network topology

  • Nodes do not maintain neighbor tables

Semi-static

Number of links

Success probability variance


Query Propagation & Data Gathering

  • In previous work treated as 2 separate phases

  • But: Can be done simultaneously

packet


Simple Solution: A simple tour

Optimal Solution: A splitting tour


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.


Problems with Splitting Tours

  • Theorem: Solving the problem is NP-hard

  • Tricky to implement:

    • Merges require complicated waiting rules


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


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…


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!


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


Simulations: Big Tours

cutting

multiple packets

hybrid

infinite packet

Using hybrid achieves performance very close to optimal with reasonably small packet size


Practical Issue II

  • Assumed semi-static topology

  • But node and link failures will still occur

  • Recovery algorithms:

    • Backtracking

    • Local flooding


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


Local Flooding

Worst case is full flood

Performance depends on exact protocol (see paper for details)


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)


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)


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