Using Algorithmic Mechanism Design to Solve the Data Redistribution Problem with Non-Cooperative Sensor Nodes Andre Chen July 23, 2015

Overview Motivation Data Redistribution Problem Related Work Algorithmic Mechanism Design Simplified Solution Future Work Acknowledgements References

Motivation Sensor networks deployed to collect data Examples: – Ecological monitoring Monitor ambient temperature Monitor wind speed and direction – Visual and acoustic networks Video cameras and microphones covering many areas – Underwater seismic networks Seismic sensors detecting earthquake activity underwater

Data Redistribution Problem Given a network of sensor nodes with… – Limited storage capacity – Limited battery power – No base station – No “infinite” power source … How do we redistribute data to minimize energy consumption and fully utilize the network?

Cooperative vs. Non-Cooperative Cooperative: Nodes work together towards common goal Non-cooperative: Nodes only look out for themselves

Real-world Example Business wants to gather seismic data Two options: – Hire business to handle everything – Hire independent contractors Which option is better?

Related Work Work in [1] presents a polynomial time algorithm to solve minimum cost flow Work in [2] shows current problem similar to minimum cost flow, but more difficult (approximate polynomial time) Work in [3] shows payment scheme but does not consider storage constraints

Main Problem Setup Network with two node types – Generator receives data from outside – Storage stores data – Both can receive and forward – Only storage nodes can store Node consumes energy per action How do we minimize energy consumption?

Simplified Problem Setup Include a base station Storage nodes only send and receive data (no storage) Energy consumed based only size of data received and transmission distance

Network Model (Simplified) Biconnected graph – Vertices are sensor nodes – Nodes transmit along edges Special base station node Each node has energy cost Edges are unweighted

Network Model (Continued) DG 1 and DG 2 are data generator nodes. S 1, S 2, and S 3 are data storage nodes.

Energy Model (Simplified) From [2], energy cost composed of: – Receiving: based on data size only – Transmission: based on data size and distance Each node already has energy cost computed.

Solution Approach Follow approach in [3] Pay nodes to make the right choices Use mechanism design to determine payment Prove that incentives yield desired result

Example: Vickrey 2 nd Price Auction Two players X and Y bid on item Item goes to player who values it the most Players do not reveal how much item is worth To prevent lying: highest bidder wins but pays second-highest bid price Can prove each player is best off telling truth

Algorithmic Mechanism Design Key paper by Nisan and Ronen [4] How do private preferences influence choice? Use algorithm techniques to study

Definitions and Concepts A node is a rational and selfish agent. “Rational” => behave according to function “Selfish” => behaves in best interest “Utility” => goal of each agent

Mechanism Design Problem – Agents have some private input t i ∈ T i called type. – An output specification defines some output, o, based on type – Valuation: v i (t i, o) is the value of a particular outcome to agent i – Utility: u i = p i + v i (t i, o) where p i is some currency provided by mechanism.

Mechanism Design (Continued) A mechanism m = (o, p) consists of two parts: – output function – payments A mechanism has all of the following: – for each agent i are strategies or actions, called A i – Defines an output function o(a 1, a 2,..., a n ) – Provides a payment p i (a 1, a 2,..., a n ) to agent i

Dominant Strategy Strategy is dominant if the strategy maximizes agent’s utility regardless of other agents’ strategies Not necessarily unique!

Solution Plan Use mechanism to motivate nodes to minimize energy cost Use Lowest Cost Paths (LCPs) to guarantee that energy cost is minimized. Only send data along LCPs

VCG Mechanism A mechanism is a VCG mechanism if: – strategy (direct revelation): tell truth or lie about type – objective = maximize sum of valuations – payment = sum of valuations of all agents except for agent i and some function of other agents’ types Telling the truth is dominant! => VCG mechanism is truthful

Mechanism Design Applied to our Problem Approach from [3] Agents = operators of each node Private input = t i = energy cost Let: c k = t k Rewrite: t = (t 1, t 2, …, t n ) to c = (c 1, c 2,..., c n ) Strategies: {tell truth, lie}

Application (Continued) Output specification: LCPs and prices Valuation: = packets set from i to j = 1 if node k is in the LCP from i to j; otherwise 0

Valuation Explanation Always reward participation Participation based on LCP only The negative sign indicates cost Total = cost for each packet * all packets

Mechanism Design Applied to our Problem (Continued) Objective = maximize Meet objective => energy minimzed This is VCG => truthful Utility of agent k = Where is the payment to agent k.

Payments Pay only nodes in LCP Compute LCP via Dijkstra’s Algorithm O(N 2 ), N is the number of nodes. Trick: Path is ABC. Treat energy cost of B as weighted edge distance. Apply Dijkstra’s.

Payments (Continued) Let p k be the payment to agent k given by where we define as the following:

Payments Explained

Payments Explained (Continued)

How much should D be paid? Send packet from X to Z. Lowest cost path is XBDZ (cost 3). Lowest cost path that AVOIDS D is XAZ (cost 5). Pay D: C D + (cost of the LCP that avoids D) – (cost of the LCP that includes D) = 1 + [5 – 3] = 3.

Summary of Results Use mechanism design to handle non- cooperate behavior VCG mechanism (truthful) reveals all private information Energy costs are minimized because only Lowest Cost Paths are used

Future Work Remove base station Energy model with potential fields [2] Additional costs – storage – redistribution – message passing – synchronization vs. asynchronization Increase complexity incrementally until general problem solved

Acknowledgements Dr. Tang for... – the research opportunity – help and guidance Dr. Beheshti for presentation advice (CSC 500) National Science Foundation for funding support under award number

References [1] Andrew V. Goldberg An efficient implementation of a scaling minimum-cost flow algorithm. J. Algorithms 22, 1 (January 1997), 1-29 [2] Bin Tang, Neeraj Jaggi, Haijie Wu, and Rohini Kurkal. "Energy-Efficient Data Redistribution in Sensor Networks," ACM Transactions on Sensor Networks, v.9, [3] Joan Feigenbaum, Christos Papadimitriou, Rahul Sami, and Scott Shenker A BGP-based mechanism for lowest-cost routing. Distrib. Comput. 18, 1 (July 2005), [4] Noam Nisan and Amir Ronen Algorithmic mechanism design (extended abstract). In Proceedings of the thirty-first annual ACM symposium on Theory of computing (STOC '99). ACM, New York, NY, USA,