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Energy-Efficient Distributed Algorithms for Ad hoc Wireless Networks

Energy-Efficient Distributed Algorithms for Ad hoc Wireless Networks. Gopal Pandurangan Department of Computer Science Purdue University. Energy-Efficient Distributed Algorithms. Ad hoc wireless sensor networks operate under severe energy constraints.

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Energy-Efficient Distributed Algorithms for Ad hoc Wireless Networks

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  1. Energy-Efficient Distributed Algorithms for Ad hoc Wireless Networks Gopal Pandurangan Department of Computer Science Purdue University

  2. Energy-Efficient Distributed Algorithms • Ad hoc wireless sensor networks operate under severe energy constraints. • Energy-Efficient distributed algorithms are critical. • Low energy algorithms even possibly at the cost of reduced quality of solution : Distributed approximation algorithms. • Algorithms use only “local” knowledge: Localized algorithms Purdue University

  3. Distributed Algorithms • Traditionally complexity measures: messages, time. • Much of theory assumes point-to-point network communication model. • Wireless needs new models for designing distributed algorithms. Purdue University

  4. Traffic Monitoring with Sensors Purdue University

  5. Data Aggregation - Low Cost Tree Data aggregation • Aggregate data on a tree • Use a low cost tree Purdue University

  6. Desirable Features • Simple and local Purdue University

  7. Desirable Features • Simple and local Purdue University

  8. Desirable Features • Simple and local • Dynamic- handle node failures Purdue University

  9. Desirable Features • Simple and local • Dynamic- handle node failures • Distributed • Low energy • Low synchronization • Small number of messages • Low degree Purdue University

  10. Problem • Network Model: Weighted unit disk graph (UDG) • Find a Minimum Spanning Tree (MST) rooted at a given node • MST is a difficult problem • Can we construct an approximately good spanning tree? Purdue University

  11. Nearest Neighbor Tree (NNT) SchemeKhan and Pandurangan. DISC, 2006, Best Student Paper Award. Given: A (connected) undirected weighted graph G. • Each node chooses a unique rank. • Each node connects to its nearest node (via a shortest path) of higher rank. Purdue University

  12. 3 6 2 4 5 1 NNT Construction Output is a spanning tree called NNT. Purdue University

  13. NNT Theorem (Khan, Pandurangan, and Kumar. Theoretical Computer Science, 2007 Theorem 1: On any graph G, NNT scheme produces a spanning tree that has a cost of at most O(log n) times the (optimal) MST. Purdue University

  14. Distributed NNT Algorithm Each node executes the same algorithm simultaneously: • Rank selection. • Finding the nearest node of higher rank. • Connecting to the nearest node of higher rank. Purdue University

  15. s u Rank Selection • Root s selects a number p(s) from [b-1, b] • s sends ID(s) and p(s) to all of its neighbor in one time step. • Any other node u after receiving the first message with ID(v) and p(v) from a neighbor v: • Selects a number p(u) from [p(v)-1, p(v)) • Sends ID(u) and p(u) to all of its neighbors Purdue University

  16. Defining Rank • For anyuandv, r(u) < r(v) iff • p(u) < p(v) • or p(u) = p(v) and ID(u) < ID(v) • A node with lower random number p() has lower rank. • Ties are broken using ID() Purdue University

  17. Tree construction • Each node knows the rank of all of its neighbors. • The leader s has the highest rank among all nodes in the graph. • For every node (except s), there is a neighbor with higher rank. It connects to that node. Purdue University

  18. NNT algorithm • Very localized. • O(|E|) messages. • O(Diameter) time. • Low energy complexity. Purdue University

  19. Energy complexity of a distributed algorithm • Energy complexityis a measure of the energy needed by the distributed algorithm. • Various factors affect energy complexity • Time needed. • Number of messages exchanged. • Radiation energy needed to transmit a message through a certain distance --- typically assumed proportional to some power of the distance. • Energy overheads of the hardware (startup energy, receiver energy etc.) • …. Purdue University

  20. Energy Complexity Purdue University

  21. A Comparison of Algorithms Algorithm Energy Complexity MST Quality GHS (log^2 n) optimal KPK (TPDS 08) O(log n) on average O(log n)approximation CKKP (SPAA 08) O(log n) on average optimal CKKP (SPAA 08) O(1) on average O(1)-approximation Purdue University

  22. Questions • Good energy model of hardware? • Distributed network computing model for wireless ? • How to design energy-efficient distributed algorithms? Approximation algorithms? • How do cross layer issues affect design? • A new theory needed. Purdue University

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