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

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G. Pandurangan 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

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G. Pandurangan 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.

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G. Pandurangan Purdue University 4 Traffic Monitoring with Sensors

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

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G. Pandurangan Purdue University 6 Desirable Features Simple and local

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G. Pandurangan Purdue University 7 Desirable Features Simple and local

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

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

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G. Pandurangan 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?

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G. Pandurangan Purdue University 11 Nearest Neighbor Tree (NNT) Scheme Khan 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.

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

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G. Pandurangan 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.

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G. Pandurangan 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.

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G. Pandurangan Purdue University 15 u s 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

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G. Pandurangan Purdue University 16 Defining Rank For any u and v, 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()

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G. Pandurangan 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.

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

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G. Pandurangan Purdue University 19 Energy complexity of a distributed algorithm Energy complexity is 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.) ….

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G. Pandurangan Purdue University 20 Energy Complexity

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G. Pandurangan 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

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G. Pandurangan 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.

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