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

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

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.

G. Pandurangan Purdue University 4 Traffic Monitoring with Sensors

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

G. Pandurangan Purdue University 6 Desirable Features Simple and local

G. Pandurangan Purdue University 7 Desirable Features Simple and local

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

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

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?

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.

G. Pandurangan Purdue University 12 NNT Construction Output is a spanning tree called NNT.

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.

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.

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

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()

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.

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

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.) ….

G. Pandurangan Purdue University 20 Energy Complexity

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

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.