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lifetimePath - Maximum Lifetime Routing In Wireless Sensor...

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Maximum Lifetime Routing In Wireless Sensor Networks Joongseok Park Sartaj Sahni Computer & Information Science & Engineering University of Florida { jpark, sahni } @cise.ufl.edu June 2, 2005 Abstract We show that the problem of routing messages in a wireless sensor network so as to maximize network lifetime is NP-hard. In our model, the online model, each message has to be routed without knowledge of future route requests. We develop also an online heuristic to maximize network lifetime. Our heuristic, which performs two shortest path computations to route each message, is superior to previously published heuristics for lifetime maximization– our heuristic results in greater lifetime and its performance is less sensitive to the selection of heuristic parameters. Additionally, our heuristic is superior on the capacity metric. Keywords : Wireless sensor networks, lifetime maximization, online power-aware routing 1 Introduction We consider message routing in wireless sensor networks in which each sensor is battery operated. We assume that the batteries are neither replaceable nor rechargeable. This, for example, is the case when the sensors are deployed in hostile (e.g., battlefield) or otherwise hard to reach (e.g., the bottom of the ocean) environments. Hence, in the wireless sensor networks we consider, energy conservation is paramount. The energy required by a sensor to transmit, under ideal conditions, a unit length message a distance r is proportional to r d for some d in the range [2 , 4] [3, 12]. (More energy is required if there are obstacles in the transmission path.) Hence, energy is conserved by using multihop routing. That is, nodes between the source and destination are used as relays. For example, * This research was supported, in part, by the National Science Foundation under grant ITR-0326155 1
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suppose that sensors A and C are a distance 4 apart and sensor B is halfway between A and C . Assume further that d = 2 and the constant of proportionality is 1. It takes A 16 units of energy to transmit a unit message directly (i.e., via a single hop) to C . However, by using B as a relay, the message may be transmitted from A to B using 4 units of energy and then from B to C using an additional 4 units. The total energy consumed by this multihop (more precisly, two hop) transmission is only 8 units 1 ! Following the deployment of a sensor network, pairs of sensors exchange messages in an unpre- dictable sequence. We assume that for proper network operation, it is critical that every attempt to transmit a message succeed. Hence, the lifetime of a sensor network is defined as the number of messages successfully routed before the first failed message route. Although several researchers have proposed heuristics to maximize network lifetime, none has actually shown that maximizing network lifetime is NP-hard. In Section 4, we show that maxi- mizing network lifetime is NP-hard. In Section 5, we develop a new heuristic, the online maximum lifetime (OML) heuristic, to maximize lifetime. Zone-based and distributed versions of OML are described in Section 6.
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