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<p><b>Abstract</b>—A radio network (RN) is a distributed system where each station or node is a small hand-held commodity device called a <it>station</it>. Typically, each station has access to a few channels for transmitting and receiving messages. By <tmath>RN(p,k)</tmath>, we denote a radio network with <tmath>p</tmath> stations, where each station has access to <tmath>k</tmath> channels. In a single-hop RN, every station is within the transmission range of every other station. Each station consumes power while transmitting or receiving a message, even when it receives a message that is not destined for it. It is extremely important that the stations consume power only when it is necessary since it is not possible to recharge batteries when the stations are on a mission. In this paper, we are interested in designing an energy-efficient protocol for permutation routing, which is one of the most fundamental problems in any distributed system. An instance of the <it>permutation routing</it> problem involves <tmath>p</tmath> stations of an RN, each storing <tmath>\frac{n}{p}</tmath> items. Each item has a unique destination address which is the identity of the destination station to which the item should be sent. The goal is to route all the items to their destinations while consuming as little energy as possible. We show that the permutation routing problem of <tmath>n</tmath> packets on an <tmath>RN(p,k)</tmath> can be solved in <tmath>{\frac{2n}{k}}+{({\frac{p}{k}})}^{2}+p+2k^{2}</tmath> slots and each station needs to be awake for at most <tmath>{\frac{6n}{p}}+{\frac{2p}{k}}+8k</tmath> slots. When <tmath>k\ll p\ll n</tmath>, our protocol is more efficient, both in terms of <it>total number of slots</it> and the <it>number of slots each station is awake</it> compared to a previously published protocol by Nakano et al. [14].</p>
Radio network, wireless communication, energy efficient protocol, permutation routing.

A. Datta and A. Y. Zomaya, "An Energy-Efficient Permutation Routing Protocol for Single-Hop Radio Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 15, no. , pp. 331-338, 2004.
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