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<p><b>Abstract</b>—A radio network (RN, for short) is a distributed system populated by small, hand-held commodity devices running on batteries. Since recharging batteries may not be possible while on mission, we are interested in designing protocols that are highly energy efficient. One of the most effective energy-saving strategies is to mandate that the stations go to sleep whenever they do not transmit or receive messages. It is well known that a station is expending power while its transceiver is active, that is, while transmitting or receiving a packet. It is perhaps surprising at first that a station is expending power even if it receives a packet that is not destined for it. Since, in single-hop radio networks, every station is within transmission range from every other station, the design of energy-efficient protocols is highly nontrivial. An instance of the <it>permutation routing</it> problem involves <tmath>$p$</tmath> stations of an RN, each storing <tmath>${n \over p}$</tmath> items. Each item has a unique <it>destination</it> which is the identity of the station to which the item must be routed. The goal is to route all the items to their destinations while expending as little energy as possible. Since, in the worst case, each item must be transmitted at least once, every permutation routing protocol must take <tmath>${n\over k}$</tmath> time slots. Similarly, each station must be awake for at least <tmath>${n\over p}$</tmath> time slots to transmit and/or receive packets. Our main contribution is to present an almost optimal energy-efficient permutation routing protocol for a <tmath>$k \hbox {-} {\rm channel}$</tmath>, a <tmath>$p \hbox {-} {\rm station}$</tmath> RN that routes <tmath>$n$</tmath> packets in at most <tmath>$(2d+2b+1){n\over k}+k$</tmath> time slots with no station being awake for more than <tmath>$(4d+7b-1){n\over p}$</tmath> time slots, where <tmath>$d=\left\lceil{\log {p\over k}\over \log {n\over p}}\right\rceil$</tmath>, <tmath>$b=\left\lceil{\log k\over \log {n\over p}}\right\rceil$</tmath>, and <tmath>$k\leq \sqrt{p\over 2}$</tmath>. Since, in most real-life situations, the number <tmath>$n$</tmath> of packets to route, the number <tmath>$p$</tmath> of stations in the RN, and the number <tmath>$k$</tmath> of channels available satisfy the relation <tmath>$k \ll p \ll n$</tmath>, it follows that <tmath>$d$</tmath> and <tmath>$b$</tmath> are very small.</p>
Radio networks, rapidly deployable networks, wireless communications, energy-efficient protocols, reservation protocols, permutation routing.

K. Nakano, S. Olariu and A. Y. Zomaya, "Energy-Efficient Permutation Routing in Radio Networks," in IEEE Transactions on Parallel & Distributed Systems, vol. 12, no. , pp. 544-557, 2001.
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