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Issue No.12 - December (1999 vol.10)

pp: 1276-1289

DOI Bookmark: http://doi.ieeecomputersociety.org/10.1109/71.819949

ABSTRACT

<p><b>Abstract</b>—The main contribution of this work is to present elegant broadcast-efficient protocols for permutation routing, ranking, and sorting on single-hop Mobile Radio Networks with <tmath>$p$</tmath> stations and <tmath>$k$</tmath> radio channels, denoted by <tmath>${\rm MRN} (p,k)$</tmath>. Clearly, any protocol performing these tasks on <tmath>$n$</tmath> items must perform <tmath>$n\over k$</tmath> broadcast rounds because each item must be broadcast at least once. We begin by presenting an optimal off-line permutation routing protocol using <tmath>$n\over k$</tmath> broadcast rounds for arbitrary <tmath>$k$</tmath>, <tmath>$p$</tmath>, and <tmath>$n$</tmath>. Further, we show that optimal on-line routing can be performed in <tmath>$n\over k$</tmath> broadcast rounds, provided that either <tmath>$k=1$</tmath> or <tmath>$p=n$</tmath>. We then go on to develop an on-line routing protocol that takes <tmath>$2{n\over k}+k-1$</tmath> broadcast rounds on the <tmath>${\rm MRN} (p,k)$</tmath>, whenever <tmath>$k\leq \sqrt{p\over 2}$</tmath>. Using these routing protocols as basic building blocks, we develop a ranking protocol that takes <tmath>$2{n \over k}+o({n\over k})$</tmath> broadcast rounds as well as a sorting protocol that takes <tmath>$3{n \over k}+o({n\over k})$</tmath> broadcast rounds, provided that <tmath>$k\in o(\sqrt{n})$</tmath> and <tmath>$p=n$</tmath>. Finally, we develop a ranking protocol that takes <tmath>$3{n \over k}+o({n\over k})$</tmath> broadcast rounds, as well as a sorting protocol that takes <tmath>$4{n \over k}+o({n\over k})$</tmath> broadcast rounds on the <tmath>${\rm MRN} (p,k)$</tmath>, provided that <tmath>$k \leq\sqrt{p\over 2}$</tmath> and <tmath>$p\in o(n)$</tmath>. Featuring very low proportionality constants, our protocols offer a vast improvement over the state of the art.</p>

INDEX TERMS

Mobile radio networks, single-hop networks, permutation routing, ranking, sorting, DAMA.

CITATION

Koji Nakano, Stephan Olariu, James L. Schwing, "Broadcast-Efficient Protocols for Mobile Radio Networks",

*IEEE Transactions on Parallel & Distributed Systems*, vol.10, no. 12, pp. 1276-1289, December 1999, doi:10.1109/71.819949