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Broadcast-Efficient Protocols for Mobile Radio Networks
December 1999 (vol. 10 no. 12)
pp. 1276-1289

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

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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 and Distributed Systems, vol. 10, no. 12, pp. 1276-1289, Dec. 1999, doi:10.1109/71.819949
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