Counting-Sort and Routing in a Single Hop Radio Network
We consider two problems. First, sorting of n integer keys from the [0,2m − 1] range, stored in p stations of a single-hop and single channel radio network. Second problem is routing of the packets between the stations of the network. We introduce counting-sort algorithm which has 3mri + si + di + 3 energetic cost and nm + n + p time cost, where station ai stores si keys (ri distinct keys) and receives di keys. On the basis of this sorting, we construct routing protocols with energetic costs (3⌈log2p⌉ + 2)ri + si + di + 5 and (3⌈log2p⌉ + 4)ri + si + di + 6, and time costs n⌈log2p⌉ + n + 3p and r⌈log2p⌉ + n + r + 3p, respectively, where r is sum of all ri. Our routing is attractive alternative for previous solutions, since it is efficient, deterministic and simple.
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