Counting-Sort and Routing in a Single Hop Radio Network

Abstract

We consider two problems. First, sorting of n integer keys from the [0,2^m − 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 3mr _i  + s _i  + d _i  + 3 energetic cost and nm + n + p time cost, where station a _i stores s _i keys (r _i distinct keys) and receives d _i keys. On the basis of this sorting, we construct routing protocols with energetic costs (3⌈log₂ p⌉ + 2)r _i  + s _i  + d _i  + 5 and (3⌈log₂ p⌉ + 4)r _i  + s _i  + d _i  + 6, and time costs n⌈log₂ p⌉ + n + 3p and r⌈log₂ p⌉ + n + r + 3p, respectively, where r is sum of all r _i . Our routing is attractive alternative for previous solutions, since it is efficient, deterministic and simple.

Partially supported by KBN grant 3 T11C 011 26.