Sorting Long Sequences in a Single Hop Radio Network

Abstract

We propose an algorithm for merging two sorted sequences of length k m stored in two sequences of m stations of single-hop single-channel radio network, where each station stores a block of of k consecutive elements. The time and energetic cost of this algorithm are 6m k+8m–4 and 8k+4⌈log₂(m+1)⌉+6, respectively. This algorithm can be applied for sorting a sequence of length N=k n in a network consisting of n stations with memory limited by Θ(k) words. For $k=\Omega(\lg n)$, the energetic cost of such sorting is $O(k\cdot\lg n)$ and the time is $O(N\lg n)$. Moreover, the constants hidden by the big “Oh” are reasonably small, to make the algorithm attractive for practical applications.

Supported by the European Union within the 6th Framework Programme under contract 001907 (DELIS).