Sorting Long Sequences in a Single Hop Radio Network
We propose an algorithm for merging two sorted sequences of length k Open image in new window 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 Open image in new window k+8m–4 and 8k+4⌈log2(m+1)⌉+6, respectively. This algorithm can be applied for sorting a sequence of length N=k Open image in new window 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.
KeywordsTime Slot Energetic Cost Merging Algorithm Comparator Network Batcher Algorithm
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