Correcting Sorted Sequences in a Single Hop Radio Network

Abstract

By k-disturbed sequence we mean a sequence obtained from a sorted sequence by changing the values of at most k elements. We present an algorithm for single-hop radio networks that sorts a k-disturbed sequence of length n (where each station stores single key) in time $4n+k\cdot(\lceil \lg k\rceil^2+\lceil \lg(n-k+1)\rceil+6\lceil \lg k\rceil)-2$ with energetic cost $3\cdot \lceil\frac{(\lceil\lg k\rceil+1)(\lceil\lg k\rceil+2)}{2\lfloor n/k\rfloor}\rceil+ 4\cdot\lceil\frac{\lceil \lg k\rceil}{\lfloor n/k\rfloor}\rceil+10$. If $\frac{(\lceil\lg k\rceil+1)(\lceil\lg k\rceil+2)}{2}+\lceil \lg k\rceil\le \lfloor n/k\rfloor$ then the energetic cost is bounded by 14.

This work has been supported by MNiSW grant N N206 1842 33.