Correction Networks

We consider the problem of sorting sequences obtained from a sorted sequence of n keys by changing the values of at most k keys at some unknown positions. Since even for k = 1 a lower bound Ω(logn) on the number of parallel comparison steps applies, any comparator network solving this problem cannot be asymptotically faster than the AKS sorting network. We design a comparator network which sorts the sequences considered for a large range of k’s, has a simple architecture and achieves a runtime c · logn, for a small constant c. We present such networks of depth 4logn+O(log2 k loglogn) with a small constant hidden behind the big “Oh”. In particular, for k = o(2 √ logn/ loglogn) the networks are of depth 4logn+o(logn).