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(log n) 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·log n, for a small constant c. We present such networks of depth 4 log n+O(log² k log log n) with a small constant hidden behind the big “Oh”. In particular, for k=o(2√(log n/log log n)) the networks are of depth 4 log n+o(log n)