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Near-Linear Time Edit Distance for Indel Channels
Workshop on Algorithms in Bioinformatics
We consider the following model for sampling pairs of strings: s₁ is a uniformly random bitstring of length n, and s₂ is the bitstring arrived at by applying substitutions, insertions, and deletions to each bit of s₁ with some probability. We show that the edit distance between s₁ and s₂ can be computed in O(n ln n) time with high probability, as long as each bit of s₁ has a mutation applied to it with probability at most a small constant. The algorithm is simple and only uses the textbookdoi:10.4230/lipics.wabi.2020.17 dblp:conf/wabi/GaneshS20 fatcat:o2orugj6rbfaldfxrqvfofjdmm