Approximating LCS and Alignment Distance over Multiple Sequences

Abstract

We study the problem of aligning multiple sequences with the goal of finding an alignment that either maximizes the number of aligned symbols (the longest common subsequence (LCS) problem), or minimizes the number of unaligned symbols (the alignment distance aka the complement of LCS). Multiple sequence alignment is a well-studied problem in bioinformatics and is used routinely to identify regions of similarity among DNA, RNA, or protein sequences to detect functional, structural, or evolutionary relationships among them. It is known that exact computation of LCS or alignment distance of m sequences each of length n requires Θ(n m ) time unless the Strong Exponential Time Hypothesis is false. However, unlike the case of two strings, fast algorithms to approximate LCS and alignment distance of multiple sequences is lacking in the literature. In this paper, we make significant progress towards that direction.• If the LCS of m sequences each of length n is λn for some λ ∈ [0, 1], then in Õm (n m 2 +1 ) 1 time, we can return a common subsequence of length at least λ 2 n