A Heuristic Approach for Solving the Longest Common Square Subsequence Problem

Abstract

The longest common square subsequence (LCSqS) problem, a variant of the longest common subsequence (LCS) problem, aims at finding a subsequence common to all input strings that is, at the same time, a square subsequence. So far the LCSqS was solved only for two input strings. We present a heuristic approach, based on randomized local search and a hybrid of variable neighborhood search and beam search, to solve the LCSqS for an arbitrary set of input strings. The beam search makes use of a novel heuristic estimation of the approximated expected length of a LCS to guide the search.