Shortest Path Approaches for the Longest Common Subsequence of a Set of Strings

Abstract

Abstract-We investigate the k-LCS problem that is finding a longest common subsequence (LCS) for k given input strings. The problem is known to have practical solutions for k = 2, but for higher dimensions it is not very well explored. We consider the algorithms by Miller and Myers as well as Wu et al. which solve the 2-LCS problem, and shed a new light on their generalization to higher dimensions. First, we redesign both algorithms such that the generalization to higher dimensions becomes natural. Then we present our algorithms for solving the k-LCS problem. We further propose a new approach to reduce the algorithms' space complexity. We demonstrate that our algorithms are practical as they significantly outperform the dynamic programming approaches. Our results stand in contrast to observations made in previous work by Irving and Fraser.

On Space Efficiency of Algorithms Working on Structural Decompositions of Graphs

“…In a recent breakthrough, Abboud et al [1] proved that the existence of an algorithm with running time O(n k−ε ), for any ε > 0, would contradict the Strong Exponential Time Hypothesis. As far as the space complexity is concerned, only modest progress has been achieved: The best known result is an algorithm of Barsky et al [8], which improves the space complexity to O(n k−1 ). This motivates us to formulate the following conjecture.…”