On Solving the Multiple Variable Gapped Longest Common Subsequence Problem

TL;DR

This paper introduces a novel search framework with heuristics for solving the Variable Gapped Longest Common Subsequence problem, demonstrating robustness and efficiency on synthetic instances.

Contribution

It presents the first comprehensive computational approach for VGLCS, employing a root-based state graph and iterative beam search with heuristics.

Findings

Robustness over baseline beam search in runtime

Effective control of diversification across iterations

Successful application to synthetic instances with up to 10 sequences and 500 characters

Abstract

This paper addresses the Variable Gapped Longest Common Subsequence (VGLCS) problem, a generalization of the classical LCS problem involving flexible gap constraints between consecutive solutions' characters. The problem arises in molecular sequence comparison, where structural distance constraints between residues must be respected, and in time-series analysis where events are required to occur within specified temporal delays. We propose a search framework based on the root-based state graph representation, in which the state space comprises a generally large number of rooted state subgraphs. To cope with the resulting combinatorial explosion, an iterative beam search strategy is employed, dynamically maintaining a global pool of promising candidate root nodes, enabling effective control of diversification across iterations. To exploit the search for high-quality solutions, several known heuristics from the LCS literature are utilized into the standalone beam search procedure. To the best of our knowledge, this is the first comprehensive computational study on the VGLCS problem comprising 320 synthetic instances with up to 10 input sequences and up to 500 characters. Experimental results show robustness of the designed approach over the baseline beam search in comparable runtimes.