Polynomial-Time Solutions for Longest Common Subsequence Related Problems Between a Sequence and a Pangenome Graph

A pangenome captures the genetic diversity across multiple individuals simultaneously, providing a more comprehensive reference for genome analysis than a single linear genome, which may introduce allele bias. A widely adopted pangenome representation is a node-labeled directed graph, wherein the paths correspond to plausible genomic sequences within a species. Consequently, evaluating sequence-to-pangenome graph similarity constitutes a fundamental task in pangenome construction and analysis. This study explores the Longest Common Subsequence (LCS) problem and three of its variants involving a sequence and a pangenome graph. We present four polynomial-time reductions that transform these LCS-related problems into the longest path problem in a directed acyclic graph (DAG). These reductions demonstrate that all four problems can be solved in polynomial time, establishing their membership in the complexity class P.