Chaining of Maximal Exact Matches in Graphs

TL;DR

This paper introduces a novel method for chaining maximal exact matches in directed acyclic graphs to efficiently solve the longest common subsequence problem, with a new symmetric formulation and specific time complexity.

Contribution

It presents a new symmetric chaining formulation in DAGs and an algorithm that solves the LCS problem between a query and a graph efficiently.

Findings

Achieves $O(m+n+k^2|V| + |E| + kN ext{log} N)$ time complexity.

Provides a method to encode full MEMs within the chaining process.

Introduces a symmetric formulation of chaining in DAGs.

Abstract

We show how to chain maximal exact matches (MEMs) between a query string $Q$ and a labeled directed acyclic graph (DAG) $G=(V,E)$ to solve the longest common subsequence (LCS) problem between $Q$ and $G$. We obtain our result via a new symmetric formulation of chaining in DAGs that we solve in $O(m+n+k^2|V| + |E| + kN\log N)$ time, where $m=|Q|$, $n$ is the total length of node labels, $k$ is the minimum number of paths covering the nodes of $G$ and $N$ is the number of MEMs between $Q$ and node labels, which we show encode full MEMs.