Computational Performance Evaluation of Two Integer Linear Programming Models for the Minimum Common String Partition Problem

TL;DR

This paper compares two ILP models for the Minimum Common String Partition problem, demonstrating that the new model offers significant computational improvements over the previous formulation.

Contribution

The paper introduces a new ILP model for MCSP and provides a comprehensive experimental comparison showing its computational advantages.

Findings

The new ILP model has better solving times than the previous one.

Linear programming relaxations of both models are equally strong.

Experimental results on real and artificial data support the new model's efficiency.

Abstract

In the minimum common string partition (MCSP) problem two related input strings are given. "Related" refers to the property that both strings consist of the same set of letters appearing the same number of times in each of the two strings. The MCSP seeks a minimum cardinality partitioning of one string into non-overlapping substrings that is also a valid partitioning for the second string. This problem has applications in bioinformatics e.g. in analyzing related DNA or protein sequences. For strings with lengths less than about 1000 letters, a previously published integer linear programming (ILP) formulation yields, when solved with a state-of-the-art solver such as CPLEX, satisfactory results. In this work, we propose a new, alternative ILP model that is compared to the former one. While a polyhedral study shows the linear programming relaxations of the two models to be equally strong, a comprehensive experimental comparison using real-world as well as artificially created benchmark instances indicates substantial computational advantages of the new formulation.