On Solving the Minimum Common String Partition Problem by Decision Diagrams

TL;DR

This paper introduces a novel exact and heuristic solution approach for the NP-hard Minimum Common String Partition Problem using Decision Diagrams, demonstrating scalability and effectiveness on benchmark instances.

Contribution

It formulates MCSP as a Dynamic Program and develops Decision Diagram-based algorithms, including a restricted version for heuristics, advancing solution methods for large instances.

Findings

The Decision Diagram approach scales well to large instances.

The heuristic method provides competitive solutions with reduced runtime.

The approach outperforms some existing methods on benchmark datasets.

Abstract

In the Minimum Common String Partition Problem (MCSP), we are given two strings on input, and we want to partition both into the same collection of substrings, minimizing the number of the substrings in the partition. This combinatorial optimization problem has applications in computational biology and is NP-hard. Many different heuristic and exact methods exist for this problem, such as a Greedy approach, Ant Colony Optimization, or Integer Linear Programming. In this paper, we formulate the MCSP as a Dynamic Program and develop an exact solution algorithm based on Decision Diagrams for it. We also introduce a restricted Decision Diagram that allows to compute heuristic solutions to the MCSP and compare the quality of solution and runtime on instances from literature with existing approaches. Our approach scales well and is suitable for heuristic solution of large-scale instances.