Experimental Evaluation of Parameterized Algorithms for Graph Separation Problems: Half-Integral Relaxations and Matroid-based Kernelization

TL;DR

This paper evaluates two key parameterized algorithm techniques for graph separation problems—half-integral relaxations and matroid-based kernelization—using new benchmarks to compare their practical effectiveness.

Contribution

It provides the first experimental comparison of these theoretical techniques and introduces new benchmark instances for the Multiway Cut problem.

Findings

Half-integral relaxation algorithms perform efficiently in practice.

Matroid-based kernelization significantly reduces problem size.

New benchmark instances facilitate future experimental studies.

Abstract

In the recent years we have witnessed a rapid development of new algorithmic techniques for parameterized algorithms for graph separation problems. We present experimental evaluation of two cornerstone theoretical results in this area: linear-time branching algorithms guided by half-integral relaxations and kernelization (preprocessing) routines based on representative sets in matroids. A side contribution is a new set of benchmark instances of (unweighted, vertex-deletion) Multiway Cut.