Arcee: An OCM-Solver

TL;DR

This paper introduces Arcee, an OCM solver that combines reduction rules, local search heuristics, and ILP-based exact methods to minimize edge crossings in bipartite graphs, addressing the 2024 PACE Challenge.

Contribution

It presents a novel OCM solver integrating reduction rules, local search, and ILP techniques, advancing solutions for the crossing minimization problem.

Findings

Effective reduction rules improve crossing minimization.

Local search techniques help escape local minima.

ILP and branch & bound solve the problem exactly.

Abstract

The 2024 PACE Challenge focused on the One-Sided Crossing Minimization (OCM) problem, which aims to minimize edge crossings in a bipartite graph with a fixed order in one partition and a free order in the other. We describe our OCM solver submission that utilizes various reduction rules for OCM and, for the heuristic track, employs local search approaches as well as techniques to escape local minima. The exact and parameterized solver uses an ILP formulation and branch & bound to solve an equivalent Feedback Arc Set instance.