Arcee: An OCM-Solver

TL;DR

This paper describes the exact and parameterized 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.

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.

Figures (10)

• Figure 1: An OCM instance with different orderings of the free vertices and the corresponding number of edge crossings.
• Figure 2: OCM instance whose penalty graph contains a cycle.
• Figure 3: Penalty graph $G_p$ and crossing numbers of the instance in \ref{['fig:ocm_cycle']}.
• Figure 4: Strongly connected components of a penalty graph.
• Figure 5: OCM instance splittable by partitioning the set of free vertices into $\{\{5, 7, 9\}, \{6, 8, 10\}\}$.