Parallel Algorithms for the One Sided Crossing Minimization Problem

Abstract: The One Sided Crossing Minimization (OSCM) problem is an optimization problem in graph drawing that aims to minimize the number of edge crossings in bipartite graph layouts. It has practical applications in areas such as network visualization and VLSI (Very Large Scale Integration) design, where reducing edge crossings improves the arrangement of circuit components and their interconnections. Despite the rise of multi-core systems, the parallelization of exact and fixed-parameter tractable (FPT) algorithms for OSCM remains largely unexplored. Parallel variants offer significant potential for scaling to larger graphs but require careful handling of synchronization and memory management. In this paper, we explore various previously studied exact and FPT algorithms for OSCM, implementing and analyzing them in both sequential and parallel forms. Our main contribution lies in empirically proving that these algorithms can achieve close to linear speedup under parallelization. In particular, our best result achieves a speedup of nearly 19 on a 16-core, 32-thread machine. We further investigate and discuss the reasons why linear speedup is not always attained.