A Variable Depth Neighborhood Search Algorithm For The Min-Max Arc Crossing Problem

The Min-Max Arc Crossing Problem (MMACP) aims to minimize the maximum number of crossings over all arcs in a layered graph. It is a recently proposed variant of the well-known graph drawing problem where the total number of arc crossings is minimized. MMACP is of interest in VLSI design and graph visualization, especially when dealing with very large graphs. In this paper, we present a variable depth neighborhood search algorithm for solving MMACP. Our algorithm exploits good data structures, efficient neighborhood search schemes, and a carefully defined ejection chain scheme. Effectively embedding these basic structures within an iterated local search framework, our algorithm produced superior outcomes. In particular, the algorithm produced new solutions improving the best-known results for 154 out of the 301 benchmark instances available in the public domain. As a result, our paper enhances the state-of-the-art knowledge in graph drawing and arc crossing minimization. We also computationally analyzed the roles and effectiveness of various crucial features of our algorithm which helped us make informed recommendations for default parameter settings.