Tabu Search for Min-Max Edge Crossing in Graphs Tommaso Pastore 1 , Anna Mart´ ınez-Gavara 2 , Antonio Napoletano 3 , Paola Festa 1 , and Rafael Mart´ ı 2 1 Department of Mathematics and Applications. University of Napoli Federico II, Italy. {tommaso.pastore, paola.festa}@unina.it 2 Department of Statistics and Operations Research. University of Valencia, Spain. {gavara, rafael.marti}@uv.es 3 Optit srl, Via Mazzini, 82, 40138 Bologna, Italy {antonio.napoletano}@optit.net September 2, 2019 Abstract Graph drawing is a key issue in the field of data analysis, given the ever-growing amount of information available today that require the use of automatic tools to represent it. Graph Drawing Problems (GDP) are hard combinatorial problems whose applications have been widely relevant in fields such as social network analysis and project manage- ment. While classically in GDPs the main aesthetic concern is related to the minimization of the total sum of crossing in the graph (min-sum), in this paper we focus on a particular variant of the problem, the Min-Max GDP, consisting in the minimization of the maxi- mum crossing among all egdes. Recently proposed in scientific literature, the Min-Max GDP is a challenging variant of the original min-sum GDP arising in the optimization of VLSI circuits and the design of interactive graph drawing tools. We propose a heuristic algorithm based on the tabu search methodology to obtain high-quality solutions. Ex- tensive experimentation on an established benchmark set with both previous heuristics and optimal solutions shows that our method is able to obtain excellent solutions in short computation time. Keywords: combinatorial optimization, graph drawing, metaheuristics. 1 Introduction Graph drawing problems consist in obtaining an automatic representation of a given graph, described in terms of its vertices and edges. Many aesthetic criteria have been proposed to identify the desirable properties that a good representation has to fulfill, with the most com- mon being: edge crossings, graph area, edge length, edge bends, and symmetries. Their main objective is to achieve readable drawings in which it is easy to obtain or extract information. This goal is particularly critical in graphs with hundreds of vertices and edges, in which an improper layout could be extremely hard to analyze. Graph drawing is an active area of research. An excellent resource on the topic is the book by Di Battista et al. [3], where many graph drawing models and related applications are introduced. 1