Approximating the Maximum Rectilinear Crossing Number

  • Samuel BaldEmail author
  • Matthew P. Johnson
  • Ou Liu
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9797)


Drawing a graph in a way that minimizes the number of edge-crossings is a well-studied problem. Recently there has been work characterizing both the minimum and maximum number of edge-crossings possible in various graph classes, assuming rectilinear (straight-line) edges. In this paper, we investigate the algorithmic problem of maximizing the number of edge-crossings over all rectilinear drawings a graph. We show that this problem is NP-hard and lies in \(\exists \mathbb {R}\). We give a nontrivial derandomization of the natural randomized 1/3-approximation algorithm, which generalizes to a weighted setting as well as to an ordering constraint satisfaction problem. We evaluate these algorithms and other heuristics in simulation.



This work was supported in part by PSC-CUNY Research Award 67665-00 45, CUNY Collaborative Incentive Research Grant (CIRG 21) 2153, and a Research in the Classroom Idea Grant.


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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.The Graduate Center of the City University of New YorkNew YorkUSA
  2. 2.Lehman CollegeCity University of New YorkNew YorkUSA

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