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Approximation Algorithms for Minimizing Edge Crossings in Radial Drawings

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Abstract

We study a crossing minimization problem of drawing a bipartite graph with a radial drawing of two orbits. Radial drawings are one of well-known drawing conventions in social network analysis and visualization, in particular, displaying centrality indices of actors (Wasserman and Faust, Social Network Analysis: Methods and Applications. Cambridge University Press, Cambridge, 1994). The main problem in this paper is called the one-sided radial crossing minimization, if the positions of vertices in the outer orbit are fixed. The problem is known to be NP-hard (Bachmaier, IEEE Trans. Vis. Comput. Graph. 13, 583–594, 2007), and a number of heuristics are available (Bachmaier, IEEE Trans. Vis. Comput. Graph. 13, 583–594, 2007). However, there is no approximation algorithm for the crossing minimization problem in radial drawings. We present the first polynomial time constant-factor approximation algorithm for the one-sided radial crossing minimization problem.

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Authors and Affiliations

  1. School of Information Technologies, University of Sydney, Sydney, Australia

    Seok-Hee Hong

  2. Department of Applied Mathematics and Physics, Kyoto University, Kyoto, Japan

    Hiroshi Nagamochi

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  1. Seok-Hee Hong
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  2. Hiroshi Nagamochi
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Correspondence to Hiroshi Nagamochi.

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Hong, SH., Nagamochi, H. Approximation Algorithms for Minimizing Edge Crossings in Radial Drawings. Algorithmica 58, 478–497 (2010). https://doi.org/10.1007/s00453-009-9277-4

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