Algorithmica

, Volume 11, Issue 4, pp 379–403

Edge crossings in drawings of bipartite graphs

  • Peter Eades
  • Nicholas C. Wormald
Article

Abstract

Systems engineers have recently shown interest in algorithms for drawing directed graphs so that they are easy to understand and remember. Each of the commonly used methods has a step which aims to adjust the drawing to decrease the number of arc crossings. We show that the most popular strategy involves an NP-complete problem regarding the minimization of the number of arcs in crossings in a bipartite graph. The performance of the commonly employed “barycenter” heuristic for this problem is analyzed. An alternative method, the “median” heuristic, is proposed and analyzed. The new method is shown to compare favorably with the old in terms of performance guarantees. As a bonus, we show that the median heuristic performs well with regard to the total length of the arcs in the drawing.

Key words

Graph Bipartite graph Directed graph Edge crossing Median 

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Copyright information

© Springer-Verlag New York Inc 1994

Authors and Affiliations

  • Peter Eades
    • 1
  • Nicholas C. Wormald
    • 2
  1. 1.Department of Computer ScienceUniversity of QueenslandQueenslandAustralia
  2. 2.Department of MathematicsUniversity of MelbourneParkvilleAustralia

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