Minimizing Intra-edge Crossings in Wiring Diagrams and Public Transportation Maps

  • Marc Benkert
  • Martin Nöllenburg
  • Takeaki Uno
  • Alexander Wolff
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4372)

Abstract

In this paper we consider a new problem that occurs when drawing wiring diagrams or public transportation networks. Given an embedded graph G = (V,E) (e.g., the streets served by a bus network) and a set L of paths in G (e.g., the bus lines), we want to draw the paths along the edges of G such that they cross each other as few times as possible. For esthetic reasons we insist that the relative order of the paths that traverse a node does not change within the area occupied by that node.

Our main contribution is an algorithm that minimizes the number of crossings on a single edge {u,v} ∈ E if we are given the order of the incoming and outgoing paths. The difficulty is deciding the order of the paths that terminate in u or v with respect to the fixed order of the paths that do not end there. Our algorithm uses dynamic programming and takes O(n2) time, where n is the number of terminating paths.

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Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Marc Benkert
    • 1
  • Martin Nöllenburg
    • 1
  • Takeaki Uno
    • 2
  • Alexander Wolff
    • 1
  1. 1.Department of Computer Science, Karlsruhe UniversityGermany
  2. 2.National Institute of Informatics, TokyoJapan

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