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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(n 2) time, where n is the number of terminating paths.

Keywords

Terminal Station Layout Problem Terminal Position Optimal Layout Embed Graph 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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