On d-Regular Schematization of Embedded Paths

  • Andreas Gemsa
  • Martin Nöllenburg
  • Thomas Pajor
  • Ignaz Rutter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6543)


In the d-regular path schematization problem we are given an embedded path P (e.g., a route in a road network) and an integer d. The goal is to find a d-schematized embedding of P in which the orthogonal order of all vertices in the input is preserved and in which every edge has a slope that is an integer multiple of 90°/d. We show that deciding whether a path can be d-schematized is NP-hard for any integer d. We further model the problem as a mixed-integer linear program. An experimental evaluation indicates that this approach generates reasonable route sketches for real-world data.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Andreas Gemsa
    • 1
  • Martin Nöllenburg
    • 1
    • 2
  • Thomas Pajor
    • 1
  • Ignaz Rutter
    • 1
  1. 1.Institute of Theoretical InformaticsKarlsruhe Institute of Technology (KIT)KarlsruheGermany
  2. 2.Department of Computer ScienceUniversity of CaliforniaIrvineUSA

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