Hamiltonian Orthogeodesic Alternating Paths

  • Emilio Di Giacomo
  • Luca Grilli
  • Marcus Krug
  • Giuseppe Liotta
  • Ignaz Rutter
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7056)


Given a set of red and blue points, an orthogeodesic alternating path is a path such that each edge is a geodesic orthogonal chain connecting points of different colour and no two edges cross. We consider the problem of deciding whether there exists a Hamiltonian orthogeodesic alternating path, i.e., an orthogeodesic alternating path visiting all points. We provide an O(n log2 n)-time algorithm for finding such a path if no two points are horizontally or vertically aligned. We show that the problem is NP-hard if bends must be at grid points. Nevertheless, we can approximate the maximum number of vertices of an orthogeodesic alternating path on the grid by roughly a factor of 3. Finally, we consider the problem of finding orthogeodesic alternating matchings, cycles, and trees.


Recursive Call Vertical Segment Horizontal Segment Blue Point Vertical Array 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Emilio Di Giacomo
    • 1
  • Luca Grilli
    • 1
  • Marcus Krug
    • 2
  • Giuseppe Liotta
    • 1
  • Ignaz Rutter
    • 2
  1. 1.Università di PerugiaItaly
  2. 2.Faculty of InformaticsKarlsruhe Institute of Technology (KIT)Germany

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