Hamiltonian orthogeodesic alternating paths

  • Authors:

  • Emilio Di Giacomo;Luca Grilli;Marcus Krug;Giuseppe Liotta;Ignaz Rutter

  • Affiliations:

  • Università di Perugia, Italy;Università di Perugia, Italy;Faculty of Informatics, Karlsruhe Institute of Technology (KIT), Germany;Università di Perugia, Italy;Faculty of Informatics, Karlsruhe Institute of Technology (KIT), Germany

  • Venue:
  • IWOCA'11 Proceedings of the 22nd international conference on Combinatorial Algorithms
  • Year:
  • 2011

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Abstract

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 log2n)-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.