IWOCA 2011: Combinatorial Algorithms pp 170-181

# Hamiltonian Orthogeodesic Alternating Paths

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

## 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 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.

## Keywords

Recursive Call Vertical Segment Horizontal Segment Blue Point Vertical Array
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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## 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