On d-regular schematization of embedded paths

Authors:
Andreas Gemsa;Martin Nöllenburg;Thomas Pajor;Ignaz Rutter
Affiliations:
Institute of Theoretical Informatics, Karlsruhe Institute of Technology, Karlsruhe, Germany;Institute of Theoretical Informatics, Karlsruhe Institute of Technology, Karlsruhe, Germany and Department of Computer Science, University of California, Irvine;Institute of Theoretical Informatics, Karlsruhe Institute of Technology, Karlsruhe, Germany;Institute of Theoretical Informatics, Karlsruhe Institute of Technology, Karlsruhe, Germany
Venue:
SOFSEM'11 Proceedings of the 37th international conference on Current trends in theory and practice of computer science
Year:
2011

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On d-regular schematization of embedded paths

Computational Geometry: Theory and Applications

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Abstract

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.