Separating point sets in polygonal environments

Authors:
Erik D. Demaine;Jeff Erickson;Ferran Hurtado;John Iacono;Stefan Langerman;Henk Meijer;Mark Overmars;Sue Whitesides
Affiliations:
MIT Laboratory for Computer Science;University of Illinois at Urbana-Champaign, IL;Universitat Politècnica de Catalunya;Polytechnic University;Université Libre de Bruxelles;Queen's University;Utrecht University;McGill University
Venue:
SCG '04 Proceedings of the twentieth annual symposium on Computational geometry
Year:
2004

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Abstract

We consider the separability of two point sets inside a polygon by means of chords or geodesic lines. Specifically, given a set of red points and a set of blue points in the interior of a polygon, we provide necessary and sufficient conditions for the existence of a chord and for the existence of a geodesic path which separate the two sets when they exist we also derive efficient algorithms for their obtention. We study as well the separation of the two sets using a minimum number of pairwise non-crossing chords.