The ordered anti-median problem with distances derived from a strictly convex norm

Authors:
Antonio J. Lozano;Juan A. Mesa;Frank Plastria
Affiliations:
Department of Mathematics, University of Huelva, Spain;Department of Applied Mathematics II, University of Seville, Spain;Department of Mathematics, Operational Research, Statistics and Information Systems for Management, Vrije Universiteit Brussels, Belgium
Venue:
Discrete Applied Mathematics
Year:
2013

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Abstract

In this paper we consider a general model for locating a repulsive facility in a bounded polygonal region. In order to have a finite set of candidates for the ordered anti-median problem, the class of strictly convex distances must be restricted. For this case an O(sn^5) time algorithm is proposed, where s is an uniform bound on the number of intersections of two bisectors.