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On condorcet and median points of simple rectilinear polygons

Extended abstract
  • Victor D. Chepoi
  • Feodor F. Dragan
Communications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 965)

Abstract

Let P be a simple rectilinear polygon with N vertices, endowed with rectilinear metric, and let the location of n users in P be given. There are a number of procedures to locate a facility for a given family of users. If a voting procedure is used, the chosen point x should satisfy the following property: no other point y of the polygon P is closer to an absolute majority of users. Such a point is called a Condorcet point. If a planning procedure is used, such as minimization of the average distance to the users, the optimal solution is called a median point.

We prove that Condorcet and median points of a simple rectilinear polygon coincide and present an O(N+nlogN) algorithm for computing these sets. If all users are located on vertices of a polygon P, then the running time of the algorithm becomes O(N+n).

Key words

computational geometry Condorcet point median point rectilinear polygon rectilinear distance 

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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Victor D. Chepoi
    • 1
  • Feodor F. Dragan
    • 1
  1. 1.Department of Mathematics & CyberneticsMoldova State UniversityChişinau

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