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).
Research supported by the Alexander von Humboldt Stiftung
Research supported by DAAD
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© 1995 Springer-Verlag Berlin Heidelberg
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Chepoi, V.D., Dragan, F.F. (1995). On condorcet and median points of simple rectilinear polygons. In: Reichel, H. (eds) Fundamentals of Computation Theory. FCT 1995. Lecture Notes in Computer Science, vol 965. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60249-6_50
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DOI: https://doi.org/10.1007/3-540-60249-6_50
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