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Location of weighted anti-ordered median straight lines with euclidean distances

Journal Contribution - Journal Article

Given a set of n weighted points in the plane, a set of non-negative (ordered) weights and a connected polygonal region S, the weighted anti-ordered median straight-line location problem consists in finding a straight line intersecting S and maximizing the sum of ordered weighted distances to the points. In this paper we show how to find such a straight line in O(n^4) time when the Euclidean distance is considered. As a consequence of the results given in the paper the weighted anti-median Euclidean straight-line problem can be solved in O(n^2) time.
Journal: Discrete Applied Mathematics
ISSN: 0166-218X
Volume: 182
Pages: 122-133
Keywords:Location, extensive facilites, obnoxious facilities, anti-ordered median, anti-median
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