The Obnoxious Center Problem on a Tree

Authors:
Rainer E. Burkard;Helidon Dollani;Yixun Lin;Günter Rote
Affiliations:
-;-;-;-
Venue:
SIAM Journal on Discrete Mathematics
Year:
2001

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Abstract

The obnoxious center problem in a graph G asks for a location on an edge of the graph such that the minimum weighted distance from this point to a vertex of the graph is as large as possible. We derive algorithms with linear running time for the cases when G is a path or a star, thus improving previous results of Tamir [SIAM J. Discrete Math, 1 (1988), pp. 377--396]. For subdivided stars we present an algorithm of running time O(n log n). For general trees, we improve an algorithm of Tamir [SIAM J. Discrete Math, 1 (1988), pp. 377--396] by a factor of log n. Moreover, a linear algorithm for the unweighted center problem on an arbitrary tree with neutral and obnoxious vertices is described.