The obnoxious center problem on weighted cactus graphs.
Janez Žerovnik and Blaž Zmazek
Discrete appl. math. Volume 136, Number 2-3, pp. 377-386, 2004. ISSN 0166-218x

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. An algorithm is given which finds the obnoxious center on a weighted cactus graph in $O(cn)$ time, where $n$ is the number of vertices and $c$ is the number of different vertex weights (called marks).

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