The obnoxious center problem on weighted cactus graphs

The obnoxious center problem on weighted cactus graphs (Extended Abstract)

The Obnoxious Center Problem on a Tree

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. For subdivided stars we present an algorithm of running time O(n log n). Fo...

On the generalized obnoxious center problem: antimedian subsets∗

The set of vertices that maximize (minimize) the remoteness is the antimedian (median) set of the profile. It is proved that for an arbitrary graph G and S ⊆ V (G) it can be decided in polynomial time whether S is the antimedian set of some profile. Graphs in which every antimedian set is connected are also considered.

Efficient Algorithms for the Weighted 2-Center Problem in a Cactus Graph

In this paper, we provide efficient algorithms for solving the weighted center problems in a cactus graph. In particular, an O(n log n) time algorithm is proposed that finds the weighted 1-center in a cactus graph, where n is the number of vertices in the graph. For the weighted 2-center problem, an O(n log n) time algorithm is devised for its continuous version and showed that its discrete ver...

Broadcasting on cactus graphs

Broadcasting is the process of dissemination of a message from one vertex (called originator) to all other vertices in the graph. This task is accomplished by placing a sequence of calls between neighboring vertices, where one call requires one unit of time and each call involves exactly two vertices. Each vertex can participate in one call per one unit of time. Determination of the broadcast t...