Locating Median Paths on Connected Outerplanar Graphs

During the last two decades, there has been a growing interest in locating extensive facilities, such as paths, on networks. In this paper we study the median path problem without restrictions on its length on the class of connected outerplanar graphs with equal weights assigned to the edges and nonnegative weights associated to the vertices. We provide a O(kn) time algorithm, where n is the number of vertices of the graph G and k is the number of blocks in G. As a byproduct, we provide a linear time algorithm to find a median path without restrictions on its length between two fixed vertices in a biconnected outerplanar graph.