An optimal algorithm for solving the weighted median problem on the weighted 4-cactus graphs

Abstract

In this paper,we solve the weighted median problem on a 4-cactus graph.The median problem has been extensively studied in the last three decades. On general graphs, the problem can be solved in O(n³),where n is the number of vertices in a graph. For three graphs, however, more efficient algorithm can be devised to find the weighted median in O(n). In this paper, we study weighted 4-cactus graphs which provide a less restrictive network structure than trees and show that the weighted median problem can be solved just as efficiently as on tree graphs.