An optimal algorithm for solving the 1‐median problem on weighted 4‐cactus graphs

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 tree networks, however, more efficient algorithms can be devised to find the medians in O(n). In this paper, we study weighted 4‐cactus (W4C) graphs which provide a less restrictive network structure than trees and show that median problem can be solved just as efficiently on W4C graphs as on trees. Many examples are provided demonstrating the rudiments of our algorithm and a linear time complexity algorithm is developed.