Computation of inverse 1-centre location problem on the weighted interval graphs

Abstract

Let TIG be the tree corresponding to the weighted interval graph G = (V, E). In an inverse 1-centre location problem the parameter of an interval tree TIG corresponding to the weighted interval graph G = (V, E), like vertex weights have to be modified at minimum total cost such that a pre-specified vertex s ∈ V becomes the 1-centre of the interval graph G. In this paper, we present an O(n) time algorithm to find an inverse 1-centre location problem on the weighted tree TIG corresponding to the weighted interval graph, where the vertex weights can be changed within certain bounds and n is the number of vertices of the graph G.