Backup 2-center on interval graphs

A graph G is called an interval graph if there exists a set of intervals corresponding to the vertex set of G and two vertices are adjacent to each other if and only if the two corresponding intervals are intersecting with each other. In this paper, we apply the reliability-based backup 2-center modal proposed by Wang, Wu and Chao, in which each server may fail with a given probability, to interval graphs and present an O(n) time algorithm.