The Weighted Integrity Problem is Polynomial for Interval Graphs

Abstract

Network reliability is an important issue in the area of distributed computing. Most of the early work in this area takes a probabilistic approach to the problem. However, sometimes it is important to incorporate subjective reliability estimates into the measure. To serve this goal, we propose the use of the weighted integrity, a measure of graph vulnerability. The weighted integrity problem is known to be NP-complete for most of the common network topologies including tree, mesh, hypercube, etc. It is known to be NP-complete even for most perfect graphs, including comparability graphs and chordal graphs. However, the computational complexity of the problem is not known for one class of perfect graphs, namely, co-comparability graphs. In this paper, we give a polynomial-time algorithm to compute the weighted integrity of interval graphs, a subclass of co-comparability graphs.