The Weighted Integrity Problem is Polynomial for Interval Graphs

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.