)-time algorithm for computing the K-terminal reliability of rooted directed path graphs

Let G denote a graph, and KV(G) represent a set of target vertices. Assume that the non-target vertices of G fail independently with given probabilities. The K-terminal reliability of G is defined as the probability that all target vertices in K are connected. Computing K-terminal reliability is #P-complete for general graphs, yet solvable in polynomial time for interval graphs. This work proposes an O(n 2 )-time algorithm for computing the K-terminal reliability of n-vertex rooted directed path graphs, which are a superclass of interval graphs.