Abstract
Computing 2-terminal reliability of probe interval graphs
Highlights
A graph is an interval graph [4] if its vertices can be placed in a one-to-one correspondence with a family of intervals on the real line such that two vertices are adjacent if and only if their corresponding intervals have a non-empty intersection
A probe interval graph (PIG) [9,11] is a generalization of an interval graph in which the vertex set is partitioned into probes and non-probes, such that two vertices are adjacent if and only if their corresponding intervals intersect and at least one of them is a probe
For a probabilistic graph G and a distinguished set of target vertices K, the K-terminal reliability (KTR) [2, 5, 6] is the probability that operational paths exist between every pair of vertices in K
Summary
A graph is an interval graph [4] if its vertices can be placed in a one-to-one correspondence with a family of intervals on the real line such that two vertices are adjacent if and only if their corresponding intervals have a non-empty intersection. A probe interval graph (PIG) [9,11] is a generalization of an interval graph in which the vertex set is partitioned into probes and non-probes, such that two vertices are adjacent if and only if their corresponding intervals intersect and at least one of them is a probe. For a probabilistic graph G and a distinguished set of target vertices K, the K-terminal reliability (KTR) [2, 5, 6] is the probability that operational paths exist between every pair of vertices in K. Lin [6] proposed a linear-time algorithm for computing the KTR (including the 2TR) of proper interval graphs, which is a subclass of interval graphs in which no interval is allowed to contain another one. This paper extends the results of that work [7] to computing the 2TR of PIGs
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