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A linear-time algorithm for computing K-terminal reliability on proper interval graphs

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1 Author(s)
Min-Sheng Lin ; Dept. of Electr. Eng., Nat. Taipei Univ. of Technol., Taiwan

Consider a probabilistic graph in which the edges are perfectly reliable, but vertices can fail with some known probabilities. The K-terminal reliability of this graph is the probability that a given set of vertices K is connected. This reliability problem is #P-complete for general graphs, and remains #P-complete for chordal graphs and comparability graphs. This paper presents a linear-time algorithm for computing K-terminal reliability on proper interval graphs. A graph G = (V, E) is a proper interval graph if there exists a mapping from V to a class of intervals I of the real line with the properties that two vertices in G are adjacent if their corresponding intervals overlap and no interval in I properly contains another. This algorithm can be implemented in O(|V| + |E|) time

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Reliability, IEEE Transactions on  (Volume:51 ,  Issue: 1 )