A linear time algorithm for computing the most reliable source on a series-parallel graph with unreliable edges

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18 Citations (Scopus)

Abstract

Given a network with n vertices and m edges where each edge has an independent operational probability, we are interested in finding a vertex of the network whose expected number of reachable vertices is maximum. Such a vertex is called a most reliable source of the network. This problem was studied by Melachrinoudis and Helander (1996) where an O(n2) time algorithm was proposed when the given network is a tree. In a more recent paper, Xue presented an O(n) time algorithm for this problem when the given network is a tree. In this paper, we present an O(n) time algorithm for computing the most reliable source on series-parallel graphs, using their embeddings in 2-trees.

Original languageEnglish (US)
Pages (from-to)331-345
Number of pages15
JournalTheoretical Computer Science
Volume209
Issue number1-2
StatePublished - Dec 6 1998
Externally publishedYes

Fingerprint

Series-parallel Graph
Linear-time Algorithm
Computing
Vertex of a graph

Keywords

  • Algorithms
  • Network reliability
  • Partial 2-trees
  • Series-parallel graph
  • Time complexity

ASJC Scopus subject areas

  • Computational Theory and Mathematics

Cite this

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abstract = "Given a network with n vertices and m edges where each edge has an independent operational probability, we are interested in finding a vertex of the network whose expected number of reachable vertices is maximum. Such a vertex is called a most reliable source of the network. This problem was studied by Melachrinoudis and Helander (1996) where an O(n2) time algorithm was proposed when the given network is a tree. In a more recent paper, Xue presented an O(n) time algorithm for this problem when the given network is a tree. In this paper, we present an O(n) time algorithm for computing the most reliable source on series-parallel graphs, using their embeddings in 2-trees.",
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