TY - JOUR

T1 - A linear time algorithm for computing the most reliable source on a series-parallel graph with unreliable edges

AU - Colbourn, Charles J.

AU - Xue, Guoliang

N1 - Funding Information:
’ E-mail: colboum@cs.uvm.edu. This research was supported in part by NSERC Canada. 2 E-mail: xue@cs.uvm.edu. This research was supported in part by US Army grant DAAH04-96-1-0233 and by NSF grants ASC-9409285 and OSR-9350540.

PY - 1998/12/6

Y1 - 1998/12/6

N2 - 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.

AB - 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.

KW - Algorithms

KW - Network reliability

KW - Partial 2-trees

KW - Series-parallel graph

KW - Time complexity

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U2 - 10.1016/S0304-3975(97)00124-2

DO - 10.1016/S0304-3975(97)00124-2

M3 - Article

AN - SCOPUS:0346498308

SN - 0304-3975

VL - 209

SP - 331

EP - 345

JO - Theoretical Computer Science

JF - Theoretical Computer Science

IS - 1-2

ER -