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 -