Counting almost minimum cutsets with reliability applications

Aparna Ramanathan; Charles J. Colbourn

doi:10.1007/BF02592076

Counting almost minimum cutsets with reliability applications

Aparna Ramanathan, Charles J. Colbourn

Research output: Contribution to journal › Article › peer-review

29 Scopus citations

Abstract

The number n₁ of i-edge network cutsets in a graph is an important parameter in reliability analysis. Using a theorem of Lomonosov and Polesskii, Ball and Provan have shown that the number n_i of minimum cardinality network cutsets can be determined in polynomial time. This paper gives a polynomial time algorithm for determining n_r+k for any fixed k, as a special case of counting cuts of specified maximum weight in an edge-weighted graph. The resulting improvement in existing reliability bounds is shown to be substantial.

Original language	English (US)
Pages (from-to)	253-261
Number of pages	9
Journal	Mathematical Programming
Volume	39
Issue number	3
DOIs	https://doi.org/10.1007/BF02592076
State	Published - Oct 1987
Externally published	Yes

Keywords

Cutset
inclusion-exclusion
network reliability
polynomial time
probabilistic graph
weighted graph

ASJC Scopus subject areas

Software
General Mathematics

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10.1007/BF02592076

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title = "Counting almost minimum cutsets with reliability applications",

abstract = "The number n1 of i-edge network cutsets in a graph is an important parameter in reliability analysis. Using a theorem of Lomonosov and Polesskii, Ball and Provan have shown that the number ni of minimum cardinality network cutsets can be determined in polynomial time. This paper gives a polynomial time algorithm for determining nr+k for any fixed k, as a special case of counting cuts of specified maximum weight in an edge-weighted graph. The resulting improvement in existing reliability bounds is shown to be substantial.",

keywords = "Cutset, inclusion-exclusion, network reliability, polynomial time, probabilistic graph, weighted graph",

author = "Aparna Ramanathan and Colbourn, {Charles J.}",

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AU - Colbourn, Charles J.

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AB - The number n1 of i-edge network cutsets in a graph is an important parameter in reliability analysis. Using a theorem of Lomonosov and Polesskii, Ball and Provan have shown that the number ni of minimum cardinality network cutsets can be determined in polynomial time. This paper gives a polynomial time algorithm for determining nr+k for any fixed k, as a special case of counting cuts of specified maximum weight in an edge-weighted graph. The resulting improvement in existing reliability bounds is shown to be substantial.

KW - Cutset

KW - inclusion-exclusion

KW - network reliability

KW - polynomial time

KW - probabilistic graph

KW - weighted graph

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JF - Mathematical Programming

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ER -

Counting almost minimum cutsets with reliability applications

Abstract

Keywords

ASJC Scopus subject areas

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