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Factoring Algorithm for Counting the Number of (s,t)-Mincuts of Each Size

Stéphane Bulteau 1
1 MODEL - Modeling Random Systems
IRISA - Institut de Recherche en Informatique et Systèmes Aléatoires, INRIA Rennes
Abstract : An efficient family of methods to evaluate network reliability is the class of factoring algorithms. Their efficiency is due to the use of reliability-preserving reductions (for instance, series-parallel ones). In this work, we follow a similar approach for the problem of counting the (s,t)-mincuts of a graph with size i, for all i. In order to take into account these possible reductions, the paper presents a technique based on a factoring formula, similar to the relation of Moskowitz, to count the number of (s,t)-mincuts of each size. This formula is applied recursively and various reductions, with computational cost polynomial in the size of the network, are used in order to reduce the size of the studied graph.
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Submitted on : Wednesday, May 24, 2006 - 12:58:12 PM
Last modification on : Friday, February 4, 2022 - 3:22:19 AM
Long-term archiving on: : Sunday, April 4, 2010 - 11:47:47 PM


  • HAL Id : inria-00073480, version 1


Stéphane Bulteau. Factoring Algorithm for Counting the Number of (s,t)-Mincuts of Each Size. [Research Report] RR-3209, INRIA. 1997. ⟨inria-00073480⟩



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