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Efficient Algorithms for the k Smallest Cuts Enumeration

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Computing and Combinatorics (COCOON 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5092))

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Abstract

In this paper, we study the problems of enumerating cuts of a graph by non-decreasing weights. There are four problems, depending on whether the graph is directed or undirected, and on whether we consider all cuts of the graph or only s-t cuts for a given pair of vertices s, t. Efficient algorithms for these problems with \({\tilde{\mbox{O}}}(n^2m)\) delay between two successive outputs have been known since 1992, due to Vazirani and Yannakakis. In this paper, improved algorithms are presented. The delays of the presented algorithms are O(nm log(n 2/m)).

This research is supported by the National Science Council of the Republic of China under grants NSC-95-2213-E-007-029 and NSC-94-2752-E-007-082.

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Authors and Affiliations

  1. Department of Computer Science, National Tsing Hua University, Hsinchu, Taiwan, 30043

    Li-Pu Yeh & Biing-Feng Wang

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  1. Li-Pu Yeh
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  2. Biing-Feng Wang
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Xiaodong Hu Jie Wang

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Yeh, LP., Wang, BF. (2008). Efficient Algorithms for the k Smallest Cuts Enumeration. In: Hu, X., Wang, J. (eds) Computing and Combinatorics. COCOON 2008. Lecture Notes in Computer Science, vol 5092. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69733-6_43

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  • DOI: https://doi.org/10.1007/978-3-540-69733-6_43

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-69732-9

  • Online ISBN: 978-3-540-69733-6

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