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Efficient Edge Splitting-Off Algorithms Maintaining All-Pairs Edge-Connectivities

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Integer Programming and Combinatorial Optimization (IPCO 2010)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6080))

Abstract

In this paper we present new edge splitting-off results maintaining all-pairs edge-connectivities of a graph. We first give an alternate proof of Mader’s theorem, and use it to obtain a deterministic \(\tilde{O}({r_{\max}}^2 \cdot n^2)\)-time complete edge splitting-off algorithm for unweighted graphs, where r max denotes the maximum edge-connectivity requirement. This improves upon the best known algorithm by Gabow by a factor of \(\tilde{\Omega}(n)\). We then prove a new structural property, and use it to further speedup the algorithm to obtain a randomized \(\tilde{O}(m + {r_{\max}}^3 \cdot n)\)-time algorithm. These edge splitting-off algorithms can be used directly to speedup various graph algorithms.

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Authors and Affiliations

  1. Department of Computer Science and Engineering, The Chinese University of Hong Kong,  

    Lap Chi Lau & Chun Kong Yung

Authors
  1. Lap Chi Lau
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  2. Chun Kong Yung
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Editors and Affiliations

  1. Institute of Mathematics, École Polytechnique Féderale de Lausanne, 1015, Lausanne, Switzerland

    Friedrich Eisenbrand

  2. McGill University, 805 Sherbrooke West, H3A 2K6, Montreal, Quebec, Canada

    F. Bruce Shepherd

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Lau, L.C., Yung, C.K. (2010). Efficient Edge Splitting-Off Algorithms Maintaining All-Pairs Edge-Connectivities. In: Eisenbrand, F., Shepherd, F.B. (eds) Integer Programming and Combinatorial Optimization. IPCO 2010. Lecture Notes in Computer Science, vol 6080. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13036-6_8

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  • DOI: https://doi.org/10.1007/978-3-642-13036-6_8

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-13035-9

  • Online ISBN: 978-3-642-13036-6

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