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Deterministic Õ(nm) Time Edge-Splitting in Undirected Graphs

Author

Listed:
  • Hiroshi Nagamochi

    (Kyoto University)

  • Toshihide Ibaraki

    (Kyoto University)

Abstract

This paper presents a deterministic O (nm log n + n2log2n) = Õ (nm) time algorithm for splitting off all edges incident to a vertex s of even degree in a multigraph G, where n and m are the numbers of vertices and links (= vertex pairs between which G has an edge) in G, respectively. Based on this, many graph algorithms using edge-splitting can run faster. For example, the edge-connectivity augmentation problem in an undirected multigraph can be solved in Õ (nm) time, which is an improvement over the previously known randomized Õ (n3) bound and deterministic Õ (n2m) bound.

Suggested Citation

  • Hiroshi Nagamochi & Toshihide Ibaraki, 1997. "Deterministic Õ(nm) Time Edge-Splitting in Undirected Graphs," Journal of Combinatorial Optimization, Springer, vol. 1(1), pages 5-46, March.
    • Handle: RePEc:spr:jcomop:v:1:y:1997:i:1:d:10.1023_a:1009739202898
    DOI: 10.1023/A:1009739202898
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    Citations

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    Cited by:

    1. Hiroshi Nagamochi & Takashi Shiraki & Toshihide Ibaraki, 2001. "Augmenting a Submodular and Posi-modular Set Function by a Multigraph," Journal of Combinatorial Optimization, Springer, vol. 5(2), pages 175-212, June.
    2. Toshimasa Ishii & Hiroshi Nagamochi & Toshihide Ibaraki, 2000. "Optimal Augmentation of a 2-Vertex-Connected Multigraph to a k-Edge-Connected and 3-Vertex-Connected Multigraph," Journal of Combinatorial Optimization, Springer, vol. 4(1), pages 35-77, March.
    3. Hiroshi Nagamochi & Peter Eades, 2003. "An Edge-Splitting Algorithm in Planar Graphs," Journal of Combinatorial Optimization, Springer, vol. 7(2), pages 137-159, June.

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