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

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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.

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Authors and Affiliations

  1. Graduate School of Engineering, Kyoto University, Kyoto, Japan, 606-01

    Hiroshi Nagamochi & Toshihide Ibaraki

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  1. Hiroshi Nagamochi
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  2. Toshihide Ibaraki
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Nagamochi, H., Ibaraki, T. Deterministic Õ(nm) Time Edge-Splitting in Undirected Graphs. Journal of Combinatorial Optimization 1, 5–46 (1997). https://doi.org/10.1023/A:1009739202898

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