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Forests, frames, and games: Algorithms for matroid sums and applications

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Abstract

This paper presents improved algorithms for matroid-partitioning problems, such as finding a maximum cardinality set of edges of a graph that can be partitioned intok forests, and finding as many disjoint spanning trees as possible. The notion of a clump in a matroid sum is introduced, and efficient algorithms for clumps are presented. Applications of these algorithms are given to problems arising in the study of the structural rigidity of graphs, the Shannon switching game, and others.

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Author information

Authors and Affiliations

  1. Department of Computer Science, University of Colorado at Boulder, 80309, Boulder, CO, USA

    Harold N. Gabow

  2. Department 3228, IBM Laboratories, Schönaidner Strasse 220, 7030, Böblingen, Germany

    Herbert H. Westermann

Authors
  1. Harold N. Gabow
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  2. Herbert H. Westermann
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Additional information

Communicated by Greg N. Frederickson.

This is a revised and expanded version of a paper appearing in theProceedings of the 20th Annual ACM Symposium on Theory of Computing, 1988. This research was supported in part by National Science Foundation Grants MCS-8302648 and DCR-851191.

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Gabow, H.N., Westermann, H.H. Forests, frames, and games: Algorithms for matroid sums and applications. Algorithmica 7, 465–497 (1992). https://doi.org/10.1007/BF01758774

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  • DOI: https://doi.org/10.1007/BF01758774

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