Forests, frames, and games: Algorithms for matroid sums and applications Authors Harold N. Gabow Department of Computer Science University of Colorado at Boulder Herbert H. Westermann Department 3228 IBM Laboratories Article

Received: 04 October 1989 Revised: 08 April 1990 DOI :
10.1007/BF01758774

Cite this article as: Gabow, H.N. & Westermann, H.H. Algorithmica (1992) 7: 465. doi:10.1007/BF01758774
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.

Key words Matroid Matroid sum Matroid partitioning Covering Arboricity Packing Bar-and-joint framework Bar-and-body framework Rigidity Shannon switching game 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.

Communicated by Greg N. Frederickson.

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