Randomized parallel algorithms for matroid union and intersection, with applications to arboresences and edge-disjoint spanning trees

The strong link between matroids and matching is used to extend the ideas that resulted in the design of Random NC algorithms for matching to obtain RNC algorithms for the well-known problems of finding an arboresence and a maximum cardinality set of edge-disjoint spanning trees in a graph. The key tools used are linear algebra and randomization.

[1]  L. Csanky,et al.  Fast Parallel Matrix Inversion Algorithms , 1976, SIAM J. Comput..

[2]  M. Iri,et al.  Use of matroid theory in operations research, circuits and systems theory , 1981 .

[3]  Richard Zippel,et al.  Probabilistic algorithms for sparse polynomials , 1979, EUROSAM.

[4]  James G. Oxley,et al.  Matroid theory , 1992 .

[5]  Allan Borodin,et al.  Parallel Computation for Well-Endowed Rings and Space-Bounded Probabilistic Machines , 1984, Inf. Control..

[6]  Ernst W. Mayr,et al.  The complexity of circuit value and network stability , 1989, [1989] Proceedings. Structure in Complexity Theory Fourth Annual Conference.

[7]  L. Csanky,et al.  Fast parallel matrix inversion algorithms , 1975, 16th Annual Symposium on Foundations of Computer Science (sfcs 1975).

[8]  J. Edmonds.  Minimum partition of a matroid into independent subsets , 1965 .

[9]  Alon Itai,et al.  The Multi-Tree Approach to Reliability in Distributed Networks , 1988, Inf. Comput..

[10]  Vijay V. Vazirani,et al.  Matching is as easy as matrix inversion , 1987, STOC.

[11]  Jacob T. Schwartz,et al.  Fast Probabilistic Algorithms for Verification of Polynomial Identities , 1980, J. ACM.

[12]  Dan Gusfield,et al.  Connectivity and Edge-Disjoint Spanning Trees , 1983, Information Processing Letters.

[13]  Richard M. Karp,et al.  A Survey of Parallel Algorithms for Shared-Memory Machines , 1988 .

[14]  L. Lovász,et al.  On Generic Rigidity in the Plane , 1982 .

[15]  Eli Upfal,et al.  Are search and decision programs computationally equivalent? , 1985, STOC '85.

[16]  Bernhard Korte,et al.  Complexity of Matroid Property Algorithms , 1982, SIAM J. Comput..

[17]  Ernst W. Mayr,et al.  The Complexity of Circuit Value and Network Stability , 1992, J. Comput. Syst. Sci..

[18]  Don Coppersmith,et al.  Matrix multiplication via arithmetic progressions , 1987, STOC.

[19]  C. Nash-Williams.  Edge-disjoint spanning trees of finite graphs , 1961 .

[20]  László Lovász,et al.  Computing ears and branchings in parallel , 1985, 26th Annual Symposium on Foundations of Computer Science (sfcs 1985).

[21]  Y. Kajitani,et al.  Maximally Distant Trees and Principal Partition of a Linear Graph , 1969 .

[22]  H. Watanabe,et al.  Topological degrees of freedom and mixed analysis of electrical networks , 1970 .

[23]  Alon Itai,et al.  The Multi-Tree Approach to Reliability in Distributed Networks , 1984, Inf. Comput..