A Weighted Linear Matroid Parity Algorithm

The matroid parity (or matroid matching) problem, introduced as a common generalization of matching and matroid intersection problems, is so general that it requires an exponential number of oracle...

[1]  Kazuo Murota,et al.  Computing the Degree of Determinants Via Combinatorial Relaxation , 1995, SIAM J. Comput..

[2]  M. Milic,et al.  General passive networks-Solvability, degeneracies, and order of complexity , 1974 .

[3]  Harold N. Gabow,et al.  An augmenting path algorithm for linear matroid parity , 1986, Comb..

[4]  Jan Vondrák,et al.  Matroid Matching: The Power of Local Search , 2013, SIAM J. Comput..

[5]  Fabrizio Grandoni,et al.  Steiner Tree Approximation via Iterative Randomized Rounding , 2013, JACM.

[6]  László Lovász,et al.  On some combinatorial properties of algebraic matroids , 1987, Comb..

[7]  Paul D. Seymour,et al.  Packing Non-Zero A-Paths In Group-Labelled Graphs , 2006, Comb..

[8]  Jonathan L. Gross,et al.  Finding a maximum-genus graph imbedding , 1988, JACM.

[9]  Jack Edmonds,et al.  Maximum matching and a polyhedron with 0,1-vertices , 1965 .

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

[11]  Lap Chi Lau,et al.  Algebraic Algorithms for Linear Matroid Parity Problems , 2011, TALG.

[12]  W. T. Tutte The Factorization of Linear Graphs , 1947 .

[13]  Shin-ichi Tanigawa,et al.  Packing non-zero A-paths via matroid matching , 2016, Discret. Appl. Math..

[14]  Winfried Hochstättler,et al.  Matroid matching in pseudomodular lattices , 1989, Comb..

[15]  Satoru Iwata,et al.  Matroid Matching Via Mixed Skew-Symmetric Matrices , 2005, Comb..

[16]  Francesco Maffioli,et al.  Random Pseudo-Polynomial Algorithms for Exact Matroid Problems , 1992, J. Algorithms.

[17]  John H. Vande Vate Fractional matroid matchings , 1992, J. Comb. Theory, Ser. B.

[18]  M. Iri,et al.  AN ALGORITHM FOR FINDING AN OPTIMAL "INDEPENDENT ASSIGNMENT" , 1976 .

[19]  Eugene L. Lawler,et al.  Matroid intersection algorithms , 1975, Math. Program..

[20]  Maria Chudnovsky,et al.  An algorithm for packing non-zero A-paths in group-labelled graphs , 2008, Comb..

[21]  László Lovász,et al.  Matroid matching and some applications , 1980, J. Comb. Theory, Ser. B.

[22]  Satoru Iwata,et al.  The linear delta-matroid parity problem , 2003, J. Comb. Theory, Ser. B.

[23]  Nicholas J. A. Harvey Algebraic Algorithms for Matching and Matroid Problems , 2009, SIAM J. Comput..

[24]  Yutaro Yamaguchi,et al.  MATHEMATICAL ENGINEERING TECHNICAL REPORTS Packing A-paths in Group-Labelled Graphs via Linear Matroid Parity , 2013 .

[25]  W. Mader Über die Maximalzahl kreuzungsfreierH-Wege , 1978 .

[26]  Gyula Pap,et al.  An algorithm for weighted fractional matroid matching , 2008, J. Comb. Theory B.

[27]  Gyula Pap,et al.  Packing Non-Returning A-Paths* , 2007, Comb..

[28]  John H. Vande Vate,et al.  Solving the linear matroid parity problem as a sequence of matroid intersection problems , 1990, Math. Program..

[29]  Hans Jürgen Prömel,et al.  A New Approximation Algorithm for the Steiner Tree Problem with Performance Ratio 5/3 , 2000, J. Algorithms.