Combinatorics for computer science
Combinatorics for computer science
Theory of linear and integer programming
Theory of linear and integer programming
An augmenting path algorithm for linear matroid parity
Combinatorica
SIAM Journal on Discrete Mathematics
Solving the linear matroid parity problem as a sequence of matroid intersection problems
Mathematical Programming: Series A and B
A hierarchy of relaxation between the continuous and convex hull representations
SIAM Journal on Discrete Mathematics
Journal of Combinatorial Theory Series B
Random pseudo-polynomial algorithms for exact matroid problems
Journal of Algorithms
New algorithms for linear k-matroid intersection and matroid k-parity problems
Mathematical Programming: Series A and B
Nonoverlapping local alignments (weighted independent sets of axis-parallel rectangles)
Discrete Applied Mathematics - Special volume on computational molecular biology
On Local Search for Weighted K-Set Packing
Mathematics of Operations Research
Greedy local improvement and weighted set packing approximation
Journal of Algorithms
Matching 2-lattice polyhedra: finding a maximum vector
Discrete Mathematics
Two-lattice polyhedra: duality and extreme points
Discrete Mathematics
Approximation algorithms
A d/2 approximation for maximum weight independent set in d-claw free graphs
Nordic Journal of Computing
A 2or3-Approximation of the Matroid Matching Problem
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
Cutting planes and the complexity of the integer hull
Cutting planes and the complexity of the integer hull
A Comparison of the Sherali-Adams, Lovász-Schrijver, and Lasserre Relaxations for 0--1 Programming
Mathematics of Operations Research
Bounds on the Chvátal Rank of Polytopes in the 0/1-Cube
Combinatorica
On the complexity of approximating k-set packing
Computational Complexity
Greedy in approximation algorithms
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
An Augmenting Path Algorithm For The Parity Problem On Linear Matroids
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Sherali-adams relaxations of the matching polytope
Proceedings of the forty-first annual ACM symposium on Theory of computing
A fast, simpler algorithm for the matroid parity problem
IPCO'08 Proceedings of the 13th international conference on Integer programming and combinatorial optimization
Applications of the linear matroid parity algorithm to approximating steiner trees
CSR'06 Proceedings of the First international computer science conference on Theory and Applications
Submodular function maximization via the multilinear relaxation and contention resolution schemes
Proceedings of the forty-third annual ACM symposium on Theory of computing
Improved approximations for k-exchange systems
ESA'11 Proceedings of the 19th European conference on Algorithms
Algebraic algorithms for linear matroid parity problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Lower bounds for the Chvátal-Gomory rank in the 0/1 cube
Operations Research Letters
Inequalities on submodular functions via term rewriting
Information Processing Letters
Matching problems with delta-matroid constraints
CATS '12 Proceedings of the Eighteenth Computing: The Australasian Theory Symposium - Volume 128
A simple PTAS for weighted matroid matching on strongly base orderable matroids
Discrete Applied Mathematics
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We consider the classical matroid matching problem. Unweighted matroid matching for linear matroids was solved by Lovasz, and the problem is known to be intractable for general matroids. We present a PTAS for unweighted matroid matching for general matroids. In contrast, we show that natural LP relaxations have an Ω(n) integrality gap and moreover, Ω(n) rounds of the Sherali-Adams hierarchy are necessary to bring the gap down to a constant. More generally, for any fixed k=2 and ε0, we obtain a (k/2+ε)-approximation for matroid matching in k-uniform hypergraphs, also known as the matroid k-parity problem. As a consequence, we obtain a (k/2+ε)-approximation for the problem of finding the maximum-cardinality set in the intersection of k matroids. We have also designed a 3/2-approximation for the weighted version of a special case of matroid matching, the matchoid problem.