Two algorithms for weighted matroid intersection
Mathematical Programming: Series A and B
Constructing a perfect matching is in random NC
Combinatorica
Matching is as easy as matrix inversion
Combinatorica
Faster scaling algorithms for network problems
SIAM Journal on Computing
Efficient theoretic and practical algorithms for linear matroid intersection problems
Journal of Computer and System Sciences
Combinatorial optimization
Mathematical Programming: Series A and B
Approximating Capacitated Routing and Delivery Problems
SIAM Journal on Computing
High-order lifting and integrality certification
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Maximum Matchings via Gaussian Elimination
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Deterministic network coding by matrix completion
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Processor efficient parallel matching
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
Minimum Bounded Degree Spanning Trees
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Algebraic Structures and Algorithms for Matching and Matroid Problems
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Matrices and Matroids for Systems Analysis
Matrices and Matroids for Systems Analysis
Weighted bipartite matching in matrix multiplication time
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Algebraic algorithms for linear matroid parity problems
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A combinatoric interpretation of dual variables for weighted matching and f-factors
Theoretical Computer Science
| Hi-index | 0.00 |
We present a new algebraic algorithm for the classical problem of weighted matroid intersection. This problem generalizes numerous well-known problems, such as bipartite matching, network flow, etc. Our algorithm has running time Õ(nrω-1W1+ε) for linear matroids with n elements and rank r, where ω is the matrix multiplication exponent, and W denotes the maximum weight of any element. This algorithm is the fastest known when W is small. Our approach builds on the recent work of Sankowski (2006) for Weighted Bipartite Matching and Harvey (2006) for Unweighted Linear Matroid Intersection.