Constructing a perfect matching is in random NC
Combinatorica
Matching is as easy as matrix inversion
Combinatorica
A Simplified Realization of the Hopcroft-Karp Approach to Maximum Matching in General Graphs
A Simplified Realization of the Hopcroft-Karp Approach to Maximum Matching in General Graphs
Matching Theory (North-Holland mathematics studies)
Matching Theory (North-Holland mathematics studies)
An algebraic algorithm for weighted linear matroid intersection
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
An O(v|v| c |E|) algoithm for finding maximum matching in general graphs
SFCS '80 Proceedings of the 21st Annual Symposium on Foundations of Computer Science
Maximum weight bipartite matching in matrix multiplication time
Theoretical Computer Science
Algorithmic Applications of Baur-Strassen's Theorem: Shortest Cycles, Diameter and Matchings
FOCS '12 Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
| Hi-index | 5.23 |
The linear program dual variables for weighted matching and its generalization to f-factors are shown to be the weights of certain subgraphs: y duals are the weights of certain maximum matchings or f-factors; z duals are the weights of certain 2-factors or 2f-factors. Similar interpretations have been given for the bipartite case of these problems, where only y duals occur, but our variant is included here for completeness. In all cases the y duals are canonical in a well-defined sense; z duals are canonical for matching and more generally for b-matchings (a special case of f-factors) but for f-factors their support can vary. As weights of combinatoric objects the duals are integral for given integral edge weights, and so they give new proofs that the linear programs for these problems are TDI.