Data structures and network algorithms
Data structures and network algorithms
Matching structure and the matching lattice
Journal of Combinatorial Theory Series B
Maximum matchings in general graphs through randomization
Journal of Algorithms
Network flows: theory, algorithms, and applications
Network flows: theory, algorithms, and applications
Randomized $\tilde{O}(M(|V|))$ Algorithms for Problems in Matching Theory
SIAM Journal on Computing
The two ear theorem on matching-covered graphs
Journal of Combinatorial Theory Series B
Maximum skew-symmetric flows and matchings
Mathematical Programming: Series A and B
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Our main result is an O(nm)-time (deterministic) algorithm for constructing an ear decomposition of a matching-covered graph, where n and m denote the number of nodes and edges. The improvement in the running time comes from new structural results that give a sharpened version of Lovász and Plummer's Two-Ear Theorem. Our algorithm is based on O(nm)-time algorithms for two other fundamental problems in matching theory, namely, finding all the allowed edges of a graph, and finding the canonical partition of an elementary graph. To the best of our knowledge, no faster deterministic algorithms are known for these two fundamental problems.