Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Directed s-t numberings, rubber bands, and testing digraph k-vertex connectivity
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Sparsification—a technique for speeding up dynamic graph algorithms
Journal of the ACM (JACM)
Random Weighted Laplacians, Lovász minimum digraphs and finding minimum separators
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Theoretical Improvements in Algorithmic Efficiency for Network Flow Problems
Journal of the ACM (JACM)
Fast Probabilistic Algorithms for Verification of Polynomial Identities
Journal of the ACM (JACM)
Matching is as easy as matrix inversion
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Probabilistic algorithms for sparse polynomials
EUROSAM '79 Proceedings of the International Symposiumon on Symbolic and Algebraic Computation
ESA '99 Proceedings of the 7th Annual European Symposium on Algorithms
Using expander graphs to find vertex connectivity
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Dynamic Transitive Closure via Dynamic Matrix Inverse (Extended Abstract)
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Theoretical Computer Science
Maintaining a large matching and a small vertex cover
Proceedings of the forty-second ACM symposium on Theory of computing
Connectivity oracles for failure prone graphs
Proceedings of the forty-second ACM symposium on Theory of computing
Dynamic approximate vertex cover and maximum matching
Property testing
Dynamic approximate vertex cover and maximum matching
Property testing
Fast matrix rank algorithms and applications
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
Dynamic matchings in convex bipartite graphs
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
Simple deterministic algorithms for fully dynamic maximal matching
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Fast matrix rank algorithms and applications
Journal of the ACM (JACM)
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We present first fully dynamic subquadratic algorithms for: computing maximum matching size, computing maximum bipartite matching weight, computing maximum number of vertex disjoint s, t paths and testing directed vertex k-connectivity of the graph. The presented algorithms are randomized. The algorithms for maximum matching size and disjoint paths support operations in O(n1.495) time. The algorithm for computing the maximum bipartite matching weight maintains the graph with integer edge weights from the set 1,..., W in O(W2.495n1.495) time. The algorithm for testing directed vertex k-connectivity supports updates in O(n1.575 + nk2) time. For all of these problems the presented dynamic algorithms break the input size barrier --- O(n2). As a side result we obtain a dynamic algorithm for the dynamic maintenance of the rank of the matrix that support updates in O(n1.495) time.