Data structures and network algorithms
Data structures and network algorithms
Computing a maximum cardinality matching in a bipartite graph in time On1.5m/logn
Information Processing Letters
ACM Computing Surveys (CSUR)
Fast parallel algorithms for graph matching problems
Fast parallel algorithms for graph matching problems
Bipartite Edge Coloring in $O(\Delta m)$ Time
SIAM Journal on Computing
Decremental dynamic connectivity
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
Near-optimal fully-dynamic graph connectivity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Linear reductions of maximum matching
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Efficient algorithms for Petersen's matching theorem
Journal of Algorithms
A data structure for dynamic trees
STOC '81 Proceedings of the thirteenth annual ACM symposium on Theory of computing
Matching Theory (North-Holland mathematics studies)
Matching Theory (North-Holland mathematics studies)
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
Linear algorithm for selecting an almost regular spanning subgraph in an almost regular graph
Problems of Information Transmission
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The main result of this paper is a new perfect matching algorithm for biconnected cubic graphs. The algorithm runs in time O(n log2 n). It is also possible, by applying randomized data structures, to get O(n logn loglog3 n) average time. Our solution improves the one given by T. Biedl et al. [3]. The algorithm of Biedl et al. runs in time O(n log4 n). We use a similar approach. However, thanks to exploring some properties of biconnected cubic graphs we are able to replace complex fully-dynamic biconnectivity data structure with much simpler, dynamic graph connectivity and dynamic tree data structures. Moreover, we present a significant modification of the new algorithm which makes application of a decremental dynamic graph connectivity data structure possible, instead of one supporting the fully dynamic graph connectivity. It gives hope for further improvements.