On the thickness and arboricity of a graph
Journal of Combinatorial Theory Series B
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Sparsification—a technique for speeding up dynamic graph algorithms
Journal of the ACM (JACM)
Average case analysis of dynamic graph algorithms
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Randomized fully dynamic graph algorithms with polylogarithmic time per operation
Journal of the ACM (JACM)
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
A fully dynamic algorithm for maintaining the transitive closure
Journal of Computer and System Sciences - STOC 1999
Dynamic Representation of Sparse Graphs
WADS '99 Proceedings of the 6th International Workshop on Algorithms and Data Structures
Fully Dynamic Maintenance of Vertex Cover
WG '93 Proceedings of the 19th International Workshop on Graph-Theoretic Concepts in Computer Science
A new approach to dynamic all pairs shortest paths
Journal of the ACM (JACM)
Trade-offs for fully dynamic transitive closure on DAGs: breaking through the O(n2 barrier
Journal of the ACM (JACM)
Combinatorica
Dynamic ordered sets with exponential search trees
Journal of the ACM (JACM)
Faster dynamic matchings and vertex connectivity
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
Maintaining a large matching and a small vertex cover
Proceedings of the forty-second ACM symposium on Theory of computing
Fully Dynamic Maximal Matching in O (log n) Update Time
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
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A maximal matching can be maintained in fully dynamic (supporting both addition and deletion of edges) n-vertex graphs using a trivial deterministic algorithm with a worst-case update time of O(n). No deterministic algorithm that outperforms the naive O(n) one was reported up to this date. The only progress in this direction is due to Ivkovic and Lloyd [14], who in 1993 devised a deterministic algorithm with an amortized update time of O((n+m)√2/2), where m is the number of edges. In this paper we show the first deterministic fully dynamic algorithm that outperforms the trivial one. Specifically, we provide a deterministic worst-case update time of O(√m). Moreover, our algorithm maintains a matching which is in fact a 3/2-approximate maximum cardinality matching (MCM). We remark that no fully dynamic algorithm for maintaining (2-ε)-approximate MCM improving upon the naive O(n) was known prior to this work, even allowing amortized time bounds and randomization. For low arboricity graphs (e.g., planar graphs and graphs excluding fixed minors), we devise another simple deterministic algorithm with sub-logarithmic update time. Specifically, it maintains a fully dynamic maximal matching with amortized update time of O(log n/log log n). This result addresses an open question of Onak and Rubinfeld [19]. We also show a deterministic algorithm with optimal space usage of O(n+m), that for arbitrary graphs maintains a maximal matching with amortized update time of O(√m).