Sparsification—a technique for speeding up dynamic graph algorithms
Journal of the ACM (JACM)
Randomized fully dynamic graph algorithms with polylogarithmic time per operation
Journal of the ACM (JACM)
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Fully Dynamic Maintenance of Vertex Cover
WG '93 Proceedings of the 19th International Workshop on Graph-Theoretic Concepts in Computer Science
Worst-case update times for fully-dynamic all-pairs shortest paths
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On graph problems in a semi-streaming model
Theoretical Computer Science - Automata, languages and programming: Algorithms and complexity (ICALP-A 2004)
Approximating the minimum vertex cover in sublinear time and a connection to distributed algorithms
Theoretical Computer Science
Distributed approximate matching
Proceedings of the twenty-sixth annual ACM symposium on Principles of distributed computing
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
Finding graph matchings in data streams
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
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We consider the problem of maintaining a large matching or a small vertex cover in a dynamically changing graph. Each update to the graph is either an edge deletion or an edge insertion. We give the first randomized data structure that simultaneously achieves a constant approximation factor and handles a sequence of k updates in k ċ polylog(n) time. Previous data structures require a polynomial amount of computation per update. The starting point of our construction is a distributed algorithm of Parnas and Ron (Theor. Comput. Sci. 2007), which they designed for their sublinear-time approximation algorithm for the vertex cover size. This leads us to wonder whether there are other connections between sublinear algorithms and dynamic data structures.