Matrix multiplication via arithmetic progressions
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Sparsification—a technique for speeding up dynamic graph algorithms
Journal of the ACM (JACM)
A fully dynamic algorithm for maintaining the transitive closure
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Randomized fully dynamic graph algorithms with polylogarithmic time per operation
Journal of the ACM (JACM)
Decremental dynamic connectivity
Journal of Algorithms
Near-optimal fully-dynamic graph connectivity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Fully Dynamic Algorithms for Maintaining All-Pairs Shortest Paths and Transitive Closure in Digraphs
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A fully dynamic reachability algorithm for directed graphs with an almost linear update time
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Dynamic Transitive Closure via Dynamic Matrix Inverse (Extended Abstract)
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of 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)
Worst-case update times for fully-dynamic all-pairs shortest paths
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Dynamic Subgraph Connectivity with Geometric Applications
SIAM Journal on Computing
Planning for Fast Connectivity Updates
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Oracles for Distances Avoiding a Failed Node or Link
SIAM Journal on Computing
Improved Dynamic Reachability Algorithms for Directed Graphs
SIAM Journal on Computing
Dynamic Connectivity: Connecting to Networks and Geometry
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Dual-failure distance and connectivity oracles
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Connectivity oracles for failure prone graphs
Proceedings of the forty-second ACM symposium on Theory of computing
Dynamic Connectivity: Connecting to Networks and Geometry
SIAM Journal on Computing
Connectivity oracles for planar graphs
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
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We study the "subgraph connectivity" problem for undirected graphs with sublinear vertex update time. In this problem, we can make vertices active or inactive in a graph G, and answer the connectivity between two vertices in the subgraph of G induced by the active vertices. Two open problems in subgraph connectivity are solved in this paper. We give the first subgraph connectivity structure with worst-case sublinear time bounds for both updates and queries. Our worst-case subgraph connectivity structure supports Õ (m4/5) update time, Õ(m1/5) query time and occupies Õ(m) space, where m is the number of edges in the whole graph G. In the second part of our paper, we describe another dynamic subgraph connectivity structure with amortized Õ (m2/3) update time, Õ(m1/3) query time and linear space, which improves the structure introduced by [Chan, Patrascu, Roditty, FOCS'08] that takes Õ(m4/3) space.