Computational geometry: an introduction
Computational geometry: an introduction
Matrix multiplication via arithmetic progressions
Journal of Symbolic Computation - Special issue on computational algebraic complexity
Maintenance of geometric extrema ∈
Journal of the ACM (JACM)
Clique partitions, graph compression and speeding-up algorithms
Journal of Computer and System Sciences
Sparsification—a technique for speeding up dynamic graph algorithms
Journal of the ACM (JACM)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Kinetic connectivity of rectangles
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
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
Simplified kinetic connectivity for rectangles and hypercubes
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
A fully dynamic algorithm for planar
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
Semi-online maintenance of geometric optima and measures
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Introduction to Algorithms
Maintaining Minimum Spanning Forests in Dynamic Graphs
SIAM Journal on Computing
On Computing Connected Components of Line Segments
IEEE Transactions on Computers
Fully dynamic transitive closure: breaking through the O(n/sup 2/) barrier
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Fast sparse matrix multiplication
ACM Transactions on Algorithms (TALG)
More algorithms for all-pairs shortest paths in weighted graphs
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Dynamic connectivity for axis-parallel rectangles
ESA'06 Proceedings of the 14th conference on Annual European Symposium - Volume 14
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
An algorithm for the difference between set covers
Discrete Applied Mathematics
Towards polynomial lower bounds for dynamic problems
Proceedings of the forty-second ACM symposium on Theory of computing
Dynamic Connectivity: Connecting to Networks and Geometry
SIAM Journal on Computing
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(MATH) Inspired by dynamic connectivity applications in computational geometry, we consider a problem we call dynamic subgraph connectivity: design a data structure for an undirected graph $G=(V,E)$ and a subset of vertices $S\on V$, to support insertions and deletions in~$S$ and connectivity queries (are two vertices connected\@?) in the subgraph induced by~$S$. We develop the first sublinear, fully dynamic method for this problem for general sparse graphs, using an elegant combination of several simple ideas. Our method requires linear space, $\OO (|E|^{4\w/(3\w+3)})=O(|E|^{0.94})$ amortized update time, and $\OO(|E|^{1/3})$ query time, where $\w$ is the matrix multiplication exponent and $\OO$ hides polylogarithmic factors.