A data structure for dynamic trees
Journal of Computer and System Sciences
Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
Ambivalent Data Structures for Dynamic 2-Edge-Connectivity and k Smallest Spanning Trees
SIAM Journal on Computing
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
Separator-Based Sparsification II: Edge and Vertex Connectivity
SIAM Journal on Computing
Randomized rounding without solving the linear program
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
Using randomized sparsification to approximate minimum cuts
SODA '94 Proceedings of the fifth annual ACM-SIAM symposium on Discrete algorithms
Minimum cuts in near-linear time
Journal of the ACM (JACM)
Decremental dynamic connectivity
Journal of Algorithms
Minimizing Diameters of Dynamic Trees
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Data structures for on-line updating of minimum spanning trees
STOC '83 Proceedings of the fifteenth annual ACM symposium on Theory of computing
Maintaining information in fully dynamic trees with top trees
ACM Transactions on Algorithms (TALG)
Dynamic Graph Cuts for Efficient Inference in Markov Random Fields
IEEE Transactions on Pattern Analysis and Machine Intelligence
Maintaining a large matching and a small vertex cover
Proceedings of the forty-second ACM symposium on Theory of computing
Dynamic approximate vertex cover and maximum matching
Property testing
Dynamic approximate vertex cover and maximum matching
Property testing
Min-cuts and shortest cycles in planar graphs in O(n log log n) time
ESA'11 Proceedings of the 19th European conference on Algorithms
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We show that we can maintain up to polylogarithmic edge connectivity for a fully-dynamic graph in \tilde O(\sqrt{n}) time per edge insertion or deletion. Within logarithmic factors, this matches the best time bound for 1-edge connectivity. Previously, no o(n) bound was known for edge connectivity above 3, and even for 3-edge connectivity, the best update time was O(n^{2/3}), dating back to FOCS'92.Our algorithm maintains a concrete min-cut in terms of a pointer to a tree spanning one side of the cut plus ability to list the cut edges in O(\log n) time per edge.By dealing with polylogarithmic edge connectivity, we immediately get a sampling based expected factor (1+o(1)) approximation to general edge connectivity in \tilde O(\sqrt{n}) time per edge insertion or deletion. This algorithm also maintains a pointer to one side of a min-cut, but if we want to list the cut edges in O(\log n) time per edge, the update time increases to \tilde O(\sqrt{m}).