A matroid approach to finding edge connectivity and packing arborescences
Selected papers of the 23rd annual ACM symposium on Theory of computing
Fast approximation algorithms for fractional packing and covering problems
Mathematics of Operations Research
An incremental algorithm for a generalization of the shortest-path problem
Journal of Algorithms
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
Computing the Local Consensus of Trees
SIAM Journal on Computing
Experimental analysis of dynamic algorithms for the single source shortest paths problem
Journal of Experimental Algorithmics (JEA)
Unique maximum matching algorithms
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Randomized rounding without solving the linear program
Proceedings of the sixth annual ACM-SIAM symposium on Discrete algorithms
A linear time 2 + &&egr; approximation algorithm for edge connectivity
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Efficient algorithms for Petersen's matching theorem
Proceedings of the tenth 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
Better random sampling algorithms for flows in undirected graphs
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Minimum cuts in near-linear time
Journal of the ACM (JACM)
OSPF: Anatomy of an Internet Routing Protocol
OSPF: Anatomy of an Internet Routing Protocol
Local Search in Combinatorial Optimization
Local Search in Combinatorial Optimization
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
The h-Index of a Graph and Its Application to Dynamic Subgraph Statistics
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
A theory and algorithms for combinatorial reoptimization
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Reoptimization of the minimum total flow-time scheduling problem
MedAlg'12 Proceedings of the First Mediterranean conference on Design and Analysis of Algorithms
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First we review amortized fully-dynamic polylogarithmic algorithms for connectivity, minimum spanning trees (MST), 2-edge- and biconnectivity. Second we discuss how they yield improved static algorithms: connectivity for constructing a tree from homeomorphic subtrees, 2-edge connectivity for finding unique matchings in graphs, and MST for packing spanning trees in graphs. The application of MST for spanning tree packing is new and when boot-strapped, it yields a fully-dynamic polylogarithmic algorithm for approximating general edge connectivity within a factor √2+o(1). Finally, on the more practical side, we will discuss how output sensitive algorithms for dynamic shortest paths have been applied successfully to speed up local search algorithms for improving routing on the internet, roughly doubling the capacity.