Two algorithms for maintaining order in a list
STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
A data structure for dynamic trees
Journal of Computer and System Sciences
Algorithms and data structures for an expanded family of matroid intersection problems
SIAM Journal on Computing
Proving relative lower bounds for incremental algorithms
Acta Informatica
On-line graph algorithms with SPQR-trees
Proceedings of the seventeenth international colloquium on Automata, languages and programming
A matroid approach to finding edge connectivity and packing arborescences
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Algorithms for parallel k-vertex connectivity and sparse certificates
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
Maintaining biconnected components of dynamic planar graphs (extended abstract)
Proceedings of the 18th international colloquium on Automata, languages and programming
Reducing edge connectivity to vertex connectivity
ACM SIGACT News
On-line maintenance of the four-components of a graph (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Applications of a poset representation to edge connectivity and graph rigidity
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Maintenance of a minimum spanning forest in a dynamic plane graph
Journal of Algorithms
Fully dynamic algorithms for 2-edge connectivity
SIAM Journal on Computing
Verification and sensitivity analysis of minimum spanning trees in linear time
SIAM Journal on Computing
Maintaining the 3-edge-connected components of a graph on-line
SIAM Journal on Computing
Scan-first search and sparse certificates: an improved parallel algorithm for k-vertex connectivity
SIAM Journal on Computing
Offline algorithms for dynamic minimum spanning tree problems
Journal of Algorithms
A randomized linear-time algorithm to find minimum spanning trees
Journal of the ACM (JACM)
Computing Minimal Spanning Subgraphs in Linear Time
SIAM Journal on Computing
Randomized dynamic graph algorithms with polylogarithmic time per operation
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
Separator based sparsification I.: planarity testing and minimum spanning trees
Journal of Computer and System Sciences
Ambivalent Data Structures for Dynamic 2-Edge-Connectivity and k Smallest Spanning Trees
SIAM Journal on Computing
An empirical study of dynamic graph algorithms
Journal of Experimental Algorithmics (JEA)
On certificates and lookahead in dynamic graph problems
Proceedings of the seventh annual ACM-SIAM symposium on Discrete algorithms
Experimental analysis of dynamic minimum spanning tree algorithms
SODA '97 Proceedings of the eighth annual ACM-SIAM symposium on Discrete algorithms
A Simpler Minimum Spanning Tree Verification Algorithm
WADS '95 Proceedings of the 4th International Workshop on Algorithms and Data Structures
Efficient Algorithms for Graphic Intersection and Parity (Extended Abstract)
Proceedings of the 12th Colloquium on Automata, Languages and Programming
Maintaining Minimum Spanning Trees in Dynamic Graphs
ICALP '97 Proceedings of the 24th International Colloquium on Automata, Languages and Programming
Certificates and Fast Algorithms for Biconnectivity in Fully-Dynamic Graphs
ESA '95 Proceedings of the Third Annual European Symposium on Algorithms
Using sparsification for parametric minimum spanning tree problems
Nordic Journal of Computing
Fully dynamic biconnectivity and transitive closure
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
Techniques for the design of parallel graph algorithms
Techniques for the design of parallel graph algorithms
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Experimental analysis of dynamic algorithms for the single source shortest paths problem
Journal of Experimental Algorithmics (JEA)
Fully dynamic planarity testing with applications
Journal of the ACM (JACM)
Kinetic connectivity of rectangles
SCG '99 Proceedings of the fifteenth annual symposium on Computational geometry
Efficient algorithms for Petersen's matching theorem
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Fully dynamic algorithms for chordal graphs
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
Randomized fully dynamic graph algorithms with polylogarithmic time per operation
Journal of the ACM (JACM)
Near-optimal fully-dynamic graph connectivity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Notes on computing peaks in k-levels and parametric spanning trees
SCG '01 Proceedings of the seventeenth annual symposium on Computational geometry
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
External memory algorithms and data structures: dealing with massive data
ACM Computing Surveys (CSUR)
Fully Dynamic Maintenance of k-Connectivity in Parallel
IEEE Transactions on Parallel and Distributed Systems
Dynamic subgraph connectivity with geometric applications
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Dynamic Graph Algorithms with Applications
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
Maintaining Dynamic Minimum Spanning Trees: An Experimental Study
ALENEX '02 Revised Papers from the 4th International Workshop on Algorithm Engineering and Experiments
Implementation an Experimental Evaluation of Graph Connectivity Algorithms Using LEDA
WAE '99 Proceedings of the 3rd International Workshop on Algorithm Engineering
Decomposable multi-parameter matroid optimization problems
Theoretical Computer Science - Latin American theoretical informatics
Handbook of massive data sets
Implementations and experimental studies of dynamic graph algorithms
Experimental algorithmics
An Experimental Study of Polylogarithmic, Fully Dynamic, Connectivity Algorithms
Journal of Experimental Algorithmics (JEA)
An Experimental Study of Dynamic Algorithms for Transitive Closure
Journal of Experimental Algorithmics (JEA)
An Experimental Study of Polylogarithmic, Fully Dynamic, Connectivity Algorithms
Journal of Experimental Algorithmics (JEA)
Testing bipartiteness of geometric intersection graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Worst-case update times for fully-dynamic all-pairs shortest paths
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Graph distances in the streaming model: the value of space
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Maintaining information in fully dynamic trees with top trees
ACM Transactions on Algorithms (TALG)
Planning Tours of Robotic Arms among Partitioned Goals
International Journal of Robotics Research
Optimal per-edge processing times in the semi-streaming model
Information Processing Letters
Faster dynamic matchings and vertex connectivity
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Dynamic bottleneck optimization for k-edge and 2-vertex connectivity
Information Processing Letters
Fully dynamic algorithms for chordal graphs and split graphs
ACM Transactions on Algorithms (TALG)
Algorithms and data structures for external memory
Foundations and Trends® in Theoretical Computer Science
Competitive Maintenance of Minimum Spanning Trees in Dynamic Graphs
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
Testing bipartiteness of geometric intersection graphs
ACM Transactions on Algorithms (TALG)
An experimental analysis of self-adjusting computation
ACM Transactions on Programming Languages and Systems (TOPLAS)
Reoptimization of minimum and maximum traveling salesman's tours
Journal of Discrete Algorithms
As Good as It Gets: Competitive Fault Tolerance in Network Structures
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
Maintaining dynamic minimum spanning trees: An experimental study
Discrete Applied Mathematics
WEA'07 Proceedings of the 6th international conference on Experimental algorithms
Maintaining a large matching and a small vertex cover
Proceedings of the forty-second ACM symposium on Theory of computing
Fast reoptimization for the minimum spanning tree problem
Journal of Discrete Algorithms
Self-adjusting computation with Delta ML
AFP'08 Proceedings of the 6th international conference on Advanced functional programming
New data structures for subgraph connectivity
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Algorithms and theory of computation handbook
f-sensitivity distance Oracles and routing schemes
ESA'10 Proceedings of the 18th annual European conference on Algorithms: Part I
Dynamic approximate vertex cover and maximum matching
Property testing
Dynamic approximate vertex cover and maximum matching
Property testing
Analyzing graph structure via linear measurements
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Reoptimization of minimum and maximum traveling salesman's tours
SWAT'06 Proceedings of the 10th Scandinavian conference on Algorithm Theory
Improved maintenance of molecular surfaces using dynamic graph connectivity
WABI'05 Proceedings of the 5th International conference on Algorithms in Bioinformatics
Research paper: The saga of minimum spanning trees
Computer Science Review
Connectivity oracles for planar graphs
SWAT'12 Proceedings of the 13th Scandinavian conference on Algorithm Theory
Linear time algorithms for two disjoint paths problems on directed acyclic graphs
Theoretical Computer Science
ASONAM '12 Proceedings of the 2012 International Conference on Advances in Social Networks Analysis and Mining (ASONAM 2012)
Simple deterministic algorithms for fully dynamic maximal matching
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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We provide data strutures that maintain a graph as edges are inserted and deleted, and keep track of the following properties with the following times: minimum spanning forests, graph connectivity, graph 2-edge connectivity, and bipartiteness in timeO(n1/2) per change; 3-edge connectivity, in time O(n2/3) per change; 4-edge connectivity, in time O(n&agr;(n)) per change; k-edge connectivity for constant k, in time O(nlogn) per change;2-vertex connectivity, and 3-vertex connectivity, in the O(n) per change; and 4-vertex connectivity, in time O(n&agr;(n)) per change. Further results speed up the insertion times to match the bounds of known partially dynamic algorithms.All our algorithms are based on a new technique that transforms an algorithm for sparse graphs into one that will work on any graph, which we call sparsification.