On finding lowest common ancestors: simplification and parallelization
SIAM Journal on Computing
A new approach to the maximum-flow problem
Journal of the ACM (JACM)
A data structure for dynamic trees
Journal of Computer and System Sciences
An efficient algorithm for the minimum capacity cut problem
Mathematical Programming: Series A and B
Parallel algorithms for shared-memory machines
Handbook of theoretical computer science (vol. A)
Fast approximation algorithms for fractional packing and covering problems
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Computing edge-connectivity in multigraphs and capacitated graphs
SIAM Journal on Discrete Mathematics
A parallel algorithm for computing minimum spanning trees
SPAA '92 Proceedings of the fourth annual ACM symposium on Parallel algorithms and architectures
Recursive star-tree parallel data structure
SIAM Journal on Computing
Cluster analysis for hypertext systems
SIGIR '93 Proceedings of the 16th annual international ACM SIGIR conference on Research and development in information retrieval
A faster algorithm for finding the minimum cut in a directed graph
SODA selected papers from the third annual ACM-SIAM symposium on Discrete algorithms
A matroid approach to finding edge connectivity and packing arborescences
Selected papers of the 23rd annual ACM symposium on Theory of computing
Randomized algorithms
Mathematics of Operations Research
Random sampling in graph optimization problems
Random sampling in graph optimization problems
A new approach to the minimum cut problem
Journal of the ACM (JACM)
On the number of small cuts in a graph
Information Processing Letters
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Global min-cuts in RNC, and other ramifications of a simple min-out algorithm
SODA '93 Proceedings of the fourth annual ACM-SIAM Symposium on Discrete algorithms
Random Sampling in Cut, Flow, and Network Design Problems
Mathematics of Operations Research
Randomized fully dynamic graph algorithms with polylogarithmic time per operation
Journal of the ACM (JACM)
SIAM Journal on Computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Suboptimal Cuts: Their Enumeration, Weight and Number (Extended Abstract)
ICALP '92 Proceedings of the 19th International Colloquium on Automata, Languages and Programming
A representation of cuts within 6/5 times the edge connectivity with applications
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
Dynamic Graph Algorithms with Applications
SWAT '00 Proceedings of the 7th Scandinavian Workshop on Algorithm Theory
A deterministic near-linear time algorithm for finding minimum cuts in planar graphs
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Compacting cuts: a new linear formulation for minimum cut
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Minimum k-way cuts via deterministic greedy tree packing
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Efficient Algorithms for the k Smallest Cuts Enumeration
COCOON '08 Proceedings of the 14th annual international conference on Computing and Combinatorics
A near-linear time algorithm for constructing a cactus representation of minimum cuts
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Compacting cuts: A new linear formulation for minimum cut
ACM Transactions on Algorithms (TALG)
Graph Sparsification in the Semi-streaming Model
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
Computing the girth of a planar graph in linear time
COCOON'11 Proceedings of the 17th annual international conference on Computing and combinatorics
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
Global minimum cuts in surface embedded graphs
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Snap-Stabilizing detection of cutsets
HiPC'05 Proceedings of the 12th international conference on High Performance Computing
Multicriteria global minimum cuts
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Ranking and sparsifying a connection graph
WAW'12 Proceedings of the 9th international conference on Algorithms and Models for the Web Graph
An overview of algorithms for network survivability
ISRN Communications and Networking
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We significantly improve known time bounds for solving the minimum cut problem on undirected graphs. We use a "semiduality" between minimum cuts and maximum spanning tree packings combined with our previously developed random sampling techniques. We give a randomized (Monte Carlo) algorithm that finds a minimum cut in an m-edge, n-vertex graph with high probability in O(m log3 n) time. We also give a simpler randomized algorithm that finds all minimum cuts with high probability in O(m log3 n) time. This variant has an optimal RNC parallelization. Both variants improve on the previous best time bound of O(n2 log3 n). Other applications of the tree-packing approach are new, nearly tight bounds on the number of near-minimum cuts a graph may have and a new data structure for representing them in a space-efficient manner.