Excluded minors, network decomposition, and multicommodity flow
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Improved bounds on the max-flow min-cut ratio for multicommodity flows
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Approximate max-flow min-(multi)cut theorems and their applications
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
The Complexity of Multiterminal Cuts
SIAM Journal on Computing
Property testing in bounded degree graphs
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
An O(log k) Approximate Min-Cut Max-Flow Theorem and Approximation Algorithm
SIAM Journal on Computing
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A Lower Bound for Testing 3-Colorability in Bounded-Degree Graphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
A New Min-Cut Max-Flow Ratio for Multicommodity Flows
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Approximation algorithms for disjoint paths problems
Approximation algorithms for disjoint paths problems
Graph decomposition and a greedy algorithm for edge-disjoint paths
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Approximation Algorithms for Unique Games
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Disjoint paths in sparse graphs
Discrete Applied Mathematics
Edge Disjoint Paths in Moderately Connected Graphs
SIAM Journal on Computing
Edge disjoint paths in moderately connected graphs
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Proceedings of the 5th conference on Innovations in theoretical computer science
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We establish several approximate max-integral-flow / min-multicut theorems. While in general this ratio can be very large, we prove strong approximation ratios in the case where the min-multicut is a constant fraction ε of the total capacity of the graph. This setting is motivated by several combinatorial and algorithmic applications. Prior to this work, a general max-integral-flow / min-multicut bound was known only for the special case where the graph is a tree. We prove that, for arbitrary graphs, the max-integral-flow / min-multicut ratio is O(ε-1 log k), where k is the number of commodites; for graphs excluding a fixed subgraph as a minor (for instance, planar graphs), O(1 / ε); and, for dense graphs, O(1√ε). Our proofs are constructive in the sense that we give efficient algorithms which compute either an integral flow achieving the claimed approximation ratios, or a witness that the precondition is violated.