The complexity of multiway cuts (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
Excluded minors, network decomposition, and multicommodity flow
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
Improved bounds for the max-flow min-multicut ratio for planar and Kr,r-free graphs
Information Processing Letters
On approximating arbitrary metrices by tree metrics
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Minimum 0-extensions of graph metrics
European Journal of Combinatorics
Rounding algorithms for a geometric embedding of minimum multiway cut
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
A constant factor approximation algorithm for a class of classification problems
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
An improved approximation algorithm for MULTIWAY CUT
Journal of Computer and System Sciences - 30th annual ACM symposium on theory of computing
ICALP '93 Proceedings of the 20th International Colloquium on Automata, Languages and Programming
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
SFCS '88 Proceedings of the 29th Annual Symposium on Foundations of Computer Science
Approximation through multicommodity flow
SFCS '90 Proceedings of the 31st Annual Symposium on Foundations of Computer Science
Approximation algorithms for the metric labeling problem via a new linear programming formulation
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Similarity estimation techniques from rounding algorithms
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
An improved approximation algorithm for the 0-extension problem
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
A tight bound on approximating arbitrary metrics by tree metrics
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Approximate classification via earthmover metrics
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Approximating metrics by tree metrics
ACM SIGACT News
Bypassing the embedding: algorithms for low dimensional metrics
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
A tight bound on approximating arbitrary metrics by tree metrics
Journal of Computer and System Sciences - Special issue: STOC 2003
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Improved embeddings of graph metrics into random trees
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Advances in metric embedding theory
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Local embeddings of metric spaces
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Embedding metric spaces in their intrinsic dimension
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Sdp gaps and ugc hardness for multiway cut, 0-extension, and metric labeling
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On low dimensional local embeddings
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Eigenvalue bounds, spectral partitioning, and metrical deformations via flows
Journal of the ACM (JACM)
How to complete a doubling metric
LATIN'08 Proceedings of the 8th Latin American conference on Theoretical informatics
Extensions and limits to vertex sparsification
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Genus and the geometry of the cut graph
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Approximability of robust network design
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Local Global Tradeoffs in Metric Embeddings
SIAM Journal on Computing
Approximating a class of classification problems
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A node-capacitated okamura-seymour theorem
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Simplex partitioning via exponential clocks and the multiway cut problem
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
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In the 0-extension problem, we are given a weighted graph with some nodes marked as terminals and a semi-metric on the set of terminals. Our goal is to assign the rest of the nodes to terminals so as to minimize the sum, over all edges, of the product of the edge's weight and the distance between the terminals to which its endpoints are assigned. This problem generalizes the multiway cut problem of Dahlhaus, Johnson, Papadimitriou, Seymour, and Yannakakis and is closely related to the metric labeling problem introduced by Kleinberg and Tardos.We present approximation algorithms for O-EXTENSION. In arbitrary graphs, we present an &Ogr;(log k)-approximation algorithm, k being the number of terminals. We also give &Ogr;(1)-approximation guarantees for weighted planar graphs. Our results are based on a natural metric relaxation of the problem, previously considered by Karzanov. It is similar in flavor to the linear programming relaxation of Garg, Vazirani, and Yannakakis for the multicut problem and similar to relaxations for other graph partitioning problems. We prove that the integrality ratio of the metric relaxation is at least c√lgk for a positive c for infinitely many k. Our results improve some of the results of Kleinberg and Tardos and they further our understanding on how to use metric relaxations.