The complexity of multiway cuts (extended abstract)
STOC '92 Proceedings of the twenty-fourth annual ACM symposium on Theory of computing
An improved approximation algorithm for multiway cut
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
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
Approximation algorithms for the 0-extension problem
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
On the power of unique 2-prover 1-round games
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
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
Optimal Inapproximability Results for Max-Cut and Other 2-Variable CSPs?
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Measured Descent: A New Embedding Method for Finite Metrics
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
A Linear Programming Formulation and Approximation Algorithms for the Metric Labeling Problem
SIAM Journal on Discrete Mathematics
Noise stability of functions with low in.uences invariance and optimality
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
On earthmover distance, metric labeling, and 0-extension
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
SDP gaps and UGC-hardness for MAXCUTGAIN
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Balanced max 2-sat might not be the hardest
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
The Hardness of Metric Labeling
SIAM Journal on Computing
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
Towards Sharp Inapproximability For Any 2-CSP
FOCS '07 Proceedings of the 48th Annual IEEE Symposium on Foundations of Computer Science
Optimal algorithms and inapproximability results for every CSP?
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
On the inapproximability of vertex cover on k-partite k-uniform hypergraphs
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Improved rounding for parallel repeated unique games
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Proceedings of the forty-third annual ACM symposium on Theory of computing
Beating the Random Ordering Is Hard: Every Ordering CSP Is Approximation Resistant
SIAM Journal on Computing
On LP-based approximability for strict CSPs
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Simplex partitioning via exponential clocks and the multiway cut problem
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
On the generalized multiway cut in trees problem
Journal of Combinatorial Optimization
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The connection between integrality gaps and computational hardness of discrete optimization problems is an intriguing question. In recent years, this connection has prominently figured in several tight UGC-based hardness results. We show in this paper a direct way of turning integrality gaps into hardness results for several fundamental classification problems. Specifically, we convert linear programming integrality gaps for the Multiway Cut, 0-Extension, and and Metric Labeling problems into UGC-based hardness results. Qualitatively, our result suggests that if the unique games conjecture is true then a linear relaxation of the latter problems studied in several papers (so-called earthmover linear program) yields the best possible approximation. Taking this a step further, we also obtain integrality gaps for a semi-definite programming relaxation matching the integrality gaps of the earthmover linear program. Prior to this work, there was an intriguing possibility of obtaining better approximation factors for labeling problems via semi-definite programming.