Probabilistic checking of proofs and hardness of approximation problems
Probabilistic checking of proofs and hardness of approximation problems
Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
The hardness of approximate optima in lattices, codes, and systems of linear equations
Journal of Computer and System Sciences - Special issue: papers from the 32nd and 34th annual symposia on foundations of computer science, Oct. 2–4, 1991 and Nov. 3–5, 1993
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
SIAM Journal on Computing
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
A threshold of ln n for approximating set cover
Journal of the ACM (JACM)
A PCP characterization of NP with optimal amortized query complexity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Approximation algorithms
Some optimal inapproximability results
Journal of the ACM (JACM)
The importance of being biased
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Relations between average case complexity and approximation complexity
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Vertex cover on 4-regular hyper-graphs is hard to approximate within 2 - &egr;
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the power of unique 2-prover 1-round games
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Hardness of Approximate Hypergraph Coloring
SIAM Journal on Computing
The Hardness of 3 - Uniform Hypergraph Coloring
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Hardness Results for Coloring 3 -Colorable 3 -Uniform Hypergraphs
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Simple analysis of graph tests for linearity and PCP
Random Structures & Algorithms
A new multilayered PCP and the hardness of hypergraph vertex cover
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
New hardness results for congestion minimization and machine scheduling
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Hardness of Approximating the Shortest Vector Problem in Lattices
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
Ruling Out PTAS for Graph Min-Bisection, Densest Subgraph and Bipartite Clique
FOCS '04 Proceedings of the 45th Annual IEEE Symposium on Foundations of Computer Science
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
Hardness of the undirected edge-disjoint paths problem
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Hardness of the undirected congestion minimization problem
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On the Hardness of Approximating Multicut and Sparsest-Cut
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Hardness of Max 3SAT with No Mixed Clauses
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
The NP-completeness column: The many limits on approximation
ACM Transactions on Algorithms (TALG)
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Some topics in analysis of boolean functions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Probabilistically checkable proofs
Communications of the ACM - Being Human in the Digital Age
Hardness of Solving Sparse Overdetermined Linear Systems: A 3-Query PCP over Integers
ACM Transactions on Computation Theory (TOCT)
Two-query PCP with subconstant error
Journal of the ACM (JACM)
A query efficient non-adaptive long code test with perfect completeness
APPROX/RANDOM'10 Proceedings of the 13th international conference on Approximation, and 14 the International conference on Randomization, and combinatorial optimization: algorithms and techniques
Guest column: algebraic construction of projection PCPs
ACM SIGACT News
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Summer has come again. And what better way is there to spend a summer than to relax on a sandy beach, on a mountain top, or at a park's picnic tables, and... think theory! Summer is a particularly good time to attack the big questions whose openness just plain annoys you. In light of Reingold's L = SL result, does L-vs.-RL tempt you? If so, take it on! (But perhaps peek first at Reingold--Trevisan--Vadhan's ECCC TR05-022.) Are you convinced that UP = NP should imply the collapse of the polynomial hierarchy? Make it so! (But if you hope to do so via showing that UP is contained in the low hierarchy, peek first at Long--Sheu's 1996 MST article.) You know that S2 ⊆ SNP∩coNP2 ⊆ ZPPNP and SNP2 ⊆ ZPPNPNP, but believe that some of those "⊆"s are "=" s or are (gasp!) provably strict containments (thus giving some insight into whether recent improvements (Cai in FOCS 2001; Cai et al. in Information and Computation 2005) in the collapses of the polynomial hierarchy from assumptions that NP is in P/poly, (NP ∩ coNP)/poly, or coNP/poly are strict improvements)? Well, prove an "=" or find evidence for a strict containment... or to really make this a summer for us all to remember, prove a strict containment! Wishing you happy theorems.This article gives an overview of recent PCP constructions based on the Long Code and the inapproximability results implied by these constructions. We cover the inapproximability results for (1) MAX-3SAT and CLIQUE (2) Results for SPARSEST CUT, VERTEX COVER and MAX-CUT implied by the Unique Games Conjecture and (3) HYPERGRAPH VERTEX COVER and coloring problems on hypergraphs. The article aims at explaining the general framework that, loosely speaking, incorporates all the above results.