Recycling queries in PCPs and in linearity tests (extended abstract)
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
Construction of extractors using pseudo-random generators (extended abstract)
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Fast algorithms for constructing optimal trees from quartets
Proceedings of the tenth annual ACM-SIAM symposium on Discrete algorithms
A PCP characterization of NP with optimal amortized query complexity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Non-approximability results for optimization problems on bounded degree instances
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
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Information and Computation
Some optimal inapproximability results
Journal of the ACM (JACM)
Extractors and pseudorandom generators
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The hardness of cache conscious data placement
POPL '02 Proceedings of the 29th ACM SIGPLAN-SIGACT symposium on Principles of programming languages
The importance of being biased
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
On the advantage over a random assignment
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
Computer assisted proof of optimal approximability results
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
SIGACT news complexity theory column 34
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Extracting all the randomness and reducing the error in Trevisan's extractors
Journal of Computer and System Sciences - STOC 1999
Clique Is Hard to Approximate within n1-o(1)
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
On Interactive Proofs with a Laconic Prover
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
Scheduling of Independent Dedicated Multiprocessor Tasks
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Small PCPs with Low Query Complexity
STACS '01 Proceedings of the 18th Annual Symposium on Theoretical Aspects of Computer Science
Inapproximability results for set splitting and satisfiability problems with no mixed clauses
APPROX '00 Proceedings of the Third International Workshop on Approximation Algorithms for Combinatorial Optimization
Hyper-encryption against Space-Bounded Adversaries from On-Line Strong Extractors
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Approximation Algorithms for Hamming Clustering Problems
COM '00 Proceedings of the 11th Annual Symposium on Combinatorial Pattern Matching
Improved Inapproximability Results for Vertex Cover on k -Uniform Hypergraphs
ICALP '02 Proceedings of the 29th International Colloquium on Automata, Languages and Programming
Approximation Algorithms for MAX 4-SAT and Rounding Procedures for Semidefinite Programs
Proceedings of the 7th International IPCO Conference on Integer Programming and Combinatorial Optimization
The Longest Common Subsequence Problem for Arc-Annotated Sequences
COM '00 Proceedings of the 11th Annual Symposium on Combinatorial Pattern Matching
Simple analysis of graph tests for linearity and PCP
Random Structures & Algorithms
Property testing in massive graphs
Handbook of massive data sets
A new multilayered PCP and the hardness of hypergraph vertex cover
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Randomness-efficient low degree tests and short PCPs via epsilon-biased sets
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Algebraic testing and weight distributions of codes
Theoretical Computer Science
Towards optimal lower bounds for clique and chromatic number
Theoretical Computer Science
On the span in channel assignment problems: bounds, computing and counting
Discrete Mathematics - Special issue: The 18th British combinatorial conference
Counterexample-guided abstraction refinement for symbolic model checking
Journal of the ACM (JACM)
On interactive proofs with a laconic prover
Computational Complexity
Computational aspects of the 2-dimension of partially ordered sets
Theoretical Computer Science
Inapproximability results for equations over finite groups
Theoretical Computer Science - Special issue on automata, languages and programming
Robust pcps of proximity, shorter pcps and applications to coding
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
The Complexity of Boolean Constraint Satisfaction Local Search Problems
Annals of Mathematics and Artificial Intelligence
On the advantage over a random assignment
Random Structures & Algorithms
Simple PCPs with poly-log rate and query complexity
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Guest column: inapproximability results via Long Code based PCPs
ACM SIGACT News
On the hardness of approximating Max-Satisfy
Information Processing Letters
Gowers uniformity, influence of variables, and PCPs
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Conditional hardness for approximate coloring
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Linear degree extractors and the inapproximability of max clique and chromatic number
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
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ACM SIGACT News
An agent-based algorithm for generalized graph colorings
Proceedings of the 8th annual conference on Genetic and evolutionary computation
The hardness of cache conscious data placement
Nordic Journal of Computing
On the complexity of distributed graph coloring
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Information Processing Letters
Locally testable codes and PCPs of almost-linear length
Journal of the ACM (JACM)
Approximating the minimum clique cover and other hard problems in subtree filament graphs
Discrete Applied Mathematics
The approximability of non-Boolean satisfiability problems and restricted integer programming
Theoretical Computer Science
Designing small keyboards is hard
Theoretical Computer Science
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
An ant-based algorithm for coloring graphs
Discrete Applied Mathematics
Vertex cover might be hard to approximate to within 2-ε
Journal of Computer and System Sciences
Approximating maximum satisfiable subsystems of linear equations of bounded width
Information Processing Letters
Inapproximability and approximability of minimal tree routing and coloring
Journal of Discrete Algorithms
An optimal sdp algorithm for max-cut, and equally optimal long code tests
STOC '08 Proceedings of the fortieth 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
Perfect Parallel Repetition Theorem for Quantum Xor Proof Systems
Computational Complexity
Partition into cliques for cubic graphs: Planar case, complexity and approximation
Discrete Applied Mathematics
The 0-1 inverse maximum stable set problem
Discrete Applied Mathematics
PCPs with small soundness error
ACM SIGACT News
Exact Max 2-Sat: Easier and Faster
SOFSEM '07 Proceedings of the 33rd conference on Current Trends in Theory and Practice of Computer Science
Why Greed Works for Shortest Common Superstring Problem
CPM '08 Proceedings of the 19th annual symposium on Combinatorial Pattern Matching
Improved Bounds for Testing Juntas
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Breaking the ε-Soundness Bound of the Linearity Test over GF(2)
APPROX '08 / RANDOM '08 Proceedings of the 11th international workshop, APPROX 2008, and 12th international workshop, RANDOM 2008 on Approximation, Randomization and Combinatorial Optimization: Algorithms and Techniques
Probabilistic Proof Systems: A Primer
Foundations and Trends® in Theoretical Computer Science
More efficient queries in PCPs for NP and improved approximation hardness of maximum CSP
Random Structures & Algorithms
ACM SIGACT News
Simple ingredients leading to very efficient heuristics for the maximum clique problem
Journal of Heuristics
3-bit dictator testing: 1 vs. 5/8
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Testing juntas nearly optimally
Proceedings of the forty-first annual ACM symposium on Theory of computing
CSP gaps and reductions in the lasserre hierarchy
Proceedings of the forty-first annual ACM symposium on Theory of computing
Conditional hardness for satisfiable 3-CSPs
Proceedings of the forty-first annual ACM symposium on Theory of computing
Testing Fourier Dimensionality and Sparsity
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Hardness of Solving Sparse Overdetermined Linear Systems: A 3-Query PCP over Integers
ACM Transactions on Computation Theory (TOCT)
A Hypergraph Dictatorship Test with Perfect Completeness
APPROX '09 / RANDOM '09 Proceedings of the 12th International Workshop and 13th International Workshop on Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques
Why greed works for shortest common superstring problem
Theoretical Computer Science
Priority algorithms for graph optimization problems
Theoretical Computer Science
On the hardness of approximating Max-Satisfy
Information Processing Letters
Algorithmic and Analysis Techniques in Property Testing
Foundations and Trends® in Theoretical Computer Science
Two-query PCP with subconstant error
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Algorithms for sensor and ad hoc networks: advanced lectures
Algorithms for sensor and ad hoc networks: advanced lectures
Inapproximability of hypergraph vertex cover and applications to scheduling problems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
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
On the approximability of robust spanning tree problems
Theoretical Computer Science
Breaking the $\epsilon$-Soundness Bound of the Linearity Test over GF(2)
SIAM Journal on Computing
Locally Testable Codes Require Redundant Testers
SIAM Journal on Computing
Limitation on the rate of families of locally testable codes
Property testing
Testing juntas: a brief survey
Property testing
Short locally testable codes and proofs: a survey in two parts
Property testing
Introduction to testing graph properties
Property testing
Invariance in property testing
Property testing
Query-efficient dictatorship testing with perfect completeness
Property testing
Limitation on the rate of families of locally testable codes
Property testing
Testing juntas: a brief survey
Property testing
Short locally testable codes and proofs: a survey in two parts
Property testing
Introduction to testing graph properties
Property testing
Invariance in property testing
Property testing
Query-efficient dictatorship testing with perfect completeness
Property testing
Strong direct product theorems for quantum communication and query complexity
Proceedings of the forty-third annual ACM symposium on Theory of computing
Using the FGLSS-reduction to prove inapproximability results for minimum vertex cover in hypergraphs
Studies in complexity and cryptography
Proximity oblivious testing and the role of invariances
Studies in complexity and cryptography
Bravely, moderately: a common theme in four recent works
Studies in complexity and cryptography
On the complexity of computational problems regarding distributions
Studies in complexity and cryptography
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Studies in complexity and cryptography
Satisfying degree-d equations over GF[2]n
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Proximity oblivious testing and the role of invariances
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SIAM Journal on Computing
Approximating Max kCSP - outperforming a random assignment with almost a linear factor
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
CPCQ: Contrast pattern based clustering quality index for categorical data
Pattern Recognition
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Routing and coloring for maximal number of trees
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
Finding small OBDDs for incompletely specified truth tables is hard
COCOON'06 Proceedings of the 12th annual international conference on Computing and Combinatorics
Approximating maximum diameter-bounded subgraphs
LATIN'10 Proceedings of the 9th Latin American conference on Theoretical Informatics
The complexity of making unique choices: approximating 1-in-k SAT
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
APPROX'05/RANDOM'05 Proceedings of the 8th international workshop on Approximation, Randomization and Combinatorial Optimization Problems, and Proceedings of the 9th international conference on Randamization and Computation: algorithms and techniques
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AAIM'05 Proceedings of the First international conference on Algorithmic Applications in Management
On greedy graph coloring in the distributed model
Euro-Par'06 Proceedings of the 12th international conference on Parallel Processing
More efficient queries in PCPs for NP and improved approximation hardness of maximum CSP
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Priority algorithms for graph optimization problems
WAOA'04 Proceedings of the Second international conference on Approximation and Online Algorithms
Linear kernels in linear time, or how to save k colors in O(n2) steps
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Guest column: algebraic construction of projection PCPs
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Survey: A survey on the structure of approximation classes
Computer Science Review
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ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Distributed computing with advice: information sensitivity of graph coloring
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On the power of many one-bit provers
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
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Column Subset Selection Problem is UG-hard
Journal of Computer and System Sciences
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This paper continues the investigation of the connection between probabilistically checkable proofs (PCPs) and the approximability of NP-optimization problems. The emphasis is on proving tight nonapproximability results via consideration of measures such as the "free-bit complexity" and the "amortized free-bit complexity" of proof systems.The first part of the paper presents a collection of new proof systems based on a new error-correcting code called the long code. We provide a proof system that has amortized free-bit complexity of $2 + \epsilon$, implying that approximating MaxClique within $N^{\frac13-\e}$, and approximating the Chromatic Number within $N^{\frac15-\e}$, are hard, assuming $\NP\neq\coRP$, for any e 0. We also derive the first explicit and reasonable constant hardness factors for Min Vertex Cover, $\MSAT{2}$, and Max Cut, and we improve the hardness factor for $\MSAT{3}$. We note that our nonapproximability factors for $\maxsnp$ problems are appreciably close to the values known to be achievable by polynomial-time algorithms. Finally, we note a general approach to the derivation of strong nonapproximability results under which the problem reduces to the construction of certain "gadgets."The increasing strength of nonapproximability results obtained via the PCP connection motivates us to ask how far this can go and whether PCPs are inherent in any way. The second part of the paper addresses this. The main result is a "reversal" of the connection due to Feige et al. (FGLSS connection) [J. ACM, 43 (1996), pp. 268--292]: where the latter had shown how to translate proof systems for NP into NP-hardness of approximation results for MaxClique, we show how any NP-hardness of approximation result for MaxClique yields a proof system for NP. Roughly, our result says that for any constant f, if MaxClique is NP-hard to approximate within N 1(1+f), then $\NP\subseteq \overline{\fpcp}[\log,f]$, the latter being the class of languages possessing proofs of logarithmic randomness and amortized free-bit complexity f. This suggests that PCPs are inherent to obtaining nonapproximability results. Furthermore, the tight relation suggests that reducing the amortized free-bit complexity is necessary for improving the nonapproximability results for MaxClique.The third part of our paper initiates a systematic investigation of the properties of PCP and FPCP (free PCP) as a function of the following various parameters: randomness, query complexity, free-bit complexity, amortized free-bit complexity, proof size, etc. We are particularly interested in triviality results, which indicate which classes are not powerful enough to capture NP. We also distill the role of randomized reductions in this area and provide a variety of useful transformations between proof checking complexity classes.