Deterministic simulation in LOGSPACE
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Unbiased bits from sources of weak randomness and probabilistic communication complexity
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A still better performance guarantee for approximate graph coloring
Information Processing Letters
Improved non-approximability results
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Eigenvalues and expansion of regular graphs
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Computational Complexity
Interactive proofs and the hardness of approximating cliques
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Proof verification and the hardness of approximation problems
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Randomness-optimal oblivious sampling
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A Chernoff Bound for Random Walks on Expander Graphs
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Free Bits, PCPs, and Nonapproximability---Towards Tight Results
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Zero knowledge and the chromatic number
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On the hardness of approximating minimization problems
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Extracting randomness: a survey and new constructions
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A PCP characterization of NP with optimal amortized query complexity
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Loss-less condensers, unbalanced expanders, and extractors
STOC '01 Proceedings of the thirty-third annual ACM symposium on Theory of computing
On the complexity of approximating the VC dimension
Journal of Computer and System Sciences - Complexity 2001
Towards optimal lower bounds for clique and chromatic number
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Hardness of Approximating Minimization Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Extracting randomness via repeated condensing
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Query Efficient PCPs with Perfect Completeness
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Improved Inapproximability Results for MaxClique, Chromatic Number and Approximate Graph Coloring
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Large Deviation Bounds for Markov Chains
Combinatorics, Probability and Computing
Extracting Randomness Using Few Independent Sources
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Simulating independence: new constructions of condensers, ramsey graphs, dispersers, and extractors
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Extractors with weak random seeds
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
A Randomness-Efficient Sampler for Matrix-valued Functions and Applications
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Extractors from Reed-Muller codes
Journal of Computer and System Sciences - Special issue on FOCS 2001
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The NP-completeness column: The many limits on approximation
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Self-improved gaps almost everywhere for the agnostic approximation of monomials
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Approximating maximum satisfiable subsystems of linear equations of bounded width
Information Processing Letters
Hardness of optimal spaced seed design
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Randomness-Efficient Sampling within NC1
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Approximating Independent Set and Coloring in Random Uniform Hypergraphs
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
Efficient techniques for document sanitization
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Single-value combinatorial auctions and algorithmic implementation in undominated strategies
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Approximating maximum weight K-colorable subgraphs in chordal graphs
Information Processing Letters
Introduction to the Maximum Solution Problem
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Reoptimization of Weighted Graph and Covering Problems
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Scheduling with conflicts: online and offline algorithms
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Affine dispersers from subspace polynomials
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Unbalanced expanders and randomness extractors from Parvaresh--Vardy codes
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A measure & conquer approach for the analysis of exact algorithms
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Approximation of min coloring by moderately exponential algorithms
Information Processing Letters
Efficient Approximation of Combinatorial Problems by Moderately Exponential Algorithms
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Computationally feasible VCG mechanisms
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The complexity of finding subgraphs whose matching number equals the vertex cover number
ISAAC'07 Proceedings of the 18th international conference on Algorithms and computation
"Rent-or-buy" scheduling and cost coloring problems
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
New results on optimizing rooted triplets consistency
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Paired approximation problems and incompatible inapproximabilities
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Efficiency of Wireless Networks: Approximation Algorithms for the Physical Interference Model
Foundations and Trends® in Networking
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On Optimal Strategies for a Hat Game on Graphs
SIAM Journal on Discrete Mathematics
Coalition formation for task allocation: theory and algorithms
Autonomous Agents and Multi-Agent Systems
Local search with edge weighting and configuration checking heuristics for minimum vertex cover
Artificial Intelligence
How to cut a graph into many pieces
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Discrete Applied Mathematics
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
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Wireless capacity with oblivious power in general metrics
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The max quasi-independent set problem
CSR'10 Proceedings of the 5th international conference on Computer Science: theory and Applications
Reoptimization of the maximum weighted Pk-free subgraph problem under vertex insertion
WALCOM'12 Proceedings of the 6th international conference on Algorithms and computation
Reoptimization of some maximum weight induced hereditary subgraph problems
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Parameterized approximation via fidelity preserving transformations
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WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
An information complexity approach to extended formulations
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AGI'13 Proceedings of the 6th international conference on Artificial General Intelligence
Goodness-of-Fit Measures for Revealed Preference Tests: Complexity Results and Algorithms
ACM Transactions on Economics and Computation
Reoptimization of maximum weight induced hereditary subgraph problems
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Approximability of the two-stage stochastic knapsack problem with discretely distributed weights
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A randomness extractor is an algorithm which extracts randomness from a low-quality random source, using some additional truly random bits. We construct new extractors which require only log n + O(1) additional random bits for sources with constant entropy rate. We further construct dispersers, which are similar to one-sided extractors, which use an arbitrarily small constant times log n additional random bits for sources with constant entropy rate. Our extractors and dispersers output 1-α fraction of the randomness, for any α0.We use our dispersers to derandomize results of Hastad [23] and Feige-Kilian [19] and show that for all ε0, approximating MAX CLIQUE and CHROMATIC NUMBER to within n1-ε are NP-hard. We also derandomize the results of Khot [29] and show that for some γ 0, no quasi-polynomial time algorithm approximates MAX CLIQUE or CHROMATIC NUMBER to within n/2(log n)1-γ, unless NP = P.Our constructions rely on recent results in additive number theory and extractors by Bourgain-Katz-Tao [11], Barak-Impagliazzo-Wigderson [5], Barak-Kindler-Shaltiel-Sudakov-Wigderson [6], and Raz [36]. We also simplify and slightly strengthen key theorems in the second and third of these papers, and strengthen a related theorem by Bourgain [10].