.879-approximation algorithms for MAX CUT and MAX 2SAT
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Polynomial time approximation schemes for dense instances of NP-hard problems
STOC '95 Proceedings of the twenty-seventh annual ACM symposium on Theory of computing
MAX-CUT has a randomized approximation scheme in dense graphs
Random Structures & Algorithms
Random sampling and approximation of MAX-CSP problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Property testers for dense constraint satisfaction programs on finite domains
Random Structures & Algorithms
On the discrepancy of combinatorial rectangles
Random Structures & Algorithms - Special issue: Proceedings of the tenth international conference "Random structures and algorithms"
The regularity lemma and approximation schemes for dense problems
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Property testing and its connection to learning and approximation
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Graph limits and parameter testing
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
Sampling from large matrices: An approach through geometric functional analysis
Journal of the ACM (JACM)
Linear programming relaxations of maxcut
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Yet another algorithm for dense max cut: go greedy
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Sampling subproblems of heterogeneous Max-Cut problems and approximation algorithms
Random Structures & Algorithms
A dichotomy for minimum cost graph homomorphisms
European Journal of Combinatorics
A discriminative framework for clustering via similarity functions
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
An efficient sparse regularity concept
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Towards a Study of Low-Complexity Graphs
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Approximate Hypergraph Partitioning and Applications
SIAM Journal on Computing
An Efficient Sparse Regularity Concept
SIAM Journal on Discrete Mathematics
Distributing data for secure database services
Proceedings of the 4th International Workshop on Privacy and Anonymity in the Information Society
Property testing
Property testing
Proceedings of the forty-third annual ACM symposium on Theory of computing
Testing odd-cycle-freeness in Boolean functions
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Subsampling mathematical relaxations and average-case complexity
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Additive approximation for edge-deletion problems
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Sampling sub-problems of heterogeneous max-cut problems and approximation algorithms
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Distributing Data for Secure Database Services
Transactions on Data Privacy
Constant-Time approximation algorithms for the knapsack problem
TAMC'12 Proceedings of the 9th Annual international conference on Theory and Applications of Models of Computation
Zero-one rounding of singular vectors
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
The approximate rank of a matrix and its algorithmic applications: approximate rank
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Proceedings of the 5th conference on Innovations in theoretical computer science
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In a maximum-r-constraint satisfaction problem with variables {x1, x2, ... ,xn}, we are given Boolean functions f1, f2, ..., fm each involving r of the n variables and are to find the maximum number of these functions that can be made true by a truth assignment to the variables. We show that for r fixed, there is an integer q ∈ O(log(1/ε)/ε4) such that if we choose q variables (uniformly) at random, the answer to the subproblem induced on the chosen variables is, with high probability, within an additive error of εqr of qr/nr times the answer to the original n-variable problem. The previous best result for the case of r = 2 (which includes many graph problems) was that there is an algorithm which given the induced sub-problem on q = O(1/ε5) variables, can find an approximation to the answer to the whole problem within additive error εn2. For r≥3, the conference version of this paper (in: Proceedings of the 34th ACM STOC, ACM, New York, 2002, pp. 232-239) and independently Andersson and Engebretsen give the first results with sample complexity q dependent only polynomially upon 1/ε. Their algorithm has a sample complexity q of O(1/ε7). They (as also the earlier papers) however do not directly prove any relation between the answer to the sub-problem and the whole problem as we do here. Our method also differs from other results in that it is linear algebraic, rather than combinatorial in nature.