The algorithmic aspects of the regularity lemma
Journal of Algorithms
A Fast Approximation Algorithm for Computing theFrequencies of Subgraphs in a Given Graph
SIAM Journal on Computing
MAX-CUT has a randomized approximation scheme in dense graphs
Random Structures & Algorithms
Szemerédi's regularity lemma for sparse graphs
FoCM '97 Selected papers of a conference on Foundations of computational mathematics
Property testing and its connection to learning and approximation
Journal of the ACM (JACM)
Polynomial time approximation schemes for dense instances of NP -hard problems
Journal of Computer and System Sciences
Gadgets, Approximation, and Linear Programming
SIAM Journal on Computing
Some optimal inapproximability results
Journal of the ACM (JACM)
Relations between average case complexity and approximation complexity
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
A spectral technique for random satisfiable 3CNF formulas
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Random sampling and approximation of MAX-CSPs
Journal of Computer and System Sciences - STOC 2002
Approximating the cut-norm via Grothendieck's inequality
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
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
Tensor decomposition and approximation schemes for constraint satisfaction problems
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Recognizing More Unsatisfiable Random k-SAT Instances Efficiently
SIAM Journal on Computing
A spectral heuristic for bisecting random graphs
Random Structures & Algorithms
Witnesses for non-satisfiability of dense random 3CNF formulas
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
Strong Refutation Heuristics for Random k-SAT
Combinatorics, Probability and Computing
Eigenvalues and graph bisection: An average-case analysis
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
Quasi-randomness and algorithmic regularity for graphs with general degree distributions
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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Let ${\bf A}$ be a $0/1$ matrix of size $m\times n$, and let $p$ be the density of ${\bf A}$ (i.e., the number of ones divided by $m\cdot n$). We show that ${\bf A}$ can be approximated in the cut norm within $\varepsilon\cdot mnp$ by a sum of cut matrices (of rank 1), where the number of summands is independent of the size $m\cdot n$ of ${\bf A}$, provided that ${\bf A}$ satisfies a certain boundedness condition. This decomposition can be computed in polynomial time. This result extends the work of Frieze and Kannan [Combinatorica, 19 (1999), pp. 175-220] to sparse matrices. As an application, we obtain efficient $1-\varepsilon$ approximation algorithms for “bounded” instances of MAX CSP problems.