A fast and simple randomized parallel algorithm for the maximal independent set problem
Journal of Algorithms
The algorithmic aspects of the regularity lemma
Journal of Algorithms
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
The space complexity of approximating the frequency moments
Journal of Computer and System Sciences
Derandomizing Approximation Algorithms Based on Semidefinite Programming
SIAM Journal on Computing
Some optimal inapproximability results
Journal of the ACM (JACM)
Random sampling and approximation of MAX-CSP problems
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Improved Rounding Techniques for the MAX 2-SAT and MAX DI-CUT Problems
Proceedings of the 9th International IPCO Conference on Integer Programming and Combinatorial Optimization
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
On Non-Approximability for Quadratic Programs
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
An efficient sparse regularity concept
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Column subset selection, matrix factorization, and eigenvalue optimization
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Learning complexity vs communication complexity
Combinatorics, Probability and Computing
Quasi-Randomness and Algorithmic Regularity for Graphs with General Degree Distributions
SIAM Journal on Computing
An Efficient Sparse Regularity Concept
SIAM Journal on Discrete Mathematics
A deterministic algorithm for the Frieze-Kannan regularity lemma
APPROX'11/RANDOM'11 Proceedings of the 14th international workshop and 15th international conference on Approximation, randomization, and combinatorial optimization: algorithms and techniques
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
On approximating complex quadratic optimization problems via semidefinite programming relaxations
IPCO'05 Proceedings of the 11th international conference on Integer Programming and Combinatorial Optimization
Rounding two and three dimensional solutions of the SDP relaxation of MAX CUT
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
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Quasi-randomness and algorithmic regularity for graphs with general degree distributions
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Efficient rounding for the noncommutative grothendieck inequality
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Hi-index | 0.00 |
The cut-norm ||A||C of a real matrix A=(aij)i∈ R,j∈S is the maximum, over all I ⊂ R, J ⊂ S of the quantity | Σi ∈ I, j ∈ J aij|. This concept plays a major role in the design of efficient approximation algorithms for dense graph and matrix problems. Here we show that the problem of approximating the cut-norm of a given real matrix is MAX SNP hard, and provide an efficient approximation algorithm. This algorithm finds, for a given matrix A=(aij)i ∈ R, j ∈ S, two subsets I ⊂ R and J ⊂ S, such that | Σi ∈ I, j ∈ J aij| ≥ ρ ||A||C, where ρ 0 is an absolute constant satisfying $ρ 0. 56. The algorithm combines semidefinite programming with a rounding technique based on Grothendieck's Inequality. We present three known proofs of Grothendieck's inequality, with the necessary modifications which emphasize their algorithmic aspects. These proofs contain rounding techniques which go beyond the random hyperplane rounding of Goemans and Williamson [12], allowing us to transfer various algorithms for dense graph and matrix problems to the sparse case.