Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Every 2-CSP allows nontrivial approximation
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
Correlation clustering with a fixed number of clusters
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
MAX k-CUT and approximating the chromatic number of random graphs
Random Structures & Algorithms
Correlation clustering in general weighted graphs
Theoretical Computer Science - Approximation and online algorithms
Balanced max 2-sat might not be the hardest
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Near-optimal algorithms for maximum constraint satisfaction problems
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
The UGC hardness threshold of the ℓp Grothendieck problem
Proceedings of the nineteenth annual ACM-SIAM symposium on 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
Towards computing the Grothendieck constant
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
Max cut and the smallest eigenvalue
Proceedings of the forty-first annual ACM symposium on Theory of computing
Near-optimal algorithms for maximum constraint satisfaction problems
ACM Transactions on Algorithms (TALG)
The UGC Hardness Threshold of the Lp Grothendieck Problem
Mathematics of Operations Research
Approximation algorithms for the sex-equal stable marriage problem
ACM Transactions on Algorithms (TALG)
Fast SDP algorithms for constraint satisfaction problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Simulating Quantum Correlations with Finite Communication
SIAM Journal on Computing
Towards Sharp Inapproximability for Any 2-CSP
SIAM Journal on Computing
Bypassing UGC from some optimal geometric inapproximability results
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Convergence and approximation in potential games
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
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
Improved approximation algorithms for MAX NAE-SAT and MAX SAT
WAOA'05 Proceedings of the Third international conference on Approximation and Online Algorithms
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
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
Approximation algorithms for graph homomorphism problems
APPROX'06/RANDOM'06 Proceedings of the 9th international conference on Approximation Algorithms for Combinatorial Optimization Problems, and 10th international conference on Randomization and Computation
IPCO'10 Proceedings of the 14th international conference on Integer Programming and Combinatorial Optimization
Convergence and approximation in potential games
Theoretical Computer Science
The Grothendieck constant of random and pseudo-random graphs
Discrete Optimization
On quadratic programming with a ratio objective
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Max-cut parameterized above the edwards-erdős bound
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
On the complexity of Newman's community finding approach for biological and social networks
Journal of Computer and System Sciences
On the usefulness of predicates
ACM Transactions on Computation Theory (TOCT)
| Hi-index | 0.00 |
This paper considers the following type of quadratic programming problem. Given an arbitrary matrix A, whose diagonal elements are zero, find x 驴 {-1, 1}^n such that x^TAx is maximized. Our approximation algorithm for this problem uses the canonical semidefinite relaxation and returns a solution whose ratio to the optimum is in 驴(1/log n). This quadratic programming problem can be seen as an extension to that of maximizing x^TAy (where y's components are also 卤1). Grothendieck's inequality states that the ratio of the optimum value of the latter problem to the optimum of its canonical semidefinite relaxation is bounded below by a constant. The study of this type of quadratic program arose from a desire to approximate the maximum correlation in correlation clustering. Nothing substantive was known about this problem; we present an 驴(1/log n) approximation, based on our quadratic programming algorithm. We can also guarantee that our quadratic programming algorithm returns a solution to the MAXCUT problem that has a significant advantage over a random assignment.