Some optimal inapproximability results
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
How Good is the Goemans--Williamson MAX CUT Algorithm?
SIAM Journal on Computing
Derandomizing Approximation Algorithms Based on Semidefinite Programming
SIAM Journal on Computing
Gadgets, Approximation, and Linear Programming
SIAM Journal on Computing
Computer assisted proof of optimal approximability results
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Constructing Worst Case Instances for Semidefinite Programming Based Approximation Algorithms
SIAM Journal on Discrete Mathematics
The RPR2 Rounding Technique for Semidefinite Programs
ICALP '01 Proceedings of the 28th International Colloquium on Automata, Languages and Programming,
63-Approximation Algorithm for MAX DICUT
APPROX '01/RANDOM '01 Proceedings of the 4th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems and 5th International Workshop on Randomization and Approximation Techniques in Computer Science: Approximation, Randomization and Combinatorial Optimization
Approximating the value of two power proof systems, with applications to MAX 2SAT and MAX DICUT
ISTCS '95 Proceedings of the 3rd Israel Symposium on the Theory of Computing Systems (ISTCS'95)
Bipartite Subgraphs and the Smallest Eigenvalue
Combinatorics, Probability and Computing
Random MAX SAT, random MAX CUT, and their phase transitions
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
ISAAC '02 Proceedings of the 13th International Symposium on Algorithms and Computation
Approximating the cut-norm via Grothendieck's inequality
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
Semidefinite programming based approaches to the break minimization problem
Computers and Operations Research
Minimum 2SAT-DELETION: Inapproximability results and relations to Minimum Vertex Cover
Discrete Applied Mathematics
Balanced max 2-sat might not be the hardest
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
Computing the types of the relationships between autonomous systems
IEEE/ACM Transactions on Networking (TON)
Near-optimal algorithms for maximum constraint satisfaction problems
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal algorithms and inapproximability results for every CSP?
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Sums of squares based approximation algorithms for MAX-SAT
Discrete Applied Mathematics
A New Upper Bound for Max-2-SAT: A Graph-Theoretic Approach
MFCS '08 Proceedings of the 33rd international symposium on Mathematical Foundations of Computer Science
WABI '08 Proceedings of the 8th international workshop on Algorithms in Bioinformatics
Near-optimal algorithms for maximum constraint satisfaction problems
ACM Transactions on Algorithms (TALG)
Local search starting from an LP solution: Fast and quite good
Journal of Experimental Algorithmics (JEA)
Complexity issues in color-preserving graph embeddings
Theoretical Computer Science
A hierarchy and probability-based approach for inferring AS relationships
AINTEC '09 Asian Internet Engineering Conference
Fast SDP algorithms for constraint satisfaction problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
A new upper bound for Max-2-SAT: A graph-theoretic approach
Journal of Discrete Algorithms
Improved orientations of physical networks
WABI'10 Proceedings of the 10th international conference on Algorithms in bioinformatics
Towards Sharp Inapproximability for Any 2-CSP
SIAM Journal on Computing
Optimal allocation in combinatorial auctions with quadratic utility functions
TAMC'11 Proceedings of the 8th annual conference on Theory and applications of models of computation
A lower bound on the value of entangled binary games
Quantum Information & Computation
Maximizing Non-monotone Submodular Functions
SIAM Journal on Computing
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
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
Randomized variants of Johnson's algorithm for MAX SAT
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Inferring AS relationships: dead end or lively beginning?
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
The power of semidefinite programming relaxations for MAX-SAT
CPAIOR'06 Proceedings of the Third international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Improved approximation for orienting mixed graphs
SIROCCO'12 Proceedings of the 19th international conference on Structural Information and Communication Complexity
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
Explicit Optimal Hardness via Gaussian Stability Results
ACM Transactions on Computation Theory (TOCT)
Complexity of approximating CSP with balance / hard constraints
Proceedings of the 5th conference on Innovations in theoretical computer science
| Hi-index | 0.00 |
Improving and extending recent results of Matuura and Matsui, and less recent results of Feige and Goemans, we obtain improved approximation algorithms for the MAX 2-SAT and MAX DI-CUT problems. These approximation algorithms start by solving semidefinite programming relaxations of these problems. They then rotate the solution obtained, as suggested by Feige and Goemans. Finally, they round the rotated vectors using random hyperplanes chosen according to skewed distributions. The performance ratio obtained by the MAX 2-SAT algorithm is at least 0.940, while that obtained by the MAX DI-CUT algorithm is at least 0.874. We show that these are essentially the best performance ratios that can be achieved using any combination of prerounding rotations and skewed distributions of hyperplanes, and even using more general families of rounding procedures. The performance ratio obtained for the MAX 2-SAT problem is fairly close to the inapproximability bound of about 0.954 obtained by H氓stad. The performance ratio obtained for the MAX DI-CUT problem is very close to the performance ratio of about 0.878 obtained by Goemans and Williamson for the MAX CUT problem.