Approximate graph coloring by semidefinite programming
Journal of the ACM (JACM)
Finding almost-satisfying assignments
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
On Semidefinite Programming Relaxations of (2+p)-SAT
Annals of Mathematics and Artificial Intelligence
On the optimality of the random hyperplane rounding technique for max cut
Random Structures & Algorithms - Probabilistic methods in combinatorial optimization
Coloring k-Colorable Semirandom Graphs in Polynomial Expected Time via Semidefinite Programming
MFCS '02 Proceedings of the 27th International Symposium on Mathematical Foundations of Computer Science
Some Afterthoughts on Hopfield Networks
SOFSEM '99 Proceedings of the 26th Conference on Current Trends in Theory and Practice of Informatics on Theory and Practice of Informatics
Approximation algorithms for the maximum satisfiability problem
Nordic Journal of Computing
Randomized approximations of the constraint satisfaction problem
Nordic Journal of Computing
Coloring 2-colorable hypergraphs with a sublinear number of colors
Nordic Journal of Computing
Tight Bound on Johnson's Algoritihm for Max-SAT
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
An approximation algorithm for scheduling two parallel machines with capacity constraints
Discrete Applied Mathematics
On the Computational Complexity of Binary and Analog Symmetric Hopfield Nets
Neural Computation
Approximation Algorithms for MAX-BISECTION on Low Degree Regular Graphs
Fundamenta Informaticae
Approximating the fixed linear crossing number
Discrete Applied Mathematics
Approximations of weighted independent set and hereditary subset problems
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Derandomization of dimensionality reduction and SDP based algorithms
WADS'05 Proceedings of the 9th international conference on Algorithms and Data Structures
Approximation Algorithms for MAX-BISECTION on Low Degree Regular Graphs
Fundamenta Informaticae
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Remarkable breakthroughs have been made recently in obtaining approximate solutions to some fundamental NP-Complete problems, namely Max-Cut, Max k-Cut, Max-Sat, Max-Dicut, Max-Bisection, k Vertex Coloring, Independent Set, etc. These breakthroughs all involve polynomial time randomized algorithms based upon semidefinite programming, a technique pioneered by M. Goemans and D. Williamson (1994). In this paper, we give techniques to derandomize the above class of randomized algorithms, thus obtaining polynomial time deterministic algorithms with the same approximation ratios for the above problems. Note that Goemans and Williamson also gave an elegant method to derandomize their Max-Cut algorithm. We show here that their technique has a fatal flaw. The techniques we subsequently develop are very different from theirs. At the heart of our technique is the use of spherical symmetry to convert a nested sequence of n integrations, which cannot be approximated sufficiently well in polynomial time, to a nested sequence of just a constant number of integrations, which can be approximated sufficiently well in polynomial time.