Computational Complexity
The complexity of approximating a nonlinear program
Mathematical Programming: Series A and B
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
SIAM Journal on Computing
Free Bits, PCPs, and Nonapproximability---Towards Tight Results
SIAM Journal on Computing
Noise-tolerant learning, the parity problem, and the statistical query model
STOC '00 Proceedings of the thirty-second annual ACM symposium on Theory of computing
Some optimal inapproximability results
Journal of the ACM (JACM)
Hardness results for approximate hypergraph coloring
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Improved Inapproximability Results for MaxClique, Chromatic Number and Approximate Graph Coloring
FOCS '01 Proceedings of the 42nd IEEE symposium on Foundations of Computer Science
Hardness results for approximate hypergraph coloring
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Algorithms with large domination ratio
Journal of Algorithms
Parameterizing above or below guaranteed values
Journal of Computer and System Sciences
Parameterizing MAX SNP problems above guaranteed values
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
Kernelization --- preprocessing with a guarantee
The Multivariate Algorithmic Revolution and Beyond
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We initiate the study of a new measure of approximation. This measure compares the performance of an approximation algorithm to the random assignment algorithm. Since the random assignment algorithm is known to give essentially the best possible polynomial time approximation algorithm for many optimization problems, this is a useful measure.In this paper, we focus on this measure for the optimization problems, Max-Lin-2, in which we need to maximize the number of satisfied linear equations in a system of linear equations modulo 2, and Max-$k$-Lin-2, a special case of the above problem in which each equation has at most $k$ variables. The main techniques we use, in our approximation algorithms and inapproximability results for this measure, are from Fourier analysis and derandomization.