Gadgets, Approximation, and Linear Programming

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Gadgets, Approximation, and Linear Programming
We present a linear programming-based method for nding \gadgets", i.e., combinatorial structures reducing constraints of one optimization problem to constraints of another. A key step in this method is a simple observation which limits the search space to a nite one. Using this new method we present a number of new, computer-constructed gadgets for several di erent reductions. This method also answers a question posed by Bellare, Goldreich and Sudan 2] of how to prove the optimality of gadgets: LP duality gives such proofs. The new gadgets, when combined with recent results of Hastad 9], improve the known inapproximability results for MAX CUT and MAX DICUT, showing that approximating these problems to within factors of 16=17 + and 12=13 + respectively is NP-hard, for every > 0. Prior to this work, the best known inapproximability thresholds for both problems was 71/72 2]. Without using the gadgets from this paper, the best possible hardness that would follow from 2, 9] is 18=1...
Luca Trevisan, Gregory B. Sorkin, Madhu Sudan, Dav
Added 19 Dec 2010
Updated 19 Dec 2010
Type Journal
Year 2000
Authors Luca Trevisan, Gregory B. Sorkin, Madhu Sudan, David P. Williamson
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