Library Header Image
LSE Research Online LSE Library Services

Gadgets, approximation, and linear programming

Trevisan, Luca, Sorkin, Gregory B., Sudan, Madhu and Williamson, David P. (2000) Gadgets, approximation, and linear programming. SIAM Journal on Computing, 29 (6). pp. 2074-2097. ISSN 0097-5397

Full text not available from this repository.


We present a linear programming-based method for finding "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 finite one. Using this new method we present a number of new, computer-constructed gadgets for several different reductions. This method also answers a question posed by Bellare, Goldreich, and Sudan [SIAM J. Comput., 27 (1998), pp. 804-915] of how to prove the optimality of gadgets: linear programming duality gives such proofs. The new gadgets, when combined with recent results of Håstad [Proceedings of the 29th ACM Symposium on Theory of Computing, 1997, pp. 1-10], 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 were 71/72 (M. Bellare, O. Goldreich, and M. Sudan [SIAM J. Comput., 27 (1998), pp. 804-915]). Without using the gadgets from this paper, the best possible hardness that would follow from Bellare, Goldreich, and Sudan and Håstad is 18/19. We also use the gadgets to obtain an improved approximation algorithm for MAX3 SAT which guarantees an approximation ratio of .801.

Item Type: Article
Official URL:
Additional Information: © 2000 Society for Industrial and Applied Mathematics
Divisions: Management
Subjects: Q Science > QA Mathematics > QA75 Electronic computers. Computer science
Q Science > QA Mathematics > QA76 Computer software
Sets: Research centres and groups > Management Science Group
Departments > Management
Date Deposited: 13 Apr 2011 14:26
Last Modified: 20 Jul 2021 00:45

Actions (login required)

View Item View Item