Gadgets, approximation, and linear programming

Trevisan, Luca, Sorkin, Gregory B. ORCID: 0000-0003-4935-7820, Sudan, Madhu and Williamson, David P. (1996) Gadgets, approximation, and linear programming. In: 37th Annual IEEE Symposium on Foundations of Computer Science, 1996-10-14 - 1996-10-16, VT, United States, USA.

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Abstract

The authors 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 they present a number of new, computer-constructed gadgets for several different reductions. This method also answers the question of how to prove the optimality of gadgets-they show how LP duality gives such proofs. The new gadgets improve hardness results for MAX CUT and MAX DICUT, showing that approximating these problems to within factors of 60/61 and 44/45 respectively is NP-hard (improving upon the previous hardness of 71/72 for both problems). They also use the gadgets to obtain an improved approximation algorithm for MAX 3SAT which guarantees an approximation ratio of 0.801, This improves upon the previous best bound of 0.7704.

Item Type:	Conference or Workshop Item (Paper)
Official URL:	http://ieeexplore.ieee.org/xpl/tocresult.jsp?isnum...
Divisions:	Management
Subjects:	Q Science > QA Mathematics > QA75 Electronic computers. Computer science Q Science > QA Mathematics > QA76 Computer software
Date Deposited:	16 May 2011 12:51
Last Modified:	01 Dec 2024 03:51
URI:	http://eprints.lse.ac.uk/id/eprint/35886

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