Gadgets, approximation, and linear programming
Trevisan, L.
Sorkin, G.B.
Sudan, M.
Williamson, D.P.
Dipartimento di Sci. dell'Inf., Univ. degli Studi di Roma;
This paper appears in: Foundations of Computer Science, 1996. Proceedings., 37th Annual Symposium on
Publication Date: 14-16 Oct 1996
On page(s): 617-626
Meeting Date: 10/14/1996 - 10/16/1996
Location: Burlington, VT, USA
ISBN: 0-8186-7594-2
References Cited: 10
INSPEC Accession Number: 5444307
Digital Object Identifier: 10.1109/SFCS.1996.548521
Current Version Published: 2002-08-06
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
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