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An Application of Combinatorial Optimization to Statistical Physics and Circuit Layout Design

Francisco Barahona, Martin Grötschel, Michael Jünger and Gerhard Reinelt
Operations Research
Vol. 36, No. 3 (May - Jun., 1988), pp. 493-513
Published by: INFORMS
Stable URL: http://www.jstor.org/stable/170992
Page Count: 21
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An Application of Combinatorial Optimization to Statistical Physics and Circuit Layout Design
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Abstract

We study the problem of finding ground states of spin glasses with exterior magnetic field, and the problem of minimizing the number of vias (holes on a printed circuit board, or contacts on a chip) subject to pin preassignments and layer preferences. The former problem comes up in solid-state physics, and the latter in very-large-scale-integrated (VLSI) circuit design and in printed circuit board design. Both problems can be reduced to the max-cut problem in graphs. Based on a partial characterization of the cut polytope, we design a cutting plane algorithm and report on computational experience with it. Our method has been used to solve max-cut problems on graphs with up to 1,600 nodes.

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