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

• Published in: Operations research Vol. 36; no. 3; pp. 493 - 513
• Main Authors: Barahona, Francisco, Grotschel, Martin, Junger, Michael, Reinelt, Gerhard
• Format: Journal Article
• Language: English
• Published: Linthicum, MD INFORMS 01.05.1988; Operations Research Society of America; Institute for Operations Research and the Management Sciences
• Subjects: 432 the max-cut polytope; 628 a cutting plane method for the max-cut problem; 633 applications of integer programming to physics and VLSI design; Algorithms; Applied sciences; Combinatorial optimization; Electronic equipment and fabrication. Passive components, printed wiring boards, connectics; Electronics; Exact sciences and technology; Ground state; Heuristics; Magnetic fields; Physics; Planar graphs; Polynomials; Polytopes; Spin glasses; Operational research; VLSI circuit; Printed circuit; Circuit design; Magnetic field; Optimization
• ISSN: 0030-364X; 1526-5463
• DOI: 10.1287/opre.36.3.493

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.