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An Application of Combinatorial Optimization to Statistical Physics and Circuit Layout Design
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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Citations
Cited by
Goemans, M. X., & Williamson, D. P. (1995) · Journal of the ACM · doi:10.1145/227683.227684 · Cited by 3,587
Variational quantum algorithms
Cerezo, M., Arrasmith, A., Babbush, R., Benjamin, S. C., Endo, S., Fujii, K., McClean, J. R., Mitarai, K., Yuan, X., Cincio, L., et al. (2021) · Nature Reviews Physics · doi:10.1038/s42254-021-00348-9 · Cited by 3,385
Boros, E., & Hammer, P. L. (2002) · Discrete Applied Mathematics · doi:10.1016/s0166-218x(01)00341-9 · Cited by 827
The unconstrained binary quadratic programming problem: a survey
Kochenberger, G., Hao, J.-K., Glover, F., Lewis, M., Lü, Z., Wang, H., & Wang, Y. (2014) · Journal of Combinatorial Optimization · doi:10.1007/s10878-014-9734-0 · Cited by 473
Energy Minimization via Graph Cuts: Settling What is Possible
Freedman, D., & Drineas, P. (2005) · 2005 IEEE Computer Society Conference on Computer Vision and Pattern Recognition (CVPR'05) · doi:10.1109/cvpr.2005.143 · Cited by 173
Metadata
- Authors
- Barahona, F., Grötschel, M., Jünger, M., & Reinelt, G.
- Venue
- Operations Research
- Published
- 1988-06
- Volume
- 36
- Issue
- 3
- Pages
- 493-513
- ISSN
- 0030-364X (ISSN-L)
- 1526-5463
- OpenAlex
- W2159739530
- Cited by
- 504
- References
- 0
- FWCI
- 5.91
- Type
- journal article
- Language
- en
- Open access
- closed
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- Barahona, F., Grötschel, M., Jünger, M., & Reinelt, G. (1988). An Application of Combinatorial Optimization to Statistical Physics and Circuit Layout Design. Operations Research. https://doi.org/10.1287/opre.36.3.493
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Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
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