Exact ground states of two-dimensional ±J Ising spin glasses

Simone, Caterina De; Diehl, M.; Jünger, Michael; Mutzel, Petra; Reinelt, Gerhard; Rinaldi, Giovanni

doi:10.1007/bf02174135

Cited by 57 publications

(49 citation statements)

References 14 publications

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“…This problem, known as the maximum weight induced subgraph problem with both node and edge weights, has interesting applications, e.g. see [4,7]. In this section, we present how 01QP can be related to other (more) well known problems in graphs, namely, the maximum-weight cut problem and the maximum weight induced subgraph problem (without node weights).…”

Section: Qp and Maxcutmentioning

confidence: 99%

Solving the fixed rank convex quadratic maximization in binary variables by a parallel zonotope construction algorithm

Ferrez

Fukuda

Liebling

2005

European Journal of Operational Research

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We address the weighted max-cut problem, or equivalently the problem of maximizing a quadratic form in n binary variables. If the underlying (symmetric) matrix is positive semidefinite of fixed rank d, then the problem can be reduced to searching the extreme points of a zonotope, thus becoming of polynomial complexity in O(n d−1 ). Reverse search is an efficient and practical means for enumerating the cells of a regular hyperplane arrangement, or equivalently, the extreme points of a zonotope. We present an enhanced version of reverse search of significantly reduced computational complexity that uses ray shooting and is well suited for parallel computation. Furthermore, a neighborhood zonotope edge following descent heuristic can be devised. We report preliminary computational experiments of a parallel implementation of our algorithms.

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Section: Qp and Maxcutmentioning

confidence: 99%

Solving the fixed rank convex quadratic maximization in binary variables by a parallel zonotope construction algorithm

Ferrez

Fukuda

Liebling

2005

European Journal of Operational Research

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“…In particular with regards to improved optimization algorithms [111,10,281,269] (see also [143] and the articles by Stariolo and Tsallis [276], Hogg [125] and Tomassini [288] in this series) significant progress in the investigation of ground state properties in spin glasses can be expected in the future.…”

Section: Energy Barriermentioning

confidence: 99%

“…Finally, by re-weighting with exp[−E/T + β(E)E − α(E)], the canonical distribution can be reconstructed. With regards to spin glasses, this ensemble has proven to be useful in particular for the investigation of ground state properties [19,20,21] (for this problem see also the above mentioned works [111,10,281,269,276,125,288]). Cluster algorithms as suggested by Swendsen and Wang [284] have become very useful in the investigation of pure systems (see [285] for an overview).…”

Section: Numerical Recipesmentioning

confidence: 99%

Monte Carlo Studies of Ising Spin Glasses and Random Field Systems

Rieger

1995

Annual Reviews of Computational Physics II

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We review recent numerical progress in the study of finite dimensional strongly disordered magnetic systems like spin glasses and random field systems. In particular we report in some details results for the critical properties and the non-equilibrium dynamics of Ising spin glasses. Furthermore we present an overview over recent investigations on the random field Ising model and finally of quantum spin glasses.

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“…Details of the algorithm, simulation parameters and more results will be given in [18]. For small system sizes L = 4, 6 we could compute for 200 randomly selected systems exact ground states with a Branch-and-Cut method [19,20] using a program which generously was made available by the group of M. Jünger in Cologne. In ALL cases our method found the exact ground states as well!…”

Section: Introductionmentioning

confidence: 99%