computer science publication server: No conditions. Results ordered -Date Deposited. 2021-04-23T00:00:20ZEPrintshttp://e-archive.informatik.uni-koeln.de/images/sitelogo.pnghttp://e-archive.informatik.uni-koeln.de/2019-04-25T14:11:30Z2019-04-25T14:11:30Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/940This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/9402019-04-25T14:11:30ZPerformance of a Quantum Annealer for Ising Ground State Computations on Chimera GraphsQuantum annealing is getting increasing attention in combinatorial optimization. The quantum processing unit by D-Wave is constructed to approximately solve Ising models
on so-called Chimera graphs. Ising models are equivalent to quadratic unconstrained binary optimization (QUBO) problems and maximum cut problems on the associated graphs.
We have tailored branch-and-cut as well as semidefinite programming algorithms for solving Ising models for Chimera graphs to provable optimality and use the strength of these
approaches for comparing our solution values to those obtained on the current quantum annealing machine D-Wave 2000Q. This allows for the assessment of the quality of solutions produced by the D-Wave hardware. It has been a matter of discussion in the literature how well the D-Wave hardware performs at its native task, and our experiments shed some more light on this issue.Michael JüngerJünger, MichaelElisabeth LobeLobe, ElisabethPetra MutzelMutzel, PetraGerhard ReineltReinelt, GerhardFranz RendlRendl, FranzGiovanni RinaldiRinaldi, GiovanniTobias StollenwerkStollenwerk, Tobias2010-09-22T10:23:24Z2014-07-04T09:02:10Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/807This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/8072010-09-22T10:23:24ZGround states in three-dimensional ±J Edwards-Anderson spin glasses with free boundaries
Frauke LiersLiers, FraukeMichael JüngerJünger, Michael2010-07-26T00:00:00Z2012-01-09T12:20:44Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/595This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/5952010-07-26T00:00:00ZA Non-Disordered Glassy Model with a Tunable Interaction RangeWe introduce a non-disordered lattice spin model, based on the principle of minimizing spin-spin correlations up to a (tunable) distance R.The model can be defined in any spatial dimension D, but already for D=1 and small values of R (e.g. R=5) the model shows the properties of a glassy system: deep and well separated energy minima, very slow relaxation dynamics, aging and non-trivial fluctuation-dissipation ratio.Frauke LiersLiers, FraukeEnzo MarinariMarinari, EnzoUlrike PagaczPagacz, UlrikeFederico Ricci-TersenghiRicci-Tersenghi, FedericoVera SchmitzSchmitz, Vera2010-03-24T00:00:00Z2012-02-06T16:12:12Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/485This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/4852010-03-24T00:00:00ZUniversality-class dependence of energy distributions in spin glassesWe study the probability distribution function of the ground-state energies of the disordered one-dimensional Ising spin chain with power-law interactions using a combination of parallel tempering Monte Carlo and branch, cut & price algorithms. By tuning the exponent of the power-law interactions we are able to scan several universality classes. Our results suggest that mean-field models have a non-Gaussian limiting distribution of the ground-state energies, whereas non-mean-field models have a Gaussian limiting distribution.Helmut G. KatzgraberKatzgraber, Helmut G.Mathias KörnerKörner, MathiasFrauke LiersLiers, FraukeMichael JüngerJünger, MichaelAlexander K. HartmannHartmann, Alexander K.2009-01-29T00:00:00Z2011-12-19T09:44:35Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/569This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/5692009-01-29T00:00:00ZExact Ground States of Large Two-Dimensional Planar Ising Spin GlassesWe present an algorithm for the calculation of exact ground states of two-dimensional Ising spin glasses with free boundary conditions in at least one direction. Studying spin-glass physics through analyzing their ground-state properties has a long history. Although there exist polynomial-time algorithms for the two-dimensional planar case, where the problem of finding ground states is transformed to a minimum weighted perfect matching problem, the reachable system sizes have been limited both by the needed CPU time and memory requirements. Using Kasteleyn cities, we calculate accurate ground states for huge two-dimensional planar Ising spin-glass lattices (up to 3000x3000 spins) within reasonable time. According to our knowledge, these are the largest sizes currently available. Kasteleyn cities were recently also used by Thomas and Middleton in the context of extended ground states on the torus. Domain walls can be computed using reoptimization. Finally, the correctness of heuristically computed ground states can easily be verified.Gregor PardellaPardella, GregorFrauke LiersLiers, Frauke2008-08-05T00:00:00Z2013-07-08T08:23:12Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/452This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/4522008-08-05T00:00:00ZComputing Exact Ground States of Hard Ising Spin Glass Problems by Branch-and-CutThis is a survey prepared on invitation.Frauke LiersLiers, FraukeMichael JüngerJünger, MichaelGerhard ReineltReinelt, GerhardGiovanni RinaldiRinaldi, Giovanni2008-04-19T00:00:00Z2012-01-12T09:03:54Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/556This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/5562008-04-19T00:00:00ZZero-temperature behavior of the random-anisotropy model in the strong-anisotropy limitWe consider the random-anisotropy model on the square and on the cubic lattice in the strong-anisotropy limit. We compute exact ground-state configurations, and we use them to determine the stiffness exponent at zero temperature; we find theta = -0.275(5) and theta approx 0.2 respectively in two and three dimensions. These results show that the low-temperature phase of the model is the same as that of the usual Ising spin-glass model. We also show that no magnetic order occurs in two dimensions, since the expectation value of the magnetization is zero and spatial correlation functions decay exponentially. In three dimensions our data strongly support the absence of spontaneous magnetization in the infinite-volume limit.Frauke LiersLiers, FraukeJovanka LukicLukic, JovankaEnzo MarinariMarinari, EnzoAndrea PelissettoPelissetto, AndreaEttore VicariVicari, Ettore2008-04-19T00:00:00Z2014-10-27T11:18:30Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/445This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/4452008-04-19T00:00:00ZLow Energy Excitations in Spin Glasses from Exact Ground StatesWe investigate the nature of the low-energy, large-scale excitations in the three-dimensional Edwards-Anderson Ising spin glass with Gaussian couplings and free boundary conditions, by studying the response of the ground state to a coupling-dependent perturbation introduced previously. The ground states are determined exactly for system sizes up to 12^3 spins using a branch and cut algorithm. The data are consistent with a picture where the surface of the excitations is not space-filling, such as the droplet or the ''TNT'' picture. When allowing for large finite size correctios, the data are also consistent with a picture with space-filling surface,such as replica symmetry breaking.We compare the results with data for periodic boundary conditions obtained with a genetic algorithm,and discuss the effects of different boundary conditions on finite-size correction. Finally, we analyze the performance of our branch and cut algorithm, finding that it is correlated with the existence of large-scale,low-energy excitations.Matteo PalassiniPalassini, MatteoFrauke LiersLiers, FraukeMichael JüngerJünger, MichaelA. Peter YoungYoung, A. Peter2008-04-19T00:00:00Z2011-12-19T09:46:27Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/539This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/5392008-04-19T00:00:00ZMagnetic exponents of two-dimensional spin glassesThe magnetic critical properties of two-dimensional spin glasses are controversial.Using exact ground state determination, we extract the properties of clusters flipped when increasing continuously a uniform field. We show that these clusters have many holes but otherwise have statistical properties similar to those of zero-field droplets. A detailed analysis gives for the magnetization exponent delta approx 1.30 pm 0.02 using lattice sizes up to 80 imes 80 ; this is compatible with the droplet model prediction delta = 1.282 . The reason for previous disagreements stems from the need to analyze both singular and analytic contributions in the low field regime.Frauke LiersLiers, FraukeOlivier C. MartinMartin, Olivier C.2008-04-19T00:00:00Z2012-02-06T16:10:57Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/446This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/4462008-04-19T00:00:00ZGround state of the Bethe lattice spin glass and running time of an exact optimization algorithmWe study the Ising spin glass on random graphs with fixed connectivity z and with a Gaussian distribution of the couplings, with mean mu and unit variance. We compute exact ground states by branch-and-cut with z=4,6 and system sizes up to 1280 spins, for different values of mu . We locate the spin-glass/ferromagnet phase transition Near the phase transition, we observe a sharp change of the median running time of our implementation of the algorithm, consistent with a change from a polynomial dependence on the system size, deep in the ferromagnetic phase, to slower than polynomial in the spin-glass phase.Frauke LiersLiers, FraukeMatteo PalassiniPalassini, MatteoAlexander K. HartmannHartmann, Alexander K.Michael JüngerJünger, Michael2008-04-19T00:00:00Z2012-02-06T16:05:58Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/531This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/5312008-04-19T00:00:00ZA Primal Branch-and-Cut Algorithm for the Degree-Constrained Minimum Spanning Tree ProblemThe degree-constrained minimum spanning tree (DCMST) is relevant in the design of networks. It consists of finding a spanning tree whose nodes do not exceed a given maximum degree and whose total edge length is minimum. We design a primal branch-and-cut algorithm that solves instances of the problem to optimality. Primal methods have not been used extensively in the past, and their performance often could not compete with their standard 'dual' counterparts. We show that primal separation procedures yield good bounds for the DCMST problem. On several instances, the primal branch-and-cut program turns out to be competitive with other methods known in the literature. This shows the potential of the primal method.Markus BehleBehle, MarkusMichael JüngerJünger, MichaelFrauke LiersLiers, Frauke2007-04-26T00:00:00Z2012-02-06T16:02:13Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/486This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/4862007-04-26T00:00:00ZDetermining Maximum Cuts in Graphs Coming from Theoretical PhysicsThis extended abstract was written for the proceedings of the Cologne-Twente Workshop CTW2005.Michael JüngerJünger, MichaelFrauke LiersLiers, Frauke2005-12-01T00:00:00Z2012-02-06T16:13:00Zhttp://e-archive.informatik.uni-koeln.de/id/eprint/504This item is in the repository with the URL: http://e-archive.informatik.uni-koeln.de/id/eprint/5042005-12-01T00:00:00ZOvercoming system-size limitations in spin glassesIn order to overcome the limitations of small system sizes in spin-glass simulations, we investigate the one-dimensional Ising spin chain with power-law interactions. The model has the advantage over traditional higher-dimensional Hamiltonians in that a large range of system sizes can be studied. In addition, the universality class of the model can be changed by tuning the power law exponent, thus allowing us to scan from the mean-field to long-range and short-range universality classes. We illustrate the advantages of this model by studying the nature of the spin glass state where our results hint towards a replica symmetry breaking scenario. We also compute ground-state energy distributions and show that mean-field and non-mean-field models are intrinsically different.Helmut G. KatzgraberKatzgraber, Helmut G.Mathias KörnerKörner, MathiasFrauke LiersLiers, FraukeAlexander K. HartmannHartmann, Alexander K.