Chapter 4. Computing Exact Ground States of Hard Ising Spin Glass Problems by Branch-and-Cut

  1. Alexander K. Hartmann4 and
  2. Heiko Rieger5
  1. Frauke Liers1,
  2. Michael Jünger1,
  3. Gerhard Reinelt2 and
  4. Giovanni Rinaldi3

Published Online: 6 JUN 2005

DOI: 10.1002/3527603794.ch4

New Optimization Algorithms in Physics

New Optimization Algorithms in Physics

How to Cite

Liers, F., Jünger, M., Reinelt, G. and Rinaldi, G. (2004) Computing Exact Ground States of Hard Ising Spin Glass Problems by Branch-and-Cut, in New Optimization Algorithms in Physics (eds A. K. Hartmann and H. Rieger), Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim, FRG. doi: 10.1002/3527603794.ch4

Editor Information

  1. 4

    Institut für Theoretische Physik, Universität Göttingen, Tammanstraße 1, D-37077 Göttingen, Germany

  2. 5

    Theoretische Physik, Universität des Saarlandes, D-66041 Saarbrücken, Germany

Author Information

  1. 1

    Institut für Informatik, Universität zu Köln, Pohligstraße 1, D-50969 Köln, Germany

  2. 2

    Institut für Informatik, Ruprecht-Karls-Universität Heidelberg, Im Neuenheimer Feld 368, D-69120 Heidelberg, Germany

  3. 3

    Istituto di Analisi dei Sistemi ed Informatica, ‘Antonio Ruberti’ - CNR, Viale Manzoni, 30, 00185 Roma, Italy

Publication History

  1. Published Online: 6 JUN 2005
  2. Published Print: 11 MAY 2004

ISBN Information

Print ISBN: 9783527404063

Online ISBN: 9783527603794

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Keywords:

  • new optimization algorithms;
  • applications in physics;
  • ground states;
  • maximum cuts;
  • solving hard max-cut problems;
  • linear programming relaxations of max-cut;
  • branch-and-cut

Summary

This chapter contains sections titled:

  • Introduction

  • Ground States and Maximum Cuts

  • A General Scheme for Solving Hard Max-cut Problems

  • Linear Programming Relaxations of Max-cut

  • Branch-and-cut

  • Results of Exact Ground-state Computations

  • Advantages of Branch-and-cut

  • Challenges for the Years to Come

  • References