Maximum Matching on Boltzmann Machines

  • Authors:

  • Xin Yao

  • Affiliations:

  • School of Computer Science, University College, The University of New South Wales, Australian Defence Force Academy, Canberra, ACT, Australia 2600. E-mail: xin@csadfa.cs.adfa.oz.au

  • Venue:
  • Neural Processing Letters
  • Year:
  • 1998

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Abstract

The Boltzmann machine is one of widely used neural network models used tocope with difficult combinatorial optimisation problems. It has been usedto find near optimum solutions to such hard problems as graph partitioningand the Travelling Salesman problem. However, very little is known aboutthe time complexity of solving combinatorial optimisation problems onBoltzmann machines. This issue is important because it will help us betterunderstand the power of Boltzmann machines in dealing with hard problems.This paper studies the time complexity of maximum matching in a graph onBoltzmann machines. It is shown that some widely-used Boltzmann machinescannot find a maximum matching in average time polynomial in the number ofnodes of the graph although there are conventional deterministicalgorithms which solve the problem in polynomial time. On the other hand,this paper also shows that a simpler model of Boltzmann machines, with the’temperature‘ parameter fixed at some constant, can find a nearmaximum matching in polynomial average time.