Statistical mechanics of combinatorial optimization problems with site disorder.

  title={Statistical mechanics of combinatorial optimization problems with site disorder.},
  author={D. Dean and D. J. Lancaster and Satya N. Majumdar},
  journal={Physical review. E, Statistical, nonlinear, and soft matter physics},
  volume={72 2 Pt 2},
We study the statistical mechanics of a class of problems whose phase space is the set of permutations of an ensemble of quenched random positions. Specific examples analyzed are the finite-temperature traveling salesman problem on several different domains and various problems in one dimension such as the so-called descent problem. We first motivate our method by analyzing these problems using the annealed approximation. Then in the limit of a large number of points we develop a formalism to… Expand
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  • Kh. Gimadi and A.I. Serdyukov in G Gutin and, A. P. Punnen (Eds), The Traveling Salesman Problem and its Variations (Combinatorial Optimization Series), Kluwer, Boston
  • 2002
  • Cam. Phil. Soc. 55 299
  • 1959
  • L01001
  • 2005
  • 37, 1125
  • 2004
  • Phys. J. B 37, 383
  • 2004
Theoretical Computer Science 265
  • 3
  • 2001
  • 94, 739
  • 1999