Statistical mechanics of combinatorial optimization problems with site disorder.

@article{Dean2005StatisticalMO,
  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},
  year={2005},
  volume={72 2 Pt 2},
  pages={
          026125
        }
}
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
5 Citations
Extreme value statistics of correlated random variables: A pedagogical review
Extreme value statistics (EVS) concerns the study of the statistics of the maximum or the minimum of a set of random variables. This is an important problem for any time-series and has applicationsExpand
Fluctuations in the site-disordered traveling salesman problem
We extend a previous statistical mechanical treatment of the traveling salesman problem by defining a discrete 'site-disordered' problem in which fluctuations about saddle points can be computed. TheExpand
Density of near-extreme events.
TLDR
Satisfactory agreement is found between the near-maximum crowding in the summer temperature reconstruction data of western Siberia and the theoretical prediction. Expand
The centred travelling salesman at high temperature
A recently formulated statistical mechanics method is used to study the phase transition occurring in a generalization of the travelling salesman problem (TSP) known as the centred TSP. The methodExpand
Application de la mécanique statistique à trois problèmes hors d'équilibre : algorithmes, épidémies, milieux granulaires
Cette these de doctorat etudie trois problemes a l'aide des outils de la mecanique statistique. Nous montrons l'existence du phenomene d'universalite critique pour la transition de phases dynamiqueExpand

References

SHOWING 1-10 OF 19 REFERENCES
Spin Glass Theory and Beyond
This book contains a detailed and self-contained presentation of the replica theory of infinite range spin glasses. The authors also explain recent theoretical developments, paying particularExpand
"J."
however (for it was the literal soul of the life of the Redeemer, John xv. io), is the peculiar token of fellowship with the Redeemer. That love to God (what is meant here is not God’s love to men)Expand
The Art in Computer Programming
TLDR
Here the authors haven’t even started the project yet, and already they’re forced to answer many questions: what will this thing be named, what directory will it be in, what type of module is it, how should it be compiled, and so on. Expand
E
  • 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
Proc
  • Cam. Phil. Soc. 55 299
  • 1959
Mech
  • L01001
  • 2005
A
  • 37, 1125
  • 2004
Eur
  • Phys. J. B 37, 383
  • 2004
Theoretical Computer Science 265
  • 3
  • 2001
Phys
  • 94, 739
  • 1999
...
1
2
...