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Volumn 271, Issue 5245, 1996, Pages 56-59

Criticality and parallelism in combinatorial optimization

Author keywords

[No Author keywords available]

Indexed keywords

ALGORITHM; ARTICLE; STATISTICAL MODEL; TEMPERATURE; THERMODYNAMICS;

EID: 0030569684     PISSN: 00368075     EISSN: None     Source Type: Journal    
DOI: 10.1126/science.271.5245.56     Document Type: Article
Times cited : (44)

References (24)
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    • (1990) ORSA J Comput. , vol.2 , pp. 4
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    • F. Glover, ORSA J Comput. 1, 190 (1989), ibid 2, 4 (1990); D Cvijović and J. Klinowski, Science 267, 664 (1995)
    • (1995) Science , vol.267 , pp. 664
    • Cvijović, D.1    Klinowski, J.2
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    • B. Demda, Phys. Rev. B 24, 2613 (1981); C. A. Macken and A. S. Perelson, Proc Natl. Acad Sci. U.S.A. 86, 6191 (1989); E. D. Weinberger, Phys Rev. A 44, 6399 (1991).
    • (1981) Phys. Rev. B , vol.24 , pp. 2613
    • Demda, B.1
  • 12
    • 0001697862 scopus 로고
    • B. Demda, Phys. Rev. B 24, 2613 (1981); C. A. Macken and A. S. Perelson, Proc Natl. Acad Sci. U.S.A. 86, 6191 (1989); E. D. Weinberger, Phys Rev. A 44, 6399 (1991).
    • (1991) Phys Rev. A , vol.44 , pp. 6399
    • Weinberger, E.D.1
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    • note
    • This transition persists for small, nonzero, fixed temperatures and broadens at larger temperatures.
  • 15
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    • note
    • The position of the transition also depends on the length of time that we allow the algonthm to run. In all of our numerical experiments, we waited sufficiently long that further increases in running time did not noticeably affect the transition.
  • 17
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    • Oxford Univ Press, Oxford
    • R. J. Creswick et al., Introduction to Renormalization Group Methods in Physics (Wiley, New York, 1992); J. J Binnet et al , The Theory of Cntical Phenomena (Oxford Univ Press, Oxford, 1992).
    • (1992) The Theory of Cntical Phenomena
    • Binnet, J.J.1
  • 19
    • 5644296142 scopus 로고    scopus 로고
    • note
    • Without interaction (K = 0), there will be no transition; this effect persists up to some nonzero degree of interaction (Fig. 1). It requires a sufficient amount of conflict between variables to overcompensate for the downward trend in energy obtained by accepting (in parallel) only spin flips that individually lower the energy
  • 21
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    • S Kirkpatrick and B. Selrnan. Science 264. 1297 (1994), P Cheeseman, B. Kanefsky, W M Taylor, in Proceedings of the 12th International Joint Conference on Artificial Intelligence, (Morgan Kaufmann. San Mateo, CA, 1991), vol. 1, pp 331-337
    • (1994) Science , vol.264 , pp. 1297
    • Kirkpatrick, S.1    Selrnan, B.2
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    • note
    • We thank D Stein for helpful discussions, and H. Abelson, G J Sussman, J. Tsitsiklis, E. Hung, N. Berker, E Todorov, J. Tenenbaum, A. Khwaja, P. Beebee, and the reviewers for useful suggestions. This work was partially supported by Advanced Research Projects Agency grant ARPA ONR-N00014-92-J-4097 and National Science Foundation grant NSF MIP-9001651 (A.G S ), and by Department of Energy grant DOE DE-FG03-93-ER61639, NSF BIR-9218746, and National Institutes of Health grant 5-R01 GM49619 (W G M and S.A K.).


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.