Kirkpatrick, S. and Swendsen, R.H. (1985). Statistical Mechanics and Disordered Systems. CACM, Vol. 28, 1985, 363--373. Home/Search Document Not in Database Summary ACM TOC Related Articles Check |
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Where the REALLY Hard Problems Are - Cheeseman, Kanefsky, Taylor (1991) (327 citations) (Correct)
....sub graph grows very rapidly as a function of the average connectivity as the critical connectivity is approached from below. Also, the sizes of the subgraphs below the threshold show a fractal distribution these properties are related to analogous physical systems, e.g. Kirkpatrick85] 7 ] Our interest in phase transitions arises from the discovery that hard to solve problems occur at such boundaries for many types of problems. The importance of phase transitions for AI is discussed in [Huberman87] 4 ] where it is argued that complex systems composed of many interacting values ....
....values can often be understood at the macroscopic level in terms of a few order parameters that are characteristic of the system as a whole. Summarizing the properties of complex systems through a small set of parameters is routine in statistical mechanics [Fu89] 2 ] Kirkpatrick85] 7 ] This is possible because a large number of local interactions can produce dramatic coordinated macroscopic behavior, such as phase transitions, that do not depend on the detailed interactions within the system. Examples of phase transitions in AI are given in [Karp83] 5 ] Purdom83] 6 ] ....
Kirkpatrick, S. and Swendsen, R. H., "Statistical Mechanics and Disordered Systems", Comm.ACM, 28, 4, 363-373, April 1985
The Statistical Mechanics of k-Satisfaction - Kirkpatrick, Gyorgyi (1994) (7 citations) Self-citation (Kirkpatrick) (Correct)
....it in Table 1. 4 Results of Finite Size Scaling Analysis From Fig. 1, it is clear that the threshold sharpens up for larger values of N . Both the threshold shift and the increasing slope in the curves of Fig. 1 can be accounted for by finite size scaling. See Stauffer and Aharony (1992) or Kirkpatrick and Swendsen (1985). We plot the fraction of samples unsatisfied against the dimensionless rescaled variable, y = N 1= ff Gamma ff c ) ff c : Values for ff c and must be derived from the experimental data. First ff c is determined as the crossing point of the curves for large N in Fig. 1. Then is determined ....
Kirkpatrick, S. and Swendsen, R.H. (1985). Statistical Mechanics and Disordered Systems. CACM, Vol. 28, 1985, 363--373.
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