I. Gent, E. MacIntyre, P. Prosser, B. Smith, and T. Walsh. Random constraint satisfaction: flaws and structure. In Constraints, 6(4), pages 345--372, 2001.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....the average number of checks and the average time required for C and T by MAC 2001 and MAC 3 d for the tasks of making the problem arc consistent before starting search and for deciding the satisfiability of each problem using MAC search. All problems were run to completion. Frost et al. s model B [Gent et al. 2001] random problem generator was used to generate the problems (http: www.lirmm.fr bessiere generator.html) 14 2.0e 04 4.0e 04 6.0e 04 8.0e 04 1.0e 05 1.2e 05 1.4e 05 1.6e 05 1.8e 05 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 tightness density = 0.05 density = 0.10 density = 0.15 density = 0.20 density ....

Ian Gent, Ewan MacIntyre, Patrick Prosser, Barbara Smith, and Toby Walsh. Random constraint satisfaction: Flaws and structure. Constraints, 6(4):345--372, 2001.

....uniform tightness T in f ( i=20; j=20 ) 1 i; j 19 g we generated 50 random CSPs. Next we computed the average number of checks and the average time that was required for deciding the satisfiability of each problem using MAC search. All problems were run to completion. Frost et al. s model B [Gent et al. 2001] random problem generator was used to generate the problems (http: www.lirmm.fr bessiere generator.html) The test was carried out in parallel on 50 identical machines. All machines were Intel Pentium III machines, running SuSe Linux 8.0, having 125 MB of RAM, having a 256 KB cach size, and ....

Ian Gent, Ewan MacIntyre, Patrick Prosser, Barbara Smith, and Toby Walsh. Random constraint satisfaction: Flaws and structure. Constraints, 6(4):345--372, 2001.

....i.e. a constraint which includes every possible restriction amongst its k variables. Model A2 avoided this particular problem, but had other equally damaging problems as long as M was of order Theta(n) as is usually the case) for all but small values of m: m d k Gamma1 (Gent et al. [11] showed that these small values of m are indeed not flawed) 11] provides a survey of models used in previous research, and found that roughly 3 4 of papers used models which were uninteresting in the sense described above. Furthermore, those models which were interesting (mostly Model A2 with m ....

....amongst its k variables. Model A2 avoided this particular problem, but had other equally damaging problems as long as M was of order Theta(n) as is usually the case) for all but small values of m: m d k Gamma1 (Gent et al. [11] showed that these small values of m are indeed not flawed) [11] provides a survey of models used in previous research, and found that roughly 3 4 of papers used models which were uninteresting in the sense described above. Furthermore, those models which were interesting (mostly Model A2 with m d k Gamma1 ) seem to have been accidentally interesting in ....

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I. Gent, E. MacIntyre, P. Prosser, B. Smith and T. Walsh. Random constraint satisfaction: flaws and structure. (submitted).

....changing the degree of the node. However, since the probability of getting the universal relation is very low, we ignore this in the following. 295 Renz Nebel This way of generating random instances is very similar to the way random CSP instances over nite domains are usually generated (Gent, MacIntyre, Prosser, Smith, Walsh, 2001). Achlioptas et al. 1997) found that the standard models for generating random CSP instances over nite domains lead to trivially awed instances for n 1, i.e. instances become locally inconsistent without having to propagate constraints. Since we are using CSP instances over in nite domains, ....

Gent, I., MacIntyre, E., Prosser, P., Smith, B., & Walsh, T. (2001). Random constraint satisfaction: Flaws and structure. CONSTRAINTS, 6 (4), 345-372.

....of Cheeseman et al. 1991] many NP complete combinatorial search problems have been shown to have the phase transition and the associated easy hard easy pattern of hardness. The hardest instances usually occur around the solubility threshold [Cook and Mitchell, 1997, Culberson and Gent, 2000, Gent et al. 1998, Kirkpatrick and Selman, 1994, Vandegriend and Culberson, 1998] In this paper, we analyze the NK landscape model from the perspective of threshold phenomena and phase transitions. We establish two random models for the decision problem of NK landscapes and study the threshold phenomena and the ....

....we study the xed ratio model N(n; k; z) In this model, we require that each local tness function has xed number of zero values so that the trivially insoluble situation in the uniform probability model is avoided. We note that the same idea has been used in the study of the awless CSP [Gent et al. 1998]. We will establish several upper bounds on the solubility threshold of the parameter z, and theoretically prove that random instances generated with the parameter z above these upper bounds can be solved with probability asymptotic to 1 by polynomial (even linear) algorithms. 3.2.1 The Upper ....

Ian Gent, Ewan MacIntyre, Patrick Prosser, Barbara Smith, and Toby Walsh. Random constraint satisfaction: Flaws and structure. Technical Report APES-08-1998, APES Research Group, 1998.

....we study the xed ratio model N(n; k; z) In this model, we require that each local tness function has xed number of zero values so that the trivially insoluble situation in the uniform probability model is avoided. We noticed that the same idea has been used in the study of the awless CSP [GMP98]. We will establish several upper bounds on the solvability threshold of the parameter z, and theoretically prove that random instances generated with the parameter z above these upper bounds can be solved with probability asymptotic to 1 by polynomial(even linear) algorithms. Recall that in ....

I.P.Gent, E.MacIntyre, P.Prosser, B.M.Smith, T.Walsh, \Random Constraint Satisfaction: Flaws and Structure", APES Research Group, University of Strathclyde Report APES-08-1998, 1998. http://www.cs.strath.ac.uk/ apes/reports/apes-08-1998.ps.gz

.... CSP tasks are computationally intractable (NP hard) Dechter, 1998) In recent years random constraint satisfaction problems have also received great attention, both from an experimental and a theoretical point of view (Achlioptas et al. 1999; Cheeseman et al. 1991; Frost Dechter, 1994; Gent et al. 1999; Hogg, 1996; Larrosa Meseguer, 1996; Prosser, 1996; Purdom, 1997; Smith Dyer, 1996; Smith, 1999; Williams c 2000 AI Access Foundation and Morgan Kaufmann Publishers. All rights reserved. Xu Li Hogg, 1994) Williams and Hogg (1994) developed a technique to predict where the hardest ....

....on the phase transition and to indicate the accuracy of the prediction. Recently, a theoretical result by Achlioptas et al. 1999) shows that many models commonly used for generating random CSP instances do not have an asymptotic threshold due to the presence of awed variables. More recently, Gent et al. 1999) have shown how to introduce structure into the con ict matrix to eliminate aws. In this paper we propose a new type of random CSP model, called Model RB, which is a revision to the standard Model B (Gent et al. 1999; Smith Dyer, 1996) It is proved that the phase transition phenomenon does ....

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Gent, I., MacIntyre, E., Prosser, P., Smith, B., & Walsh, T. (1999). Random constraint satisfaction: Flaws and structure. Constraints. submitted. Online at \ http://www.cs.strath.edu.uk/~apes/apesreports.html".

....popular CSP models do not have a phase transition in this asymptotic sense: asymptotically they are almost always unsatisfiable, regardless of constraint density. As the number of variables gets large, almost all instances from these models have a very small unsatisfiable sub problem. Following [1, 8, 13, 14] we denote by Model B the distribution of random binary CSPs generated as follows. For an instance with n variables, domain size d, constraint probability p (0 p 1; p is proportional to 1=n) and constraint tightness t, 0 t 1; constant) select uniformly at random a collection of p ....

....and p2 for tightness) Achlioptas et al. showed that, when t 1=d, instances distributed according to Models B and C are asymptotically almost always unsatisfiable, and thus have no phase transition. Recently, Gent [7] showed that Models B and C do have a phase transition when t 1=d. Gent et al. [8] proposed a flawless version of Model B, in which the nature of the constraints is restricted so that the particular unsatisfiable sub problems observed by Achlioptas et al. cannot occur. For a particular version of this, which they call strongly flawless , they show that a phase transition ....

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Ian P. Gent, Ewan MacIntyre, Patrick Prosser, Barbara M. Smith, and Toby Walsh, `Random constraint satisfaction: Flaws and structure', Technical Report APES-08-1998, APES Group, (1998).

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Gent, I.P., MacIntyre, E., Prosser, P., Smith, B.M., Walsh, T.: Random constraint satisfaction: Flaws and structure. Constraints 6 (2001) 345--372

....all con icts for a constraint are selected together, there is a simple way to generate awless instances. Given a pair of variables between which we wish to construct a constraint, we choose a random 1 Unfortunately the mistake is present in the original Research Report version of this paper [25], so we ask readers to use de nitions from this paper and not the original report. In particular, note that our de nition of awless here corresponds to the de nition of strongly awless in the original. v2 1 2 3 1 0 0 1 v1 2 0 0 1 3 1 1 0 Fig. 1. A con ict matrix which is arc consistent ....

I.P. Gent, E. MacIntyre, P. Prosser, B.M. Smith, and T. Walsh. Random constraint satisfaction: Flaws and structure. Technical Report APES-08-1998, APES Research Group, 1998.

....independently with probability p 2 . If both p 1 and p 2 are treated as probabilities, we get the model termed Model A in [14] if both p 1 and p 2 are proportions, we get Model B. Many experimental and theoretical studies of random binary CSPs have used a model equivalent to one of these (see [5] or [11] for a survey) Sometimes, p 1 is treated as a proportion and p 2 as a probability, giving Model D, and for completeness, Model C has p 1 as a probability and p 2 as a proportion. In Models B and D, the constraint density, p 1 , cannot vary continuously, since the number of constraints ....

....the expected number of solutions, E(N) is equal to 1. Since E(N) m n (1 p 2 ) nd=2 , if m and d are xed as n increases, the value of p 2 for which E(N) 1 will also be constant. However, this has been shown to be a poor predictor of the crossover point when the constraint graph is sparse. In [5], it was shown that, if the degree of the constraint graph rather than the constraint density is kept constant, the diculties identi ed by Achlioptas at al. emerge much more slowly as problem size increases. Nevertheless, their asymptotic result still holds, so that the crossover point will not ....

I. Gent, E. MacIntyre, P. Prosser, B. Smith, and T. Walsh. Random Constraint Satisfaction: Flaws and Structure. Research Report 98.23, School of Computer Studies, University of Leeds, 1998. Revised following reviewers' comments for Constraints.

....constraint, we choose a random permutation of 1; 2; 3 : m. The set of goods based on this permutation is simply f(1; 1) 2; 2) 3; 3) m; m) g. Any conflict matrix that contains 2 Unfortunately the mistake is present in the original Research Report version of this paper [25], so we ask readers to use definitions from this paper and not the original report. these goods cannot give a flawed value. We therefore remove the goods just chosen from the set of all possible conflicts. We now randomly reorder the remaining set, and take the first p 2 m 2 elements as the ....

I.P. Gent, E. MacIntyre, P. Prosser, B.M. Smith, and T. Walsh. Random constraint satisfaction: Flaws and structure. Technical Report APES-08-1998, APES Research Group, 1998.

No context found.

I. Gent, E. MacIntyre, P. Prosser, B. Smith, and T. Walsh. Random constraint satisfaction: flaws and structure. In Constraints, 6(4), pages 345--372, 2001.

No context found.

Ian P. Gent, Ewan MacIntyre, Patrick Prosser, Barbara M. Smith, and Toby Walsh. Random constraint satisfaction: Flaws and structure. Constraints, 6(4):345--372, 2001.

No context found.

Ian Gent, Ewan MacIntyre, Patrick Prosser, Barbara Smith, and Toby Walsh. Random constraint satisfaction: Flaws and structure. Constraints, 6(4):345--372, 2001.

No context found.

I.P. Gent, E. MacIntyre, P. Prosser, B.M. Smith, and T. Walsh. Random constraint satisfaction: Flaws and structure. Technical Report APES-08-1998, APES Research Group, 1998.

No context found.

I. Gent, E. MacIntyre, P. Prosser, B. Smith, and T. Walsh. Random constraint satisfaction: flaws and structure. Journal of Constraints, 6(4):345--372, 2001.

No context found.

Ian P. Gent, Ewan MacIntyre, Patrick Prosser, Barbara M. Smith, and Toby Walsh. Random constraint satisfaction: Flaws and structure. Technical Report APES-08-1998, APES Group, 1998.

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