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Abstract: . We outline a technique for studying phase transition behaviour in computational problems using number partitioning as a case study. We first build an "annealed" theory that assumes independence between parts of the number partition problem. Using this theory, we identify a parameter which represents the "constrainedness" of a problem. We determine experimentally the critical value of this parameter at which a rapid transition between soluble and insoluble problems occurs. Finite-size scaling... (Update)
Context of citations to this paper: More
...wish to find a partition into two bags with the same sum. To study this problem, Gent and Walsh have developed an annealed theory [22, 24] in which they average probabilities independently over the different binary digit positions. They call this an annealed theory by...
.... Numerical investigations have shown, however, that large instances of partitioning can be solved exactly within reasonable time [8,4,9]. This surprising fact is based on the existence of perfect partitions, partitions with E 1. The moment an algorithm nds a perfect...
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5: From approximate to optimal solutions: A case study of number partitioning (context) - Korf - 1995
5: Where the really hard problems are - Cheeseman, Kanefsky et al. - 1991
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BibTeX entry: (Update)
Gent, I., and Walsh, T. 1996. Phase transitions and annealed theories: Number partitioning as a case study. In Proceedings of ECAI-96. http://citeseer.ist.psu.edu/article/gent96phase.html More
@inproceedings{ gent96phase,
author = "Ian P. Gent and Toby Walsh",
title = "Phase Transitions and Annealed Theories: Number Partitioning as a Case Study",
booktitle = "European Conference on Artificial Intelligence",
pages = "170-174",
year = "1996",
url = "citeseer.ist.psu.edu/article/gent96phase.html" }
Citations (may not include all citations):4212 Computers and intractability : a guide to the theory of NP-c.. (context) - Garey, Johnson - 1979
329 Where the really hard problems are - Cheeseman, Kanefsky et al. - 1991
320 Hard and easy distributions of SAT problems - Mitchell, Selman et al. - 1992
78 Phase transition and the mushy region in constraint satisfac.. (context) - Smith - 1994
76 Exploiting the deep structure of constraint problems (context) - Williams, Hogg - 1994
63 Easy problems are sometimes hard - Gent, Walsh - 1994
62 The hardest constraint problems: A double phase transition (context) - Hogg, Williams - 1994
59 The constrainedness of search - Gent, MacIntryre et al. - 1996
28 Scaling effects in the CSP phase transition - Gent, MacIntyre et al. - 1995
23 From approximate to optimal solutions: A case study of numbe.. (context) - Korf - 1995
20 Critical behavior in the computational cost of satisfiabilit.. (context) - Selman, Kirkpatrick - 1996
17 The TSP phase transition - Gent, Walsh - 1995
17 Finite-size scaling (context) - Barber - 1983
14 Probabilistic analysis of optimum partitioning (context) - Karmarkar, Karp et al. - 1986
8 The uses and abuses of statistical mechanics in computationa.. (context) - Fu - 1989
4 Criticial behaviour in the satisfiability of random boolean .. (context) - Kirkpatrick, Selman - 1994
1 Pruning with modular arithmetic in NP problems - Gent, Walsh - 1995
The graph only includes citing articles where the year of publication is known.
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Random Constraint Satisfaction: theory meets practice - MacIntyre, Prosser, Smith.. (1998) (Correct)
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