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The solution space structure of random constraint satisfaction problems with growing domains
Xu, Wei1,2; Zhang, Pan3,4; Liu, Tian5; Gong, Fuzhou6
2015-12-01
Source PublicationJOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
ISSN1742-5468
Pages12
AbstractIn this paper we study the solution space structure of model RB, a standard prototype of the constraint satisfaction problem (CSP), with growing domains. Using the first moment method and the second moment method, we rigorously show that in the satisfiable phase close to the satisfiability transition, solutions are clustered into an exponential number of well-separated clusters, with each cluster containing a sub-exponential number of solutions. As a consequence, the system has a clustering (dynamical) transition but no condensation transition. This picture of the phase diagram is different to other classic random CSPs that possess a fixed domain size, such as the K-satisfiability (K-SAT) problem and the graph colouring problem, where a condensation transition exists and is distinctly different to the satisfiability transition. Our result verifies some non-rigorous results obtained using the cavity method from spin glass theory.
Keyworddisordered systems (theory) phase transformations (theory)
DOI10.1088/1742-5468/2015/12/P12006
Language英语
WOS Research AreaMechanics ; Physics
WOS SubjectMechanics ; Physics, Mathematical
WOS IDWOS:000368901900006
PublisherIOP PUBLISHING LTD
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Document Type期刊论文
Identifierhttp://ir.amss.ac.cn/handle/2S8OKBNM/21854
Collection应用数学研究所
Corresponding AuthorLiu, Tian
Affiliation1.Beihang Univ, LMIB, Beijing 100191, Peoples R China
2.Beihang Univ, Sch Math & Syst Sci, Beijing 100191, Peoples R China
3.Santa Fe Inst, Santa Fe, NM 87501 USA
4.Chinese Acad Sci, Inst Theoret Phys, State Key Lab Theoret Phys, Beijing 100190, Peoples R China
5.Peking Univ, Sch EECS, Minist Educ, Key Lab High Confidence Software Technol, Beijing 100871, Peoples R China
6.Chinese Acad Sci, Acad Math & Syst Sci, Inst Appl Math, Beijing 100190, Peoples R China
Recommended Citation
GB/T 7714
Xu, Wei,Zhang, Pan,Liu, Tian,et al. The solution space structure of random constraint satisfaction problems with growing domains[J]. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT,2015:12.
APA Xu, Wei,Zhang, Pan,Liu, Tian,&Gong, Fuzhou.(2015).The solution space structure of random constraint satisfaction problems with growing domains.JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT,12.
MLA Xu, Wei,et al."The solution space structure of random constraint satisfaction problems with growing domains".JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2015):12.
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