ITP OpenIR  > 理论物理所2015年知识产出
The solution space structure of random constraint satisfaction problems with growing domains
Xu, W; Zhang, P; Liu, T; Gong, FZ; Liu, T (reprint author), Peking Univ, Sch EECS, Minist Educ, Key Lab High Confidence Software Technol, Beijing 100871, Peoples R China.
2015
发表期刊JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
期号0页码:P12006
文章类型Article
摘要In 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.
关键词Disordered Systems (Theory) Phase Transformations (Theory)
学科领域Mechanics ; Physics
DOIhttp://dx.doi.org/10.1088/1742-5468/2015/12/P12006
关键词[WOS]EXACT PHASE-TRANSITIONS ; RANDOM K-SAT ; SATISFIABILITY ; THRESHOLD
收录类别SCI
语种英语
WOS类目Mechanics ; Physics, Mathematical
引用统计
文献类型期刊论文
条目标识符http://ir.itp.ac.cn/handle/311006/20762
专题理论物理所2015年知识产出
通讯作者Liu, T (reprint author), Peking Univ, Sch EECS, Minist Educ, Key Lab High Confidence Software Technol, Beijing 100871, Peoples R China.
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GB/T 7714
Xu, W,Zhang, P,Liu, T,et al. The solution space structure of random constraint satisfaction problems with growing domains[J]. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT,2015(0):P12006.
APA Xu, W,Zhang, P,Liu, T,Gong, FZ,&Liu, T .(2015).The solution space structure of random constraint satisfaction problems with growing domains.JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT(0),P12006.
MLA Xu, W,et al."The solution space structure of random constraint satisfaction problems with growing domains".JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT .0(2015):P12006.
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