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题名: The solution space structure of random constraint satisfaction problems with growing domains
作者: Xu, W;  Zhang, P;  Liu, T;  Gong, FZ
刊名: JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
出版日期: 2015
期号: 0, 页码:P12006
关键词: disordered systems (theory) ;  phase transformations (theory)
学科分类: Mechanics ;  Physics
DOI: http://dx.doi.org/10.1088/1742-5468/2015/12/P12006
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.
文章类型: Article
英文摘要: 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.
类目[WOS]: Mechanics ;  Physics, Mathematical
关键词[WOS]: EXACT PHASE-TRANSITIONS ;  RANDOM K-SAT ;  SATISFIABILITY ;  THRESHOLD
收录类别: SCI
语种: 英语
Citation statistics: 
内容类型: 期刊论文
URI标识: http://ir.itp.ac.cn/handle/311006/20762
Appears in Collections:理论物理所2015年知识产出_期刊论文

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Recommended Citation:
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.
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