The solution space structure of random constraint satisfaction problems with growing domains

CORC > 理论物理研究所 > 中国科学院理论物理研究所 > 理论物理所科研产出 > 理论物理所1978-2010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
刊名	JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
	2015
期号	0 页码:P12006
关键词	disordered systems (theory) phase transformations (theory)
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.
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.
学科主题	Mechanics ; Physics
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
内容类型	期刊论文
源URL	[http://ir.itp.ac.cn/handle/311006/20762]
专题	理论物理研究所_理论物理所1978-2010年知识产出
推荐引用方式 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.(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.