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

doi:10.1088/1742-5468/2015/12/P12006

CORC > 数学与系统科学研究院 > 中国科学院数学与系统科学研究院 > 应用数学研究所

	The solution space structure of random constraint satisfaction problems with growing domains
	Xu, Wei 1,2; Zhang, Pan 3,4; Liu, Tian 5; Gong, Fuzhou6
刊名	JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
	2015-12-01
页码	12
关键词	disordered systems (theory) phase transformations (theory)
ISSN号	1742-5468
DOI	10.1088/1742-5468/2015/12/P12006
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.
WOS研究方向	Mechanics ; Physics
语种	英语
出版者	IOP PUBLISHING LTD
WOS记录号	WOS:000368901900006
内容类型	期刊论文
源URL	[http://ir.amss.ac.cn/handle/2S8OKBNM/21853]
专题	应用数学研究所
通讯作者	Liu, Tian
作者单位	1.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
推荐引用方式 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.