KMS Of Academy of mathematics and systems sciences, CAS
| The solution space structure of random constraint satisfaction problems with growing domains | |
Xu, Wei1,2; Zhang, Pan3,4; Liu, Tian5; Gong, Fuzhou6
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| 2015-12-01 | |
| Source Publication | JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
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| ISSN | 1742-5468 |
| Pages | 12 |
| Abstract | 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. |
| Keyword | disordered systems (theory) phase transformations (theory) |
| DOI | 10.1088/1742-5468/2015/12/P12006 |
| Language | 英语 |
| WOS Research Area | Mechanics ; Physics |
| WOS Subject | Mechanics ; Physics, Mathematical |
| WOS ID | WOS:000368901900006 |
| Publisher | IOP PUBLISHING LTD |
| Citation statistics | |
| Document Type | 期刊论文 |
| Identifier | http://ir.amss.ac.cn/handle/2S8OKBNM/21854 |
| Collection | 应用数学研究所 |
| Corresponding Author | Liu, Tian |
| Affiliation | 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 |
| 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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