Knowledge Management System of Institute of Theoretical Physics, CAS
Qin, SM; Zeng, Y; Zhou, HJ; Qin, SM (reprint author), Chinese Acad Sci, Inst Theoret Phys, Zhong Guan Cun East Rd 55, Beijing 100190, Peoples R China. | |
Spin-glass phase transitions and minimum energy of the random feedback vertex set problem | |
发表期刊 | PHYSICAL REVIEW E |
语种 | 英语 |
摘要 | A feedback vertex set (FVS) of an undirected graph contains vertices from every cycle of this graph. Constructing a FVS of sufficiently small cardinality is very difficult in the worst cases, but for random graphs this problem can be efficiently solved by converting it into an appropriate spin-glass model [H.-J. Zhou, Eur. Phys. J. B 86, 455 (2013)]. In the present work we study the spin-glass phase transitions and the minimum energy density of the random FVS problem by the first-step replica-symmetry-breaking (1RSB) mean-field theory. For both regular random graphs and Erdos-Renyi graphs, we determine the inverse temperature beta(1) at which the replica-symmetric mean-field theory loses its local stability, the inverse temperature beta(d) of the dynamical (clustering) phase transition, and the inverse temperature beta(s) of the static (condensation) phase transition. These critical inverse temperatures all change with the mean vertex degree in a nonmonotonic way, and beta(d) is distinct from beta(s) for regular random graphs of vertex degrees K > 60, while beta(d) are identical to beta(s) for Erdos-Renyi graphs at least up to mean vertex degree c = 512. We then derive the zero-temperature limit of the 1RSB theory and use it to compute the minimum FVS cardinality. |
2016 | |
卷号 | 94期号:2页码:22146 |
合作性质 | 国内 |
学科领域 | Physics |
DOI | http://dx.doi.org/10.1103/PhysRevE.94.022146 |
收录类别 | SCI |
引用统计 | |
文献类型 | 期刊论文 |
条目标识符 | http://ir.itp.ac.cn/handle/311006/21262 |
专题 | SCI期刊论文 计算平台成果 |
通讯作者 | Qin, SM (reprint author), Chinese Acad Sci, Inst Theoret Phys, Zhong Guan Cun East Rd 55, Beijing 100190, Peoples R China. |
推荐引用方式 GB/T 7714 | Qin, SM,Zeng, Y,Zhou, HJ,et al. Spin-glass phase transitions and minimum energy of the random feedback vertex set problem[J]. PHYSICAL REVIEW E,2016,94(2):22146. |
APA | Qin, SM,Zeng, Y,Zhou, HJ,&Qin, SM .(2016).Spin-glass phase transitions and minimum energy of the random feedback vertex set problem.PHYSICAL REVIEW E,94(2),22146. |
MLA | Qin, SM,et al."Spin-glass phase transitions and minimum energy of the random feedback vertex set problem".PHYSICAL REVIEW E 94.2(2016):22146. |
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文件名称/大小 | 文献类型 | 版本类型 | 开放类型 | 使用许可 | ||
Spin-glass phase tra(416KB) | 期刊论文 | 出版稿 | 开放获取 | CC BY-NC-SA | 请求全文 |
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