Spin-glass phase transitions and minimum energy of the random feedback vertex set problem

doi:http://dx.doi.org/10.1103/PhysRevE.94.022146

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

	Spin-glass phase transitions and minimum energy of the random feedback vertex set problem
	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.
刊名	PHYSICAL REVIEW E
	2016
卷号	94 期号:2 页码:22146
DOI	http://dx.doi.org/10.1103/PhysRevE.94.022146
英文摘要	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.
学科主题	Physics
语种	英语
内容类型	期刊论文
源URL	[http://ir.itp.ac.cn/handle/311006/21554]
专题	理论物理研究所_理论物理所1978-2010年知识产出
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.