Spin glass approach to the feedback vertex set problem

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	Spin glass approach to the feedback vertex set problem
	Zhou, HJ
刊名	EUROPEAN PHYSICAL JOURNAL B
	2013
卷号	86 期号:11 页码:455
关键词	REGULATORY NETWORKS GRAPHS ALGORITHM DYNAMICS
ISSN号	1434-6028
通讯作者	Zhou, HJ (reprint author), Chinese Acad Sci, Inst Theoret Phys, State Key Lab Theoret Phys, Zhong Guan Cun East Rd 55, Beijing 100190, Peoples R China.
英文摘要	A feedback vertex set (FVS) of an undirected graph is a set of vertices that contains at least one vertex of each cycle of the graph. The feedback vertex set problem consists of constructing a FVS of size less than a certain given value. This combinatorial optimization problem has many practical applications, but it is in the nondeterministic polynomial-complete class of worst-case computational complexity. In this paper we define a spin glass model for the FVS problem and then study this model on the ensemble of finite-connectivity random graphs. In our model the global cycle constraints are represented through the local constraints on all the edges of the graph, and they are then treated by distributed message-passing procedures such as belief propagation. Our belief propagation-guided decimation algorithm can construct nearly optimal feedback vertex sets for single random graph instances and regular lattices. We also design a spin glass model for the FVS problem on a directed graph. Our work will be very useful for identifying the set of vertices that contribute most significantly to the dynamical complexity of a large networked system.
学科主题	Physics
收录类别	SCI
资助信息	National Basic Research Program of China [2013CB932804]; Chinese Academy of Sciences [KJCX2-EW-J02]; National Science Foundation of China [11121403, 11225526]
原文出处	http://dx.doi.org/10.1140/epjb/e2013-40690-1
语种	英语
WOS记录号	WOS:000326722600002
公开日期	2014-04-25
内容类型	期刊论文
源URL	[http://ir.itp.ac.cn/handle/311006/15246]
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	Zhou, HJ. Spin glass approach to the feedback vertex set problem[J]. EUROPEAN PHYSICAL JOURNAL B,2013,86(11):455.
APA	Zhou, HJ.(2013).Spin glass approach to the feedback vertex set problem.EUROPEAN PHYSICAL JOURNAL B,86(11),455.
MLA	Zhou, HJ."Spin glass approach to the feedback vertex set problem".EUROPEAN PHYSICAL JOURNAL B 86.11(2013):455.