A spin glass approach to the directed feedback vertex set problem

doi:http://dx.doi.org/10.1088/1742-5468/2016/07/073303

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	A spin glass approach to the directed feedback vertex set problem
	Zhou, HJ
刊名	JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
	2016
页码	73303
关键词	spin glasses (theory) RANDOM REGULAR GRAPHS message-passing algorithms COMPLEX NETWORKS ALGORITHM DYNAMICS
DOI	http://dx.doi.org/10.1088/1742-5468/2016/07/073303
英文摘要	A directed graph (digraph) is formed by vertices and arcs (directed edges) from one vertex to another. A feedback vertex set (FVS) is a set of vertices that contains at least one vertex of every directed cycle in this digraph. The directed feedback vertex set problem aims at constructing a FVS of minimum cardinality. This is a fundamental cycle-constrained hard combinatorial optimization problem with wide practical applications. In this paper we construct a spin glass model for the directed FVS problem by converting the global cycle constraints into local arc constraints, and study this model through the replica-symmetric (RS) mean field theory of statistical physics. We then implement a belief propagation-guided decimation (BPD) algorithm for single digraph instances. The BPD algorithm slightly outperforms the simulated annealing algorithm on large random graph instances. The RS mean field results and algorithmic results can be further improved by working on a more restrictive (and more difficult) spin glass model.
学科主题	Mechanics ; Physics
语种	英语
资助机构	National Basic Research Program of China [2013CB932804] ; National Natural Science Foundation of China [11121403, 11225526] ; Knowledge Innovation Program of Chinese Academy of Sciences [KJCX2-EW-J02]
内容类型	期刊论文
源URL	[http://ir.itp.ac.cn/handle/311006/23027]
专题	理论物理研究所_理论物理所1978-2010年知识产出
作者单位	Chinese Acad Sci, Key Lab Theoret Phys, Inst Theoret Phys, Zhong Guan Cun East Rd 55, Beijing 100190, Peoples R China
推荐引用方式 GB/T 7714	Zhou, HJ. A spin glass approach to the directed feedback vertex set problem[J]. JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT,2016:73303.
APA	Zhou, HJ.(2016).A spin glass approach to the directed feedback vertex set problem.JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT,73303.
MLA	Zhou, HJ."A spin glass approach to the directed feedback vertex set problem".JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2016):73303.