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A spin glass approach to the directed feedback vertex set problem
Zhou, HJ; Zhou, HJ (reprint author), Chinese Acad Sci, Key Lab Theoret Phys, Inst Theoret Phys, Zhong Guan Cun East Rd 55, Beijing 100190, Peoples R China.
2016
发表期刊JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT
页码73303
文章类型Article
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.
关键词Spin Glasses (Theory) Message-passing Algorithms
学科领域Mechanics ; Physics
资助者National Basic Research Program of China [2013CB932804] ; National Basic Research Program of China [2013CB932804] ; National Basic Research Program of China [2013CB932804] ; National Basic Research Program of China [2013CB932804] ; National Natural Science Foundation of China [11121403, 11225526] ; National Natural Science Foundation of China [11121403, 11225526] ; National Natural Science Foundation of China [11121403, 11225526] ; National Natural Science Foundation of China [11121403, 11225526] ; Knowledge Innovation Program of Chinese Academy of Sciences [KJCX2-EW-J02] ; Knowledge Innovation Program of Chinese Academy of Sciences [KJCX2-EW-J02] ; Knowledge Innovation Program of Chinese Academy of Sciences [KJCX2-EW-J02] ; Knowledge Innovation Program of Chinese Academy of Sciences [KJCX2-EW-J02] ; National Basic Research Program of China [2013CB932804] ; National Basic Research Program of China [2013CB932804] ; National Basic Research Program of China [2013CB932804] ; National Basic Research Program of China [2013CB932804] ; National Natural Science Foundation of China [11121403, 11225526] ; National Natural Science Foundation of China [11121403, 11225526] ; National Natural Science Foundation of China [11121403, 11225526] ; National Natural Science Foundation of China [11121403, 11225526] ; Knowledge Innovation Program of Chinese Academy of Sciences [KJCX2-EW-J02] ; Knowledge Innovation Program of Chinese Academy of Sciences [KJCX2-EW-J02] ; Knowledge Innovation Program of Chinese Academy of Sciences [KJCX2-EW-J02] ; Knowledge Innovation Program of Chinese Academy of Sciences [KJCX2-EW-J02]
DOIhttp://dx.doi.org/10.1088/1742-5468/2016/07/073303
关键词[WOS]RANDOM REGULAR GRAPHS ; COMPLEX NETWORKS ; ALGORITHM ; DYNAMICS
收录类别SCI
语种英语
资助者National Basic Research Program of China [2013CB932804] ; National Basic Research Program of China [2013CB932804] ; National Basic Research Program of China [2013CB932804] ; National Basic Research Program of China [2013CB932804] ; National Natural Science Foundation of China [11121403, 11225526] ; National Natural Science Foundation of China [11121403, 11225526] ; National Natural Science Foundation of China [11121403, 11225526] ; National Natural Science Foundation of China [11121403, 11225526] ; Knowledge Innovation Program of Chinese Academy of Sciences [KJCX2-EW-J02] ; Knowledge Innovation Program of Chinese Academy of Sciences [KJCX2-EW-J02] ; Knowledge Innovation Program of Chinese Academy of Sciences [KJCX2-EW-J02] ; Knowledge Innovation Program of Chinese Academy of Sciences [KJCX2-EW-J02] ; National Basic Research Program of China [2013CB932804] ; National Basic Research Program of China [2013CB932804] ; National Basic Research Program of China [2013CB932804] ; National Basic Research Program of China [2013CB932804] ; National Natural Science Foundation of China [11121403, 11225526] ; National Natural Science Foundation of China [11121403, 11225526] ; National Natural Science Foundation of China [11121403, 11225526] ; National Natural Science Foundation of China [11121403, 11225526] ; Knowledge Innovation Program of Chinese Academy of Sciences [KJCX2-EW-J02] ; Knowledge Innovation Program of Chinese Academy of Sciences [KJCX2-EW-J02] ; Knowledge Innovation Program of Chinese Academy of Sciences [KJCX2-EW-J02] ; Knowledge Innovation Program of Chinese Academy of Sciences [KJCX2-EW-J02]
WOS类目Mechanics ; Physics, Mathematical
引用统计
文献类型期刊论文
条目标识符http://ir.itp.ac.cn/handle/311006/21602
专题理论物理所SCI论文
通讯作者Zhou, HJ (reprint author), 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,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,&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,et al."A spin glass approach to the directed feedback vertex set problem".JOURNAL OF STATISTICAL MECHANICS-THEORY AND EXPERIMENT (2016):73303.
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