A Polyhedral Description of Kernels

doi:10.1287/moor.2015.0764

CSpace > 应用数学研究所

	A Polyhedral Description of Kernels
	Chen, Qin 1; Chen, Xujin2 ; Zang, Wenan 3
	2016-08-01
发表期刊	MATHEMATICS OF OPERATIONS RESEARCH
ISSN	0364-765X
卷号	41 期号:3 页码:969-990
摘要	Let G be a digraph and let pi(G) be the linear system consisting of nonnegativity, stability, and domination inequalities. We call G kernel ideal if pi(H) defines an integral polytope for each induced subgraph H of G, and we call G kernel Mengerian if pi(H) is totally dual integral (TDI) for each induced subgraph H of G. In this paper we show that a digraph is kernel ideal iff it is kernel Mengerian iff it contains none of three forbidden structures; our characterization yields a polynomial-time algorithm for the minimum weighted kernel problem on kernel ideal digraphs. We also prove that it is NP-hard to find a kernel of minimum size even in a planar bipartite digraph with maximum degree at most three.
关键词	digraph kernel polytope algorithm complexity
DOI	10.1287/moor.2015.0764
语种	英语
资助项目	National Natural Science Foundation of China[11222109] ; Chinese Academy of Sciences Program for Cross and Cooperative Team of Science and Technology Innovation ; Research Grants Council of Hong Kong
WOS研究方向	Operations Research & Management Science ; Mathematics
WOS类目	Operations Research & Management Science ; Mathematics, Applied
WOS记录号	WOS:000379496000014
出版者	INFORMS
引用统计
文献类型	期刊论文
条目标识符	http://ir.amss.ac.cn/handle/2S8OKBNM/23141
专题	应用数学研究所
通讯作者	Chen, Qin
作者单位	1.China Jiliang Univ, Dept Math, Hangzhou 310018, Zhejiang, Peoples R China 2.Chinese Acad Sci, Inst Appl Math, Beijing 100190, Peoples R China 3.Univ Hong Kong, Dept Math, Hong Kong, Hong Kong, Peoples R China
推荐引用方式 GB/T 7714	Chen, Qin,Chen, Xujin,Zang, Wenan. A Polyhedral Description of Kernels[J]. MATHEMATICS OF OPERATIONS RESEARCH,2016,41(3):969-990.
APA	Chen, Qin,Chen, Xujin,&Zang, Wenan.(2016).A Polyhedral Description of Kernels.MATHEMATICS OF OPERATIONS RESEARCH,41(3),969-990.
MLA	Chen, Qin,et al."A Polyhedral Description of Kernels".MATHEMATICS OF OPERATIONS RESEARCH 41.3(2016):969-990.