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A Polyhedral Description of Kernels
Chen, Qin1; Chen, Xujin2; Zang, Wenan3
AbstractLet 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.
Keyworddigraph kernel polytope algorithm complexity
Funding ProjectNational 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 Research AreaOperations Research & Management Science ; Mathematics
WOS SubjectOperations Research & Management Science ; Mathematics, Applied
WOS IDWOS:000379496000014
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Document Type期刊论文
Corresponding AuthorChen, Qin
Affiliation1.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
Recommended Citation
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.
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