| Regular Decomposition in Integer Programming |
| Received:June 07, 2017 Revised:July 20, 2017 |
| Key Words:
integer programming regular decompositions binomial ideal universal Gr\"{o}bner bases state polytope
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| Fund Project:Supported by the National Natural Science Foundation of China (Grant Nos.11671068; 11271060), Fundamental Research of Civil Aircraft (Grant No.MJ-F-2012-04) and the Fundamental Research Funds for the Central Universities (Grant No.DUT16LK38). |
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| Abstract: |
| In this paper, we study the problem of regular decomposition in integer programming. We apply the radical of binomial ideal and universal Gr\"{o}bner bases to get the regular decomposition forms of a finite integer lattice point set. We indicate the relationship between state polytope and regular decompositions, i.e., an edge of state polytope corresponds to a binomial which decides one of regular decomposition forms of a finite integer lattice point set. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2018.02.009 |
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