Regular Decomposition in Integer Programming
Received:June 07, 2017  Revised:July 20, 2017
Key Word: integer programming   regular decompositions   binomial ideal   universal Gr\"{o}bner bases   state polytope  
Fund ProjectL: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).
Author NameAffiliation
Han WANG School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
Chungang ZHU School of Mathematical Sciences, Dalian University of Technology, Liaoning 116024, P. R. China 
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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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