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Generating All Minimal Integral Solutions to Monotone ∧,∨-Systems of Linear, Transversal and Polymatroid Inequalities

  • L. Khachiyan
  • E. Boros
  • K. Elbassioni
  • V. Gurvich
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3618)

Abstract

We consider monotone ∨, ∧-formulae φ of m atoms, each of which is a monotone inequality of the form f i (x)≥ t i over the integers, where for i = 1,...,m, \(f_i : \mathbb{Z}^n \mapsto \mathbb{R}\) is a given monotone function and t i is a given threshold. We show that if the ∨-degree of φ is bounded by a constant, then for linear, transversal and polymatroid monotone inequalities all minimal integer vectors satisfying φ can be generated in incremental quasi-polynomial time. In contrast, the enumeration problem for the disjunction of m inequalities is NP-hard when m is part of the input. We also discuss some applications of the above results in disjunctive programming, data mining, matroid and reliability theory.

Keywords

Association Rule Disjunctive Normal Form Discrete Apply Mathematic Transversal Function Monotone System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • L. Khachiyan
    • 1
  • E. Boros
    • 2
  • K. Elbassioni
    • 3
  • V. Gurvich
    • 2
  1. 1.Department of Computer ScienceRutgers UniversityPiscatawayUSA
  2. 2.RUTCORRutgers UniversityPiscatawayUSA
  3. 3.Max-Planck-Institut für InformatikSaarbrückenGermany

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