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The Expressive Power of Binary Linear Programming

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Principles and Practice of Constraint Programming — CP 2001 (CP 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2239))

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Abstract

Very efficient solvers for Integer Programming exist, when the constraints and the objective function are linear. In this paper we tackle a fundamental question: what is the expressive power of Integer Linear Programming? We are able to prove that ILP, more precisely Binary LP, expresses the complexity class NP. As a consequence, in principle all specifications of combinatorial problems in NP formulated in constraint languages can be translated as BLP models.

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References

  1. S. Abiteboul, R. Hull, and V. Vianu. Foundations of Databases. Addison Wesley Publ. Co., Reading, Massachussetts, 1995.

    MATH  Google Scholar 

  2. R. Fagin. Generalized First-Order Spectra and Polynomial-Time Recognizable Sets. In R. M. Karp, editor, Complexity of Computation, pages 43–74. AMS, 1974.

    Google Scholar 

  3. Robert Fourer, David M. Gay, and Brian W. Kernigham. AMPL: A Modeling Language for Mathematical Programming. International Thomson Publishing, 1993.

    Google Scholar 

  4. P. G. Kolaitis and C. H. Papadimitriou. Why not negation by fixpoint? J. of Computer and System Sciences, 43:125–144, 1991.

    Article  MathSciNet  Google Scholar 

  5. Philippe Refalo. Linear formulation of constraint programming models and hybrid solvers. In Proc. of CP 2000, LNCS, pages 369–383. Springer-Verlag, 2000.

    MATH  Google Scholar 

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica e Sistemistica, Universitá di Roma “La Sapienza”, Via Salaria 113, I-00198, Roma, Italy

    Marco Cadoli

Authors
  1. Marco Cadoli
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Editor information

Editors and Affiliations

  1. Department of Computer Science, The University of York, YO10 5DD, Heslington, York, UK

    Toby Walsh

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© 2001 Springer-Verlag Berlin Heidelberg

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Cadoli, M. (2001). The Expressive Power of Binary Linear Programming. In: Walsh, T. (eds) Principles and Practice of Constraint Programming — CP 2001. CP 2001. Lecture Notes in Computer Science, vol 2239. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45578-7_41

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  • DOI: https://doi.org/10.1007/3-540-45578-7_41

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-42863-3

  • Online ISBN: 978-3-540-45578-3

  • eBook Packages: Springer Book Archive

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