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Linear Programming Using Limited-Precision Oracles

  • Ambros Gleixner
  • Daniel E. SteffyEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11480)

Abstract

Linear programming is a foundational tool for many aspects of integer and combinatorial optimization. This work studies the complexity of solving linear programs exactly over the rational numbers through use of an oracle capable of returning limited-precision LP solutions. Under mild assumptions, it is shown that a polynomial number of calls to such an oracle and a polynomial number of bit operations, is sufficient to compute an exact solution to an LP. Previous work has often considered oracles that provide solutions of an arbitrary specified precision. While this leads to polynomial-time algorithms, the level of precision required is often unrealistic for practical computation. In contrast, our work provides a foundation for understanding and analyzing the behavior of the methods that are currently most effective in practice for solving LPs exactly.

Keywords

Linear programming Oracle complexity Diophantine approximation Exact solutions Symbolic computation Rational arithmetic Extended-precision arithmetic Iterative refinement 

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Konrad-Zuse-Zentrum für Informationstechnik BerlinBerlinGermany
  2. 2.Mathematics and StatisticsOakland UniversityRochesterUSA

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