Solving a Linear Diophantine Equation with Lower and Upper Bounds on the Variables

  • Karen Aardal
  • Cor Hurkens
  • Arjen K. Lenstra
Conference paper

DOI: 10.1007/3-540-69346-7_18

Part of the Lecture Notes in Computer Science book series (LNCS, volume 1412)
Cite this paper as:
Aardal K., Hurkens C., Lenstra A.K. (1998) Solving a Linear Diophantine Equation with Lower and Upper Bounds on the Variables. In: Bixby R.E., Boyd E.A., Ríos-Mercado R.Z. (eds) Integer Programming and Combinatorial Optimization. IPCO 1998. Lecture Notes in Computer Science, vol 1412. Springer, Berlin, Heidelberg

Abstract

We develop an algorithm for solving a linear diophantine equation with lower and upper bounds on the variables. The algorithm is based on lattice basis reduction, and first finds short vectors satisfying the diophantine equation. The next step is to branch on linear combi- nations of these vectors, which either yields a vector that satisfies the bound constraints or provides a proof that no such vector exists. The research was motivated by the need for solving constrained linear dio- phantine equations as subproblems when designing integrated circuits for video signal processing. Our algorithm is tested with good result on real-life data.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Karen Aardal
    • 1
  • Cor Hurkens
    • 2
  • Arjen K. Lenstra
    • 3
  1. 1.Department of Computer ScienceUtrecht UniversityUtrecht
  2. 2.Department of Mathematics and Computing ScienceEindhoven University of TechnologyEindhoven
  3. 3.Emerging TechnologyCitibank

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