Fast methods for solving linear diophantine equations

  • Miguel Filgueiras
  • Ana Paula Tomás
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 727)


We present some recent results from our research on methods for finding the minimal solutions to linear Diophantine equations over the naturals. We give an overview of a family of methods we developed and describe two of them, called Slopes algorithm and Rectangles algorithm. From empirical evidence obtained by directly comparing our methods with others, and which is partly presented here, we are convinced that ours are the fastest known to date when the equation coefficients are not too small (ie., greater than 2 or 3).


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Copyright information

© Springer-Verlag Berlin Heidelberg 1993

Authors and Affiliations

  • Miguel Filgueiras
    • 1
  • Ana Paula Tomás
    • 1
  1. 1.LIACCUniversidade do PortoPortoPortugal

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