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International Conference on Principles and Practice of Constraint Programming

CP 1995: Principles and Practice of Constraint Programming — CP '95 pp 18–35Cite as

From Elliott-MacMahon to an algorithm for general linear constraints on naturals

  • Efficient Constraint Handling
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Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 976))

Abstract

We describe a new algorithm for solving a conjunction of linear diophantine equations, inequations and disequations in natural numbers. We derive our algorithm from one proposed by Elliott in 1903 for solving a single homogeneous equation. This algorithm was then extended to solve homogeneous systems of equations by MacMahon. We show how it further extends to an algorithm which solves general linear constraints in nonnegative integers and allows a parallel implementation. This algorithm provides a parametric representation of the solutions from which minimal solutions may be extracted immediately. Moreover, it may be easily implemented in parallel. It has however one drawback: it is redundant which means that the same minimal solution is usually generated many times. We show how this redundancy may be eliminated at the cost of an increase in the space complexity.

This work was partly supported by the SOL project, HCM #CHRX CT92 0053

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Authors and Affiliations

  1. CRIN/CNRS & INRIA-Lorraine, France

    Eric Domenjoud

  2. LIACC/University of Porto, Portugal

    Ana Paula Tomás

Authors
  1. Eric Domenjoud
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  2. Ana Paula Tomás
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Editor information

Ugo Montanari Francesca Rossi

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© 1995 Springer-Verlag Berlin Heidelberg

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Domenjoud, E., Tomás, A.P. (1995). From Elliott-MacMahon to an algorithm for general linear constraints on naturals. In: Montanari, U., Rossi, F. (eds) Principles and Practice of Constraint Programming — CP '95. CP 1995. Lecture Notes in Computer Science, vol 976. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60299-2_2

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  • DOI: https://doi.org/10.1007/3-540-60299-2_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-60299-6

  • Online ISBN: 978-3-540-44788-7

  • eBook Packages: Springer Book Archive

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