Use of extended euclidean algorithm in solving a system of linear diophantine equations with bounded variables

Authors:
Parthasarathy Ramachandran
Affiliations:
Indian Institute of Science, Bangalore, KA, India
Venue:
ANTS'06 Proceedings of the 7th international conference on Algorithmic Number Theory
Year:
2006

Citing 4
Cited 1

Theory of linear and integer programming

Theory of linear and integer programming
Solution of a linear diophantine equation for nonnegative integers

Journal of Algorithms
A fast method for finding the basis of nonnegative solutions to a linear Diophantine equation

Journal of Symbolic Computation
Solving a System of Linear Diophantine Equations with Lower and Upper Bounds on the Variables

Mathematics of Operations Research

Reachability determination in acyclic Petri nets by cell enumeration approach

Automatica (Journal of IFAC)

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Abstract

We develop an algorithm to generate the set of all solutions to a system of linear Diophantine equations with lower and upper bounds on the variables. The algorithm is based on the Euclid’s algorithm for computing the GCD of rational numbers. We make use of the ability to parametrise the set of all solutions to a linear Diophantine equation in two variables with a single parameter. The bounds on the variables are translated to bounds on the parameter. This is used progressively by reducing a n variable problem into a two variable problem. Computational experiments indicate that for a given number of variables the running times decreases with the increase in the number of equations in the system.