Balanced Integer Solutions of Linear Equations

Konstantinos A. Draziotis ()
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Konstantinos A. Draziotis: Aristotle University of Thessaloniki

A chapter in Applications of Mathematics and Informatics in Science and Engineering, 2014, pp 173-188 from Springer

Abstract: Abstract We use lattice-based methods in order to get an integer solution of the linear equation a 1 x 1 + ⋯ + a n x n = a 0 , $$a_{1}x_{1} + \cdots + a_{n}x_{n} = a_{0},$$ which satisfies the bound constraints | x j | ≤ X j . Further we study the corresponding homogeneous linear equation under constraints and finally we apply our method to Knapsack problem.

Keywords: Linear diophantine equation; Lattice; LLL; CVP; Primary 11D04; Secondary 11Y50 (search for similar items in EconPapers)
Date: 2014
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Persistent link: https://EconPapers.repec.org/RePEc:spr:spochp:978-3-319-04720-1_11

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DOI: 10.1007/978-3-319-04720-1_11

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