Balanced Integer Solutions of Linear Equations

Part of the Springer Optimization and Its Applications book series (SOIA, volume 91)


We use lattice-based methods in order to get an integer solution of the linear equation \(a_{1}x_{1} + \cdots + a_{n}x_{n} = a_{0},\) 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.


Linear diophantine equation Lattice LLL CVP 

2000 Mathematics Subject Classification:

Primary 11D04 Secondary 11Y50 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Department of InformaticsAristotle University of ThessalonikiThessalonikiGreece

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