Integer Programming and Combinatorial Optimization

Volume 1412 of the series Lecture Notes in Computer Science pp 229-242


Solving a Linear Diophantine Equation with Lower and Upper Bounds on the Variables

  • Karen AardalAffiliated withDepartment of Computer Science, Utrecht University
  • , Cor HurkensAffiliated withDepartment of Mathematics and Computing Science, Eindhoven University of Technology
  • , Arjen K. LenstraAffiliated withEmerging Technology

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We develop an algorithm for solving a linear diophantine equation with lower and upper bounds on the variables. The algorithm is based on lattice basis reduction, and first finds short vectors satisfying the diophantine equation. The next step is to branch on linear combi- nations of these vectors, which either yields a vector that satisfies the bound constraints or provides a proof that no such vector exists. The research was motivated by the need for solving constrained linear dio- phantine equations as subproblems when designing integrated circuits for video signal processing. Our algorithm is tested with good result on real-life data.