Dependence System Solvers

• Integer programming problem
• Exact solvers very expensive (exponential or worse)
• Dependence systems trade-off between
  • Efficiency, speed of solver
  • Precision, reducing, number of ‘false positives’
• All systems are conservative
  • Never return ‘no soln’ when there is a solution
  • May return ‘possible soln’ where there is no solution
• Three possible results from a solver

  • ‘no soln’ means there is no integer solution
  • ‘has soln’ means there is an integer solution. Some solvers may enumerate solution
  • ‘possible soln’ means result is inexact.
    Solver cannot prove that there is no solution or a soln
• Characteristics of solvers:
  • Cost
  • Applicability
  • Imprecision

Single Equation

A single dependence eqn can be written as:

Where n: Number of unknowns
: coefficients