On the approximability of finding maximum feasible subsystems of linear systems

  • Edoardo Amaldi
  • Viggo Kann
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 775)


We consider the combinatorial problem MAXFLS which consists, given a system of linear relations, of finding a maximum feasible subsystem, that is a solution satisfying as many relations as possible. The approximability of this general problem is investigated for the three types of relations =, ≥ and >. Various constrained versions of MAXFLS where a subset of relations must be satisfied or where the variables take bounded discrete values, are also considered. We show that MAXFLS with =, ≥ or > relations is NP-hard even when restricted to homogeneous systems with bipolar coefficients. The various NP-hard versions of MAXFLS belong to different approximability classes depending on the type of relations and the additional constraints. While MAXFLS with equations and integer coefficients cannot be approximated within ε for some ε > 0 where p is the number of relations, MAXFLS with strict or nonstrict inequalities can be approximated within 2 but not within every constant factor.


Polynomial Time Polynomial Time Approximation Scheme Satisfy Equation Elsevier Science Publishing Company Feasible Subsystem 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1994

Authors and Affiliations

  • Edoardo Amaldi
    • 1
  • Viggo Kann
    • 2
  1. 1.Dep. of MathematicsSwiss Federal Institute of TechnologyLausanne
  2. 2.Dep. of Numerical Analysis and Computing ScienceRoyal Institute of TechnologyStockholm

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