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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)

Abstract

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.

Keywords

Polynomial Time Polynomial Time Approximation Scheme Satisfy Equation Elsevier Science Publishing Company Feasible Subsystem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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