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Some Structural and Algorithmic Properties of the Maximum Feasible Subsystem Problem

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Book cover Integer Programming and Combinatorial Optimization (IPCO 1999)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1610))

Abstract

We consider the problem Max FS: For a given infeasible linear system, determine a largest feasible subsystem. This problem has interesting applications in linear programming as well as in fields such as machine learning and statistical discriminant analysis. Max FS is N P-hard and also difficult to approximate. In this paper we examine structural and algorithmic properties of Max FS and of irreducible infeasible subsystems (IISs), which are intrinsically related, since one must delete at least one constraint from each IIS to attain feasibility. In particular, we establish: (i) that finding a smallest cardinality IIS is N P-hard as well as very difficult to approximate; (ii) a new simplex decomposition characterization of IISs; (iii) that for a given clutter, realizability as the IIS family for an infeasible linear system subsumes the Steinitz problem for polytopes; (iv) some results on the feasible subsystem polytope whose vertices are incidence vectors of feasible subsystems of a given infeasible system.

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Author information

Authors and Affiliations

  1. School of OR&IE, Rhodes Hall, Cornell University, Ithaca, NY, 14853, USA

    Edoardo Amaldi & Leslie E. Trotter Jr.

  2. Department of Mathematics, MA 7-1, TU Berlin, Germany

    Marc E. Pfetsch

Authors
  1. Edoardo Amaldi
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  2. Marc E. Pfetsch
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  3. Leslie E. Trotter Jr.
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Editor information

Editors and Affiliations

  1. GSIA, Carnegie Mellon University, Schenley Park, Pittsburgh, PA, 15213, USA

    Gérard Cornuéjols

  2. Institut für Mathematik, Technische Universität Graz, Steyrergasse 30, A-8010, Graz, Austria

    Rainer E. Burkard  & Gerhard J. Woeginger  & 

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© 1999 Springer-Verlag Berlin Heidelberg

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Amaldi, E., Pfetsch, M.E., Trotter, L.E. (1999). Some Structural and Algorithmic Properties of the Maximum Feasible Subsystem Problem. In: Cornuéjols, G., Burkard, R.E., Woeginger, G.J. (eds) Integer Programming and Combinatorial Optimization. IPCO 1999. Lecture Notes in Computer Science, vol 1610. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-48777-8_4

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  • DOI: https://doi.org/10.1007/3-540-48777-8_4

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-66019-4

  • Online ISBN: 978-3-540-48777-7

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