On the structure of combinatorial problems and structure preserving reductions

  • Giorgio Ausiello
  • Alessandro D'Atri
  • Marco Protasi
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 52)


In this paper the concept of combinatorial problem associated to an optimization problem is defined. A partial ordering over an optimization problem is then introduced: all input elements of an optimization problem are classified according to their "structure" (based on the number of approximate solutions of different measure) and then the classes of elements are partially ordered according to the richness of their structures. In this way structure preserving reductions among NP-complete problems can be introduced and some conditions for a reduction to preserve the structure of a combinatorial problem are given.


Approximate Solution Combinatorial Problem Combinatorial Structure Structure Preserve Finite Graph 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1977

Authors and Affiliations

  • Giorgio Ausiello
    • 1
  • Alessandro D'Atri
    • 2
  • Marco Protasi
    • 3
  1. 1.Centro di Studio dei Sistemi di Controllo e Calcolo Automatici del CNRRoma
  2. 2.Istituto di Automatica dell'Università di RomaRoma
  3. 3.Istituto di Matematica dell'Università di Roma, Piazzale delle ScienzeRoma

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