Approximation Classes for Real Number Optimization Problems

  • Uffe Flarup
  • Klaus Meer
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4135)


A fundamental research area in relation with analyzing the complexity of optimization problems are approximation algorithms. For combinatorial optimization a vast theory of approximation algorithms has been developed, see [1]. Many natural optimization problems involve real numbers and thus an uncountable search space of feasible solutions. A uniform complexity theory for real number decision problems was introduced by Blum, Shub, and Smale [4]. However, approximation algorithms were not yet formally studied in their model.

In this paper we develop a structural theory of optimization problems and approximation algorithms for the BSS model similar to the above mentioned one for combinatorial optimization. We introduce a class NPO of real optimization problems closely related to NP . The class NPO has four natural subclasses. For each of those we introduce and study real approximation classes APX and PTAS together with reducibility and completeness notions. As main results we establish the existence of natural complete problems for all these classes.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Uffe Flarup
    • 1
  • Klaus Meer
    • 1
  1. 1.Department of Mathematics and Computer ScienceSyddansk UniversitetOdense MDenmark

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