Polynomial-TimeMaximisation Classes: Syntactic Hierarchy

  • Authors:

  • Orestes Bueno;Prabhu Manyem

  • Affiliations:

  • Instituto de Matemática y Ciencias Afines - IMCA, Calle Los Biólogos 245, Urb. San César, Primera Etapa Lima 12, Lima, Perú. E-mail: obueno@imca.edu.pe;Centre for Informatics and Applied Optimisation, School of IT and Mathematical Sciences, University of Ballarat Mount Helen, VIC 3350, Australia. E-mail: prabhu.manyem@gmail.com

  • Venue:
  • Fundamenta Informaticae - Workshop on Combinatorial Algorithms
  • Year:
  • 2008

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Abstract

In Descriptive Complexity, there is a vast amount of literature on decision problems, and their classes such as P, NP, L and NL. However, research on the descriptive complexity of optimisation problems has been limited. In a previous paper [13], we characterised the optimisation versions of P via expressions in second order logic, using universal Horn formulae with successor relations. In this paper, we study the syntactic hierarchy within the class of polynomially bound maximisation problems. We extend the result in the previous paper by showing that the class of polynomially-boundNP (not just P) maximisation problems can be expressed in second-order logic using Horn formulae with successor relations. Finally, we provide an application - we show that the Bin Packing problem with online LIB constraints can be approximated to within a Θ (log n) bound, by providing a syntactic characterisation for this problem.