On the relative complexity of subproblems of intractable problems

  • Klaus Ambos-Spies
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 182)


A subproblem of a problem A is the restriction of A to some polynomial time computable set. A set A is subproblem complete (s.c.) if every polynomial time (p-) degree below the p-degree of A contains a subproblem of A. A is decomposition complete (d.c.) if every splitting of the p-degree of A is witnessed by a decomposition of A into two subproblems. We show that all p-cylinders and thus most of the "natural" problems are s.c. and d.c. with respect to p-many-one (Karp) reducibility. We also show, however, that not every problem has these properties. Furthermore, we discuss these completeness properties with respect to p-Turing (Cook) reducibility.


Polynomial Time Natural Problem Complete Problem Intractable Problem Completeness Property 
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 1984

Authors and Affiliations

  • Klaus Ambos-Spies
    • 1
  1. 1.Lehrstuhl für Informatik IIUniversität DortmundGermany

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