Journal of Mathematical Sciences

, Volume 188, Issue 1, pp 7–16 | Cite as

Optimal heuristic algorithms for the image of an injective function

  • E. A. Hirsch
  • D. M. Itsykson
  • V. O. Nikolaenko
  • A. V. Smal

The existence of optimal algorithms is not known for any decision problem in NP\P. We consider the problem of testing the membership in the image of an injective function. We construct optimal heuristic algorithms for this problem in both the randomized and deterministic settings (a heuristic algorithm may err on a small fraction \( \frac{1}{d} \) of the inputs; the parameter d is given to it as an additional input.) Thus for this problem we improve an earlier construction of an optimal acceptor (that is optimal on the negative instances only) and also give a deterministic version. Bibliography: 12 titles.


Optimal Algorithm Decision Problem Heuristic Algorithm Additional Input Injective Function 
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Copyright information

© Springer Science+Business Media New York 2012

Authors and Affiliations

  • E. A. Hirsch
    • 1
  • D. M. Itsykson
    • 1
  • V. O. Nikolaenko
    • 2
  • A. V. Smal
    • 1
  1. 1.St. Petersburg Department of the Steklov Mathematical InstituteSt. PetersburgRussia
  2. 2.St. Petersburg Academic UniversitySt. PetersburgRussia

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