Optimal heuristic algorithms for the image of an injective function

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

Research output: Contribution to journalArticlepeer-review


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 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.

Original languageEnglish
Pages (from-to)7-16
Number of pages10
JournalJournal of Mathematical Sciences
Issue number1
StatePublished - Jan 2013
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Mathematics(all)
  • Applied Mathematics


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