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Zapiski Nauchnykh Seminarov POMI, 2012, Volume 399, Pages 15–31 (Mi znsl5219)  
Optimal heuristic algorithms for the image of an injective function

E. A. Hirscha, D. M. Itsyksona, V. O. Nikolaenkob, A. V. Smala

a St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg, Russia
b St. Petersburg Academic University, St. Petersburg, Russia
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Abstract: The existence of optimal algorithms is not known for any decision problem in $\mathbf{NP}\setminus\mathbf{P}$. 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 randomized and deterministic settings (a heuristic algorithm can err on a small fraction $\frac1d$ 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.
Key words and phrases: optimal algorithm, heuristic algorithm.
Received: 31.07.2011
English version:
Journal of Mathematical Sciences (New York), 2013, Volume 188, Issue 1, Pages 7–16
DOI: https://doi.org/10.1007/s10958-012-1102-y
Bibliographic databases:
Document Type: Article
UDC: 510.52
Language: English
Citation: E. A. Hirsch, D. M. Itsykson, V. O. Nikolaenko, A. V. Smal, “Optimal heuristic algorithms for the image of an injective function”, Computational complexity theory. Part X, Zap. Nauchn. Sem. POMI, 399, POMI, St. Petersburg, 2012, 15–31; J. Math. Sci. (N. Y.), 188:1 (2013), 7–16
Citation in format AMSBIB
\Bibitem{HirItsNik12}
\by E.~A.~Hirsch, D.~M.~Itsykson, V.~O.~Nikolaenko, A.~V.~Smal
\paper Optimal heuristic algorithms for the image of an injective function
\inbook Computational complexity theory. Part~X
\serial Zap. Nauchn. Sem. POMI
\yr 2012
\vol 399
\pages 15--31
\publ POMI
\publaddr St.~Petersburg
\mathnet{http://mi.mathnet.ru/znsl5219}
\mathscinet{https://mathscinet.ams.org/mathscinet-getitem?mr=2944998}
\transl
\jour J. Math. Sci. (N. Y.)
\yr 2013
\vol 188
\issue 1
\pages 7--16
\crossref{https://doi.org/10.1007/s10958-012-1102-y}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84871931503}
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