TY - JOUR

T1 - Optimal heuristic algorithms for the image of an injective function

AU - Hirsch, E. A.

AU - Itsykson, D. M.

AU - Nikolaenko, V. O.

AU - Smal, A. V.

PY - 2013/1/1

Y1 - 2013/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84871931503&partnerID=8YFLogxK

U2 - 10.1007/s10958-012-1102-y

DO - 10.1007/s10958-012-1102-y

M3 - Article

AN - SCOPUS:84871931503

VL - 188

SP - 7

EP - 16

JO - Journal of Mathematical Sciences

JF - Journal of Mathematical Sciences

SN - 1072-3374

IS - 1

ER -