Abstract
Assuming random computational errors in the execution of a RAM program, we discuss how to obtain a correct result with a given confidence bound. An algorithm ALG (requiring A operations) is used in connection with a certificate CERT (requiring C operations, C≤A). CERT assesses the result of ALG, however, it may fail as well. Each operation of ALG (resp. CERT) is repeated k (resp. h) times, and the result of the operation is established by majority voting. Letting π be the success probability of an operation, and 1−δ be the desired confidence on the overall result, k and h are evaluated as functions of A, C, π and δ. The resulting running time is reduced by a factor of up to A/C over the time required without using CERT, for the same value of δ. Two case studies with C
Cite
CITATION STYLE
Luccio, F., & Pedrotti, A. (1997). Design of reliable combinatorial algorithms using certificates. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1203, pp. 147–158). Springer Verlag. https://doi.org/10.1007/3-540-62592-5_68
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