Abstract
We consider the problem of deterministically selecting s uniformly random different m-element subsets of {1,..., k}. The only known lower bound for the time to solve this problem is the trivial Ω(sm). The best two previously known solutions are of time O(sm 3 log m log log m) and O(s(k+m)), respectivly. In this paper we present an algorithm whose time comlexity is O(s 2 m 2+sm 2 log m log log m + sm log sm). Thus, for s<m log m log log m this algorithm is the fastest known deterministic algorithm.
The main idea of the algorithm is using a uniform random number generator to efficiently construct biased random numbers.
Partially support by NSF grant CCR-92-23699 and Israel Ministry of Science and Arts grant 6297.
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© 1997 Springer-Verlag Berlin Heidelberg
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Amir, A., Dar, E. (1997). An improved deterministic algorithm for generalized random sampling. In: Bongiovanni, G., Bovet, D.P., Di Battista, G. (eds) Algorithms and Complexity. CIAC 1997. Lecture Notes in Computer Science, vol 1203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62592-5_69
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DOI: https://doi.org/10.1007/3-540-62592-5_69
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