Summary: An Improved Deterministic Algorithm for Generating Different
ManyElement Random Samples
Amihood Amir \Lambda
Emanuel Dar y
November 19, 1996
We consider the problem of deterministically selecting s uniformly random different melement subsets
of f1; :::; kg. The only known lower bound for the time to solve this problem is the
trivial\Omega\Gamma 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.
When writing heuristics or randomized algorithms one needs efficient souces of randomness. We distinguish