An Improved Deterministic Algorithm for Generating Different Many-Element Random Samples

We consider the problem of deterministically selecting s uniformly random diierent m-element subsets of f1; :::; kg. The only known lower bound for the time to solve this problem is the trivial (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 eeciently construct biased random numbers.