Abstract

We present and analyze efficient new algorithms for generating a random variate distributed according to a dynamically changing set of weights. The base version of each algorithm generates the discrete random variate in O(log N) expected time and updates a weight in O(2 time in the worst case. We then show how to reduce the update time to O(log N) amortized expected time. The algorithms are simple, practical, and easy to implement. We show how to apply our techniques to a recent lookup table technique in order to obtain expected constant time in the worst case for generation and update, with no assumptions about the input being made. We give parallel algorithms for parallel generation and update having optimal processor-time product. We also apply our techniques to obtain an efficient dynamic algorithm for maintaining ffl-heaps of elements; each query is required to return an element whose value is within an ffl relative factor of the maximal element value. For ffl = 1=polylog(n), each query, insertion, or deletion takes O(log log log n) time.

Citations