Competitive analysis of on-line stream merging algorithms

A popular approach to reduce the server bandwidth in a video-on-demand system is to merge the streams initiated at different times. In recent years, a number of on-line algorithms for stream merging have been proposed; the objective is to minimize either the total bandwidth or the maximum bandwidth over all time. The performance of these algorithms was better understood with respect to the first objective. In particular, the connector algorithm [9] is known to be 0(l)competitive, and the dyadic algorithm [12] is known to have an almost tight bounds on its average total bandwidth requirement. For minimizing maximum bandwidth, existing results are limited to empirical studies only and no algorithm has been known to be competitive. The main contribution of this paper is the first competitive analysis of the connector and the dyadic algorithms with respect to the maximum bandwidth, showing that both algorithms are 4-competitive. We also give a worst-case analysis of the dyadic algorithm with respect to the total bandwidth, revealing that the dyadic algorithm can be tuned to be 3-competitive.