Improved Online Algorithm for Weighted Flow Time

We discuss one of the most fundamental scheduling problem of processing jobs on a single machine to minimize the weighted flow time (weighted response time). Our main result is a O(log P)-competitive algorithm, where P is the maximum-to-minimum processing time ratio, improving upon the O(log(2) P)-competitive algorithm of Chekuri, Khanna and Zhu (STOC 2001). We also design a O(logD)-competitive algorithm, where D is the maximum-to-minimum density ratio of jobs. Finally, we show how to combine these results with the result of Bansal and Dhamdhere (SODA 2003) to achieve a O(log(min(P, D, W)))-competitive algorithm (where W is the maximum-tominimum weight ratio), without knowing P, D, W in advance. As shown by Bansal and Chan (SODA 2009), no constant-competitive algorithm is achievable for this problem.