Improved Online Algorithm for Weighted Flow Time

TL;DR

This paper presents improved online algorithms for scheduling jobs to minimize weighted flow time, achieving better competitive ratios that depend logarithmically on job parameter ratios, advancing the state of the art.

Contribution

The authors develop new online algorithms with improved competitive ratios for weighted flow time scheduling, including methods that adapt without prior knowledge of job parameters.

Findings

Achieved an $O( ext{log } P)$-competitive algorithm, improving previous $O( ext{log}^2 P)$ bounds.

Designed an $O( ext{log } D)$-competitive algorithm based on density ratios.

Combined results to create a $O( ext{log}( ext{min}(P,D,W)))$-competitive algorithm without prior parameter knowledge.

Abstract

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 $O(\log D)$-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-to-minimum 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.