Distortion-Oblivious Algorithms for Minimizing Flow Time

TL;DR

This paper introduces the first distortion-oblivious online scheduling algorithms for minimizing flow time, achieving nearly optimal competitive ratios without prior knowledge of input distortion levels.

Contribution

It presents the first algorithms that are competitive for all distortions without prior knowledge, improving previous results from STOC 2021 with nearly optimal bounds.

Findings

Achieves () competitive ratio for all distortions

Improves previous algorithms from (^2) to ()

Establishes a nearly tight lower bound of  on competitiveness

Abstract

We consider the classic online problem of scheduling on a single machine to minimize total flow time. In STOC 2021, the concept of robustness to distortion in processing times was introduced: for every distortion factor $\mu$, an $O(\mu^2)$-competitive algorithm $\operatorname{ALG}_{\mu}$ which handles distortions up to $\mu$ was presented. However, using that result requires one to know the distortion of the input in advance, which is impractical. We present the first \emph{distortion-oblivious} algorithms: algorithms which are competitive for \emph{every} input of \emph{every} distortion, and thus do not require knowledge of the distortion in advance. Moreover, the competitive ratios of our algorithms are $\tilde{O}(\mu)$, which is a quadratic improvement over the algorithm from STOC 2021, and is nearly optimal (we show a randomized lower bound of $\Omega(\mu)$ on competitiveness).