Distortion-Oblivious Algorithms for Minimizing Flow Time

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 𝜇, an 𝑂 (𝜇 2 )-competitive algorithm ALG 𝜇 which handles distortions up to 𝜇 was presented. However, using that result requires one to know the distortion of the input in advance, which is impractical.

We present the first distortion-oblivious algorithms: algorithms which are competitive for every input of every distortion, and thus do not require knowledge of the distortion in advance. Moreover, the competitive ratios of our algorithms are Õ (𝜇), which is a quadratic improvement over the algorithm from STOC 2021, and is nearly optimal (we show a randomized lower bound of Ω(𝜇) on competitiveness).