Online variable-weight scheduling with preempting on jobs with linear and exponential penalties

TL;DR

This paper studies online job scheduling with preemption, focusing on weighted jobs with linear or exponential penalties, and proposes algorithms with improved competitive ratios over naive approaches.

Contribution

The paper introduces new online algorithms for preemptive job scheduling with weighted penalties, achieving better competitive ratios than existing methods.

Findings

Naive algorithm has high competitive ratio ($rac{M}{s_{min}}$).

Improved algorithm reduces the ratio to $4\sqrt{rac{M}{s_{min}}} + n\log{rac{Mn}{s_{min}}}$.

Further modification yields an even better ratio of $n\log{rac{Mn}{s_{min}}}$.

Abstract

We analyze the problem of job scheduling with preempting on weighted jobs that can have either linear or exponential penalties. We review relevant literature on the problem and create and describe a few online algorithms that perform competitively with the optimal scheduler. We first describe a na{\" i}ve algorithm, which yields a high competitive ratio ($\Omega(\frac{M}{s_{\min}})$) with the optimal, then provide an algorithm that yields a lower competitive ratio ($4\sqrt{\frac{M}{s_{\min}}} + n\log{\frac{Mn}{s_{\min}}}$). Finally, we make a minor modification to our algorithm to yield an algorithm that has an even better competitive ratio ($n\log{\frac{Mn}{s_{\min}}}$).