Scheduling Algorithms for Procrastinators

TL;DR

This paper investigates scheduling algorithms tailored for procrastinators, focusing on optimal offline policies for increasing speed functions, the challenges of online scheduling, and introducing a new approximation algorithm for minimizing maximum interval stretch.

Contribution

It provides optimal offline scheduling policies for linearly increasing speed functions and introduces a a(1) approximation algorithm for online scheduling to minimize maximum interval stretch.

Findings

Optimal offline policies for linearly increasing speed functions.

Impossibility of perfect online scheduling due to adversarial conditions.

Thrashing policy as a a(1) approximation for maximum interval stretch.

Abstract

This paper presents scheduling algorithms for procrastinators, where the speed that a procrastinator executes a job increases as the due date approaches. We give optimal off-line scheduling policies for linearly increasing speed functions. We then explain the computational/numerical issues involved in implementing this policy. We next explore the online setting, showing that there exist adversaries that force any online scheduling policy to miss due dates. This impossibility result motivates the problem of minimizing the maximum interval stretch of any job; the interval stretch of a job is the job's flow time divided by the job's due date minus release time. We show that several common scheduling strategies, including the "hit-the-highest-nail" strategy beloved by procrastinators, have arbitrarily large maximum interval stretch. Then we give the "thrashing" scheduling policy and show that it is a \Theta(1) approximation algorithm for the maximum interval stretch.