The Complexity of Scheduling for p-norms of Flow and Stretch

TL;DR

This paper investigates the computational complexity of finding optimal preemptive schedules based on p-norms of flow and stretch, proving strong NP-hardness for various values of p.

Contribution

It establishes the strong NP-hardness of computing optimal p-norm schedules for flow and stretch, extending understanding of scheduling complexity.

Findings

Optimal p-norm flow scheduling is strongly NP-hard for p in (0,1) and integers p > 1.

Optimal p-norm stretch scheduling is strongly NP-hard for p in (0,1) and integers p > 1.

The results highlight fundamental computational challenges in scheduling optimization.

Abstract

We consider computing optimal k-norm preemptive schedules of jobs that arrive over time. In particular, we show that computing the optimal k-norm of flow schedule, is strongly NP-hard for k in (0, 1) and integers k in (1, infinity). Further we show that computing the optimal k-norm of stretch schedule, is strongly NP-hard for k in (0, 1) and integers k in (1, infinity).