Shared multi-processor scheduling

TL;DR

This paper investigates a shared multi-processor scheduling problem aiming to maximize total weighted overlap, providing optimal synchronized schedules and polynomial algorithms for equal weights, with NP-hardness proven for arbitrary weights.

Contribution

It introduces the concept of synchronized schedules for shared multi-processor scheduling and proves NP-hardness for arbitrary weights while offering efficient solutions for equal weights.

Findings

Synchronized schedules are optimal for the problem.

NP-hardness is established for arbitrary weights.

Polynomial-time algorithm exists for equal weights.

Abstract

We study shared multi-processor scheduling problem where each job can be executed on its private processor and simultaneously on one of many processors shared by all jobs in order to reduce the job's completion time due to processing time overlap. The total weighted overlap of all jobs is to be maximized. The problem models subcontracting scheduling in supply chains and divisible load scheduling in computing. We show that synchronized schedules that complete each job at the same time on its private processor and shared processors, if any is actually used by the job, include optimal schedules. We prove that the problem is NP-hard in the strong sense for jobs with arbitrary weights, and we give an efficient, polynomial-time algorithm for the problem with equal weights.