Phase Transition in Multiprocessor Scheduling

TL;DR

This paper investigates the phase transition phenomenon in the NP-hard multiprocessor scheduling problem, analyzing its critical parameters and how it affects the performance of practical algorithms using concepts from physics and crystallography.

Contribution

It introduces a novel analytical framework combining crystallography and statistical mechanics to understand the phase transition in multiprocessor scheduling.

Findings

Identifies the control parameter and critical value of the phase transition.

Shows the transition impacts the performance of practical scheduling algorithms.

Provides finite size corrections to the transition analysis.

Abstract

The problem of distributing the workload on a parallel computer to minimize the overall runtime is known as Multiprocessor Scheduling Problem. It is NP-hard, but like many other NP-hard problems, the average hardness of random instances displays an ``easy-hard'' phase transition. The transition in Multiprocessor Scheduling can be analyzed using elementary notions from crystallography (Bravais lattices) and statistical mechanics (Potts vectors). The analysis reveals the control parameter of the transition and its critical value including finite size corrections. The transition is identified in the performance of practical scheduling algorithms.