Scheduling Chained Multiprocessor Tasks onto Large Multiprocessor System

TL;DR

This paper introduces an optimal scheduling algorithm for uniform and monotone chains of multiprocessor tasks, compares heuristics for arbitrary chains, and discusses the complexity of scheduling splitable and non-splitable tasks.

Contribution

It presents a longest chain maximum processor scheduling algorithm proven optimal for specific chain types and evaluates heuristics for more complex chain scheduling.

Findings

Longest chain maximum processor heuristic outperforms others in most cases.

Scheduling arbitrary non-splitable chains is NP-complete.

Open problem: scheduling splitable chains efficiently.

Abstract

In this paper, we proposed an effective approach for scheduling of multiprocessor unit time tasks with chain precedence on to large multiprocessor system. The proposed longest chain maximum processor scheduling algorithm is proved to be optimal for uniform chains and monotone (non-increasing/non-decreasing) chains for both splitable and non-splitable multiprocessor unit time tasks chain. Scheduling arbitrary chains of non-splitable multiprocessor unit time tasks is proved to be NP-complete problem. But scheduling arbitrary chains of splitable multiprocessor unit time tasks is still an open problem to be proved whether it is NP-complete or can be solved in polynomial time. We have used three heuristics (a) maximum criticality first, (b) longest chain maximum criticality first and (c) longest chain maximum processor first for scheduling of arbitrary chains. Also compared performance of all three scheduling heuristics and found out that the proposed longest chain maximum processor first performs better in most of the cases.