On the approximability of multiprocessor task scheduling problems

Abstract

The multiprocessor job scheduling problem has received considerable attention recently. An extensive list of approximation algorithms has been developed and studied for the problem under a variety of constraints. In this paper, we show that from the viewpoint of approx-imability, the general multiprocessor job scheduling problem has a very rich structures such that by putting simple constraints on the number of processors in the system, we can obtain four versions of the problem, which are NP-hard with a fully polynomial time approximation scheme, strongly NP-hard with a polynomial time approximation scheme, APX-complete (thus with a constant approximation ratio in polynomial time), and with no constant approximation ratio in polynomial time, respectively. © Springer-Verlag Berlin Heidelberg 2002.