Scheduling with an Orthogonal Resource Constraint

Abstract

Abstract. We address a scheduling problem that arises in highly parallelized environments like modern multi-core CPU/GPU computer architectures. Here simultaneously active jobs share a common limited resource, e.g., memory cache. The scheduler must ensure that the demand for the common resource never exceeds the available capacity. This introduces an orthogonal constraint to the classical minimum makespan scheduling problem. Such a constraint also arises in many other contexts where a common resource is shared across the machines. We study the non-preemptive case of this problem and give a (2 + )-approximation algorithm which relies on the interplay of several classical and modern techniques in scheduling like grouping, job-classification, and the use of configuration-LPs. This improves upon previous bound of 3 that can be obtained by list scheduling approaches, and gets close to the (3/2 − ) inapproximability bound. If the number of machines or the number of different resource requirements are bounded by a constant we have a polynomial time approximation scheme.

A Log-Linear $$(2 +5/6)$$-Approximation Algorithm for Parallel Machine Scheduling with a Single Orthogonal Resource

“…Our algorithm improves the 3 − 3 m -approximation ratio of Garey and Graham [6]. It is also considerably easier to implement than the approximation algorithms proposed by Niemeier and Wiese [21] and Jansen, Maack and Rau [14].…”

“…for resource-dependent job processing times. In [21], a (2 + ε)-approximation algorithm for the P|res1••|C max problem is presented. This algorithm can be transformed into a PTAS if the number of machines or the number of different resource requirements is upper-bounded by a constant.…”

“…We thus directly improve the classic 3 − 3 m -approximation algorithm by Garey and Graham [6]. Although a (2 + ε)-approximation algorithm [21] and an asymptotic FPTAS [14] are known, their time and implementation complexities are considerable. Our algorithm can be easily implemented and it runs in log-linear time.…”

Closing the gap for single resource constraint scheduling

“…The algorithm with the best absolute ratio so far is a (2 + ε)-approximation by Niemeier and Wiese [36]. In this paper, we close this gap between approximation and lower bound by presenting an algorithm with approximation ratio (3/2 + ε).…”

“…In the same year Garey and Johnson [13] showed that this general scheduling problem is NP-complete even if just one resource is given, i.e., s = 1. Lately, Niemeier and Wiese [36] presented a (2 + ε)-approximation for single resource constraint scheduling, and this is the best known ratio so far.…”