Optimal Algorithms and a PTAS for Cost-Aware Scheduling - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2015

Optimal Algorithms and a PTAS for Cost-Aware Scheduling

Abstract

We consider a natural generalization of classical scheduling problems in which using a time unit for processing a job causes some time-dependent cost which must be paid in addition to the standard scheduling cost. We study the scheduling objectives of minimizing the makespan and the sum of (weighted) completion times. It is not difficult to derive a polynomial-time algorithm for preemptive scheduling to minimize the makespan on unrelated machines. The problem of minimizing the total (weighted) completion time is considerably harder, even on a single machine. We present a polynomial-time algorithm that computes for any given sequence of jobs an optimal schedule, i.e., the optimal set of time-slots to be used for scheduling jobs according to the given sequence. This result is based on dynamic programming using a subtle analysis of the structure of optimal solutions and a potential function argument. With this algorithm, we solve the unweighted problem optimally in polynomial time. Furthermore, we argue that there is a (4+ε)-approximation algorithm for the strongly NP-hard problem with individual job weights. For this weighted version, we also give a PTAS based on a dual scheduling approach introduced for scheduling on a machine of varying speed.
Fichier principal
Vignette du fichier
ChenMRSV-MFCS15.pdf (328.71 Ko) Télécharger le fichier
Origin : Files produced by the author(s)
Loading...

Dates and versions

hal-01249098 , version 1 (16-06-2017)

Identifiers

Cite

Lin Chen, Nicole Megow, Roman Rischke, Leen Stougie, José Verschae. Optimal Algorithms and a PTAS for Cost-Aware Scheduling. Mathematical Foundations of Computer Science (MFCS), Aug 2015, Milan, Italy. pp.211-222, ⟨10.1007/978-3-662-48054-0_18⟩. ⟨hal-01249098⟩
106 View
147 Download

Altmetric

Share

Gmail Facebook Twitter LinkedIn More