eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2020-08-26
41:1
41:15
10.4230/LIPIcs.ESA.2020.41
article
Optimally Handling Commitment Issues in Online Throughput Maximization
Eberle, Franziska
1
https://orcid.org/0000-0001-8636-9711
Megow, Nicole
1
https://orcid.org/0000-0002-3531-7644
Schewior, Kevin
2
https://orcid.org/0000-0003-2236-0210
Department for Mathematics and Computer Science, University of Bremen, Germany
Universität zu Köln, Department of Mathematics and Computer Science, Germany
We consider a fundamental online scheduling problem in which jobs with processing times and deadlines arrive online over time at their release dates. The task is to determine a feasible preemptive schedule on m machines that maximizes the number of jobs that complete before their deadline. Due to strong impossibility results for competitive analysis, it is commonly required that jobs contain some slack ε > 0, which means that the feasible time window for scheduling a job is at least 1+ε times its processing time. In this paper, we answer the question on how to handle commitment requirements which enforce that a scheduler has to guarantee at a certain point in time the completion of admitted jobs. This is very relevant, e.g., in providing cloud-computing services and disallows last-minute rejections of critical tasks. We present the first online algorithm for handling commitment on parallel machines for arbitrary slack ε. When the scheduler must commit upon starting a job, the algorithm is Θ(1/ε)-competitive. Somewhat surprisingly, this is the same optimal performance bound (up to constants) as for scheduling without commitment on a single machine. If commitment decisions must be made before a job’s slack becomes less than a δ-fraction of its size, we prove a competitive ratio of 𝒪(1/(ε - δ)) for 0 < δ < ε. This result nicely interpolates between commitment upon starting a job and commitment upon arrival. For the latter commitment model, it is known that no (randomized) online algorithms admits any bounded competitive ratio.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol173-esa2020/LIPIcs.ESA.2020.41/LIPIcs.ESA.2020.41.pdf
Deadline scheduling
throughput
online algorithms
competitive analysis