Document

**Published in:** LIPIcs, Volume 283, 34th International Symposium on Algorithms and Computation (ISAAC 2023)

We revisit the classical non-clairvoyant problem of scheduling a set of n jobs on a set of m parallel identical machines where the processing time of a job is not known until the job finishes. Our objective is the minimization of the makespan, i.e., the date at which the last job terminates its execution. We adopt the framework of learning-augmented algorithms and we study the question of whether (possibly erroneous) predictions may help design algorithms with a competitive ratio which is good when the prediction is accurate (consistency), deteriorates gradually with respect to the prediction error (smoothness), and not too bad and bounded when the prediction is arbitrarily bad (robustness). We first consider the non-preemptive case and we devise lower bounds, as a function of the error of the prediction, for any deterministic learning-augmented algorithm. Then we analyze a variant of Longest Processing Time first (LPT) algorithm (with and without release dates) and we prove that it is consistent, smooth, and robust. Furthermore, we study the preemptive case and we provide lower bounds for any deterministic algorithm with predictions as a function of the prediction error. Finally, we introduce a variant of the classical Round Robin algorithm (RR), the Predicted Proportional Round Robin algorithm (PPRR), which we prove to be consistent, smooth and robust.

Evripidis Bampis, Alexander Kononov, Giorgio Lucarelli, and Fanny Pascual. Non-Clairvoyant Makespan Minimization Scheduling with Predictions. In 34th International Symposium on Algorithms and Computation (ISAAC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 283, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{bampis_et_al:LIPIcs.ISAAC.2023.9, author = {Bampis, Evripidis and Kononov, Alexander and Lucarelli, Giorgio and Pascual, Fanny}, title = {{Non-Clairvoyant Makespan Minimization Scheduling with Predictions}}, booktitle = {34th International Symposium on Algorithms and Computation (ISAAC 2023)}, pages = {9:1--9:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-289-1}, ISSN = {1868-8969}, year = {2023}, volume = {283}, editor = {Iwata, Satoru and Kakimura, Naonori}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2023.9}, URN = {urn:nbn:de:0030-drops-193114}, doi = {10.4230/LIPIcs.ISAAC.2023.9}, annote = {Keywords: scheduling, online, learning-augmented algorithm} }

Document

**Published in:** LIPIcs, Volume 150, 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)

We consider the problem of scheduling jobs to minimize the maximum weighted flow-time on a set of related machines. When jobs can be preempted this problem is well-understood; for example, there exists a constant competitive algorithm using speed augmentation. When jobs must be scheduled non-preemptively, only hardness results are known. In this paper, we present the first online guarantees for the non-preemptive variant. We present the first constant competitive algorithm for minimizing the maximum weighted flow-time on related machines by relaxing the problem and assuming that the online algorithm can reject a small fraction of the total weight of jobs. This is essentially the best result possible given the strong lower bounds on the non-preemptive problem without rejection.

Giorgio Lucarelli, Benjamin Moseley, Nguyen Kim Thang, Abhinav Srivastav, and Denis Trystram. Online Non-Preemptive Scheduling to Minimize Maximum Weighted Flow-Time on Related Machines. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 24:1-24:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{lucarelli_et_al:LIPIcs.FSTTCS.2019.24, author = {Lucarelli, Giorgio and Moseley, Benjamin and Thang, Nguyen Kim and Srivastav, Abhinav and Trystram, Denis}, title = {{Online Non-Preemptive Scheduling to Minimize Maximum Weighted Flow-Time on Related Machines}}, booktitle = {39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019)}, pages = {24:1--24:12}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-131-3}, ISSN = {1868-8969}, year = {2019}, volume = {150}, editor = {Chattopadhyay, Arkadev and Gastin, Paul}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2019.24}, URN = {urn:nbn:de:0030-drops-115867}, doi = {10.4230/LIPIcs.FSTTCS.2019.24}, annote = {Keywords: Online Algorithms, Scheduling, Resource Augmentation} }

Document

**Published in:** LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

In this paper, we consider the online problem of scheduling independent jobs non-preemptively so as to minimize the weighted flow-time on a set of unrelated machines. There has been a considerable amount of work on this problem in the preemptive setting where several competitive algorithms are known in the classical competitive model. However, the problem in the non-preemptive setting admits a strong lower bound. Recently, Lucarelli et al. presented an algorithm that achieves a O(1/epsilon^2)-competitive ratio when the algorithm is allowed to reject epsilon-fraction of total weight of jobs and has an epsilon-speed augmentation. They further showed that speed augmentation alone is insufficient to derive any competitive algorithm. An intriguing open question is whether there exists a scalable competitive algorithm that rejects a small fraction of total weights.
In this paper, we affirmatively answer this question. Specifically, we show that there exists a O(1/epsilon^3)-competitive algorithm for minimizing weighted flow-time on a set of unrelated machine that rejects at most O(epsilon)-fraction of total weight of jobs. The design and analysis of the algorithm is based on the primal-dual technique. Our result asserts that alternative models beyond speed augmentation should be explored when designing online schedulers in the non-preemptive setting in an effort to find provably good algorithms.

Giorgio Lucarelli, Benjamin Moseley, Nguyen Kim Thang, Abhinav Srivastav, and Denis Trystram. Online Non-Preemptive Scheduling to Minimize Weighted Flow-time on Unrelated Machines. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 59:1-59:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

Copy BibTex To Clipboard

@InProceedings{lucarelli_et_al:LIPIcs.ESA.2018.59, author = {Lucarelli, Giorgio and Moseley, Benjamin and Thang, Nguyen Kim and Srivastav, Abhinav and Trystram, Denis}, title = {{Online Non-Preemptive Scheduling to Minimize Weighted Flow-time on Unrelated Machines}}, booktitle = {26th Annual European Symposium on Algorithms (ESA 2018)}, pages = {59:1--59:12}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-081-1}, ISSN = {1868-8969}, year = {2018}, volume = {112}, editor = {Azar, Yossi and Bast, Hannah and Herman, Grzegorz}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.59}, URN = {urn:nbn:de:0030-drops-95226}, doi = {10.4230/LIPIcs.ESA.2018.59}, annote = {Keywords: Online Algorithms, Scheduling, Resource Augmentation} }

Document

**Published in:** LIPIcs, Volume 57, 24th Annual European Symposium on Algorithms (ESA 2016)

Resource augmentation is a well-established model for analyzing algorithms, particularly in the online setting. It has been successfully used for providing theoretical evidence for several heuristics in scheduling with good performance in practice. According to this model, the algorithm is applied to a more powerful environment than that of the adversary. Several types of resource augmentation for scheduling problems have been proposed up to now, including speed augmentation, machine augmentation and more recently rejection. In this paper, we present a framework that unifies the various types of resource augmentation. Moreover, it allows generalize the notion of resource augmentation for other types of resources. Our framework is based on mathematical programming and it consists of extending the domain of feasible solutions for the algorithm with respect to the domain of the adversary. This, in turn allows the natural concept of duality for mathematical programming to be used as a tool for the analysis of the algorithm's performance. As an illustration of the above ideas, we apply this framework and we propose a primal-dual algorithm for the online scheduling problem of minimizing the total weighted flow time of jobs on unrelated machines when the preemption of jobs is not allowed. This is a well representative problem for which no online algorithm with performance guarantee is known. Specifically, a strong lower bound of Omega(sqrt{n}) exists even for the offline unweighted version of the problem on a single machine. In this paper, we first show a strong negative result even when speed augmentation is used in the online setting. Then, using the generalized framework for resource augmentation and by combining speed augmentation and rejection, we present an (1+epsilon_s)-speed O(1/(epsilon_s epsilon_r))-competitive algorithm if we are allowed to reject jobs whose total weight is an epsilon_r-fraction of the weights of all jobs, for any epsilon_s > 0 and epsilon_r in (0,1). Furthermore, we extend the idea for analysis of the above problem and we propose an (1+\epsilon_s)-speed epsilon_r-rejection O({k^{(k+3)/k}}/{epsilon_{r}^{1/k}*epsilon_{s}^{(k+2)/k}})-competitive algorithm for the more general objective of minimizing the weighted l_k-norm of the flow times of jobs.

Giorgio Lucarelli, Nguyen Kim Thang, Abhinav Srivastav, and Denis Trystram. Online Non-Preemptive Scheduling in a Resource Augmentation Model Based on Duality. In 24th Annual European Symposium on Algorithms (ESA 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 57, pp. 63:1-63:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{lucarelli_et_al:LIPIcs.ESA.2016.63, author = {Lucarelli, Giorgio and Kim Thang, Nguyen and Srivastav, Abhinav and Trystram, Denis}, title = {{Online Non-Preemptive Scheduling in a Resource Augmentation Model Based on Duality}}, booktitle = {24th Annual European Symposium on Algorithms (ESA 2016)}, pages = {63:1--63:17}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-015-6}, ISSN = {1868-8969}, year = {2016}, volume = {57}, editor = {Sankowski, Piotr and Zaroliagis, Christos}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2016.63}, URN = {urn:nbn:de:0030-drops-64047}, doi = {10.4230/LIPIcs.ESA.2016.63}, annote = {Keywords: Online algorithms, Non-preemptive scheduling, Resource augmentation, Primal-dual} }

Document

**Published in:** LIPIcs, Volume 24, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)

We propose a unifying framework based on configuration linear programs and randomized rounding, for different energy optimization problems in the dynamic speed-scaling setting. We apply our framework to various scheduling and routing problems in heterogeneous computing and networking environments. We first consider the energy minimization problem of scheduling a set of jobs on a set of parallel speed-scalable processors in a fully heterogeneous setting.
For both the preemptive-non-migratory and the preemptive-migratory variants, our approach allows us to obtain solutions of almost the same quality as for the homogeneous environment. By exploiting the result for the preemptive-non-migratory variant, we are able to improve the best known approximation ratio for the single processor non-preemptive problem. Furthermore, we show that our approach allows to obtain a constant-factor approximation algorithm for the power-aware preemptive job shop scheduling problem. Finally, we consider the min-power routing problem where we are given a network modeled by an undirected graph and a set of uniform demands that have to be routed on integral routes from their sources to their destinations so that the energy consumption is minimized. We improve the best known approximation ratio for this problem.

Evripidis Bampis, Alexander Kononov, Dimitrios Letsios, Giorgio Lucarelli, and Maxim Sviridenko. Energy Efficient Scheduling and Routing via Randomized Rounding. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 449-460, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)

Copy BibTex To Clipboard

@InProceedings{bampis_et_al:LIPIcs.FSTTCS.2013.449, author = {Bampis, Evripidis and Kononov, Alexander and Letsios, Dimitrios and Lucarelli, Giorgio and Sviridenko, Maxim}, title = {{Energy Efficient Scheduling and Routing via Randomized Rounding}}, booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)}, pages = {449--460}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-64-4}, ISSN = {1868-8969}, year = {2013}, volume = {24}, editor = {Seth, Anil and Vishnoi, Nisheeth K.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013.449}, URN = {urn:nbn:de:0030-drops-43923}, doi = {10.4230/LIPIcs.FSTTCS.2013.449}, annote = {Keywords: Randomized rounding; scheduling; approximation; energy-aware; configuration linear program} }

X

Feedback for Dagstuhl Publishing

Feedback submitted

Please try again later or send an E-mail