3 Search Results for "Eberle, Franziska"


Document
O(1/ε) Is the Answer in Online Weighted Throughput Maximization

Authors: Franziska Eberle

Published in: LIPIcs, Volume 289, 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)


Abstract
We study a fundamental online scheduling problem where jobs with processing times, weights, and deadlines arrive online over time at their release dates. The task is to preemptively schedule these jobs on a single or multiple (possibly unrelated) machines with the objective to maximize the weighted throughput, the total weight of jobs that complete before their deadline. To overcome known lower bounds for the competitive analysis, we assume that each job arrives with some slack ε > 0; that is, the time window for processing job j on any machine i on which it can be executed has length at least (1+ε) times j’s processing time on machine i. Our contribution is a best possible online algorithm for weighted throughput maximization on unrelated machines: Our algorithm is 𝒪(1/ε)-competitive, which matches the lower bound for unweighted throughput maximization on a single machine. Even for a single machine, it was not known whether the problem with weighted jobs is "harder" than the problem with unweighted jobs. Thus, we answer this question and close weighted throughput maximization on a single machine with a best possible competitive ratio Θ(1/ε). While we focus on non-migratory schedules, on identical machines, our algorithm achieves the same (up to constants) performance guarantee when compared to an optimal migratory schedule.

Cite as

Franziska Eberle. O(1/ε) Is the Answer in Online Weighted Throughput Maximization. In 41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 289, pp. 32:1-32:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


Copy BibTex To Clipboard

@InProceedings{eberle:LIPIcs.STACS.2024.32,
  author =	{Eberle, Franziska},
  title =	{{O(1/\epsilon) Is the Answer in Online Weighted Throughput Maximization}},
  booktitle =	{41st International Symposium on Theoretical Aspects of Computer Science (STACS 2024)},
  pages =	{32:1--32:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-311-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{289},
  editor =	{Beyersdorff, Olaf and Kant\'{e}, Mamadou Moustapha and Kupferman, Orna and Lokshtanov, Daniel},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2024.32},
  URN =		{urn:nbn:de:0030-drops-197428},
  doi =		{10.4230/LIPIcs.STACS.2024.32},
  annote =	{Keywords: Deadline scheduling, weighted throughput, online algorithms, competitive analysis}
}
Document
Fully Dynamic Algorithms for Knapsack Problems with Polylogarithmic Update Time

Authors: Franziska Eberle, Nicole Megow, Lukas Nölke, Bertrand Simon, and Andreas Wiese

Published in: LIPIcs, Volume 213, 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)


Abstract
Knapsack problems are among the most fundamental problems in optimization. In the Multiple Knapsack problem, we are given multiple knapsacks with different capacities and items with values and sizes. The task is to find a subset of items of maximum total value that can be packed into the knapsacks without exceeding the capacities. We investigate this problem and special cases thereof in the context of dynamic algorithms and design data structures that efficiently maintain near-optimal knapsack solutions for dynamically changing input. More precisely, we handle the arrival and departure of individual items or knapsacks during the execution of the algorithm with worst-case update time polylogarithmic in the number of items. As the optimal and any approximate solution may change drastically, we maintain implicit solutions and support polylogarithmic time query operations that can return the computed solution value and the packing of any given item. While dynamic algorithms are well-studied in the context of graph problems, there is hardly any work on packing problems (and generally much less on non-graph problems). Motivated by the theoretical interest in knapsack problems and their practical relevance, our work bridges this gap.

Cite as

Franziska Eberle, Nicole Megow, Lukas Nölke, Bertrand Simon, and Andreas Wiese. Fully Dynamic Algorithms for Knapsack Problems with Polylogarithmic Update Time. In 41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 213, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


Copy BibTex To Clipboard

@InProceedings{eberle_et_al:LIPIcs.FSTTCS.2021.18,
  author =	{Eberle, Franziska and Megow, Nicole and N\"{o}lke, Lukas and Simon, Bertrand and Wiese, Andreas},
  title =	{{Fully Dynamic Algorithms for Knapsack Problems with Polylogarithmic Update Time}},
  booktitle =	{41st IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2021)},
  pages =	{18:1--18:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-215-0},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{213},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Chekuri, Chandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2021.18},
  URN =		{urn:nbn:de:0030-drops-155297},
  doi =		{10.4230/LIPIcs.FSTTCS.2021.18},
  annote =	{Keywords: Fully dynamic algorithms, knapsack problem, approximation schemes}
}
Document
Optimally Handling Commitment Issues in Online Throughput Maximization

Authors: Franziska Eberle, Nicole Megow, and Kevin Schewior

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)


Abstract
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.

Cite as

Franziska Eberle, Nicole Megow, and Kevin Schewior. Optimally Handling Commitment Issues in Online Throughput Maximization. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 41:1-41:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


Copy BibTex To Clipboard

@InProceedings{eberle_et_al:LIPIcs.ESA.2020.41,
  author =	{Eberle, Franziska and Megow, Nicole and Schewior, Kevin},
  title =	{{Optimally Handling Commitment Issues in Online Throughput Maximization}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{41:1--41:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.41},
  URN =		{urn:nbn:de:0030-drops-129076},
  doi =		{10.4230/LIPIcs.ESA.2020.41},
  annote =	{Keywords: Deadline scheduling, throughput, online algorithms, competitive analysis}
}
  • Refine by Author
  • 3 Eberle, Franziska
  • 2 Megow, Nicole
  • 1 Nölke, Lukas
  • 1 Schewior, Kevin
  • 1 Simon, Bertrand
  • Show More...

  • Refine by Classification
  • 2 Theory of computation → Online algorithms
  • 2 Theory of computation → Scheduling algorithms
  • 1 Theory of computation → Packing and covering problems

  • Refine by Keyword
  • 2 Deadline scheduling
  • 2 competitive analysis
  • 2 online algorithms
  • 1 Fully dynamic algorithms
  • 1 approximation schemes
  • Show More...

  • Refine by Type
  • 3 document

  • Refine by Publication Year
  • 1 2020
  • 1 2021
  • 1 2024

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail