2 Search Results for "Degener, Bastian"

Document
DOI: 10.4230/LIPIcs.OPODIS.2022.15
A Unifying Approach to Efficient (Near)-Gathering of Disoriented Robots with Limited Visibility

Authors: Jannik Castenow, Jonas Harbig, Daniel Jung, Peter Kling, Till Knollmann, and Friedhelm Meyer auf der Heide

Published in: LIPIcs, Volume 253, 26th International Conference on Principles of Distributed Systems (OPODIS 2022)

Abstract
We consider a swarm of n robots in a d-dimensional Euclidean space. The robots are oblivious (no persistent memory), disoriented (no common coordinate system/compass), and have limited visibility (observe other robots up to a constant distance). The basic formation task Gathering requires that all robots reach the same, not predefined position. In the related NearGathering task, they must reach distinct positions in close proximity such that every robot sees the entire swarm. In the considered setting, Gathering can be solved in 𝒪(n + Δ²) synchronous rounds both in two and three dimensions, where Δ denotes the initial maximal distance of two robots [Hideki Ando et al., 1999; Michael Braun et al., 2020; Bastian Degener et al., 2011]. In this work, we formalize a key property of efficient Gathering protocols and use it to define λ-contracting protocols. Any such protocol gathers n robots in the d-dimensional space in 𝒪(Δ²) synchronous rounds, for d ≥ 2. For d = 1, any λ-contracting protocol gathers in optimal time 𝒪(Δ). Moreover, we prove a corresponding lower bound stating that any protocol in which robots move to target points inside the local convex hulls of their neighborhoods - λ-contracting protocols have this property - requires Ω(Δ²) rounds to gather all robots (d > 1). Among others, we prove that the d-dimensional generalization of the GTC-protocol [Hideki Ando et al., 1999] is λ-contracting. Remarkably, our improved and generalized runtime bound is independent of n and d. We also introduce an approach to make any λ-contracting protocol collision-free (robots never occupy the same position) to solve NearGathering. The resulting protocols maintain the runtime of Θ (Δ²) and work even in the semi-synchronous model. This yields the first NearGathering protocols for disoriented robots and the first proven runtime bound. In particular, combined with results from [Paola Flocchini et al., 2017] for robots with global visibility, we obtain the first protocol to solve Uniform Circle Formation (arrange the robots on the vertices of a regular n-gon) for oblivious, disoriented robots with limited visibility.
Cite as

Jannik Castenow, Jonas Harbig, Daniel Jung, Peter Kling, Till Knollmann, and Friedhelm Meyer auf der Heide. A Unifying Approach to Efficient (Near)-Gathering of Disoriented Robots with Limited Visibility. In 26th International Conference on Principles of Distributed Systems (OPODIS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 253, pp. 15:1-15:25, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{castenow_et_al:LIPIcs.OPODIS.2022.15,
  author =	{Castenow, Jannik and Harbig, Jonas and Jung, Daniel and Kling, Peter and Knollmann, Till and Meyer auf der Heide, Friedhelm},
  title =	{{A Unifying Approach to Efficient (Near)-Gathering of Disoriented Robots with Limited Visibility}},
  booktitle =	{26th International Conference on Principles of Distributed Systems (OPODIS 2022)},
  pages =	{15:1--15:25},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-265-5},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{253},
  editor =	{Hillel, Eshcar and Palmieri, Roberto and Rivi\`{e}re, Etienne},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2022.15},
  URN =		{urn:nbn:de:0030-drops-176350},
  doi =		{10.4230/LIPIcs.OPODIS.2022.15},
  annote =	{Keywords: mobile robots, gathering, limited visibility, runtime, collision avoidance, near-gathering}
}
Document
DOI: 10.4230/DagSemProc.09261.24
Production planning and control with discrete lotsizing and a rolling horizon

Authors: Wilhelm Dangelmaier and Bastian Degener

Published in: Dagstuhl Seminar Proceedings, Volume 9261, Models and Algorithms for Optimization in Logistics (2009)

Abstract
We consider a production system with discrete lotsizing as it is given in the automotive índustry. At any point of time only orders in the near future are known, but still the production has to be planned - leading to rolling horizons. Decisions that are made today should avoid bottlenecks in stock and capacity that will handicap future production. First we discuss approaches used in computing. Second we propose an approach that perform with good competivity compared to an optimal algorithm that knows the entire sequence of orders in advance.
Cite as

Wilhelm Dangelmaier and Bastian Degener. Production planning and control with discrete lotsizing and a rolling horizon. In Models and Algorithms for Optimization in Logistics. Dagstuhl Seminar Proceedings, Volume 9261, pp. 1-15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)

Copy BibTex To Clipboard

@InProceedings{dangelmaier_et_al:DagSemProc.09261.24,
  author =	{Dangelmaier, Wilhelm and Degener, Bastian},
  title =	{{Production planning and control with discrete lotsizing and a rolling horizon}},
  booktitle =	{Models and Algorithms for Optimization in Logistics},
  pages =	{1--15},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2009},
  volume =	{9261},
  editor =	{Cynthia Barnhart and Uwe Clausen and Ulrich Lauther and Rolf H. M\"{o}hring},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.09261.24},
  URN =		{urn:nbn:de:0030-drops-21864},
  doi =		{10.4230/DagSemProc.09261.24},
  annote =	{Keywords: Online optimization, rolling horizon, lot size production, production planning and control}
}
  • Refine by Author
  • 1 Castenow, Jannik
  • 1 Dangelmaier, Wilhelm
  • 1 Degener, Bastian
  • 1 Harbig, Jonas
  • 1 Jung, Daniel
  • Show More...

  • Refine by Classification
  • 1 Theory of computation → Distributed algorithms

  • Refine by Keyword
  • 1 Online optimization
  • 1 collision avoidance
  • 1 gathering
  • 1 limited visibility
  • 1 lot size production
  • Show More...

  • Refine by Type
  • 2 document

  • Refine by Publication Year
  • 1 2009
  • 1 2023

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
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact