---
_id: '20817'
author:
- first_name: Marcin
full_name: Bienkowski, Marcin
last_name: Bienkowski
- first_name: Björn
full_name: Feldkord, Björn
id: '22704'
last_name: Feldkord
- first_name: Pawel
full_name: Schmidt, Pawel
last_name: Schmidt
citation:
ama: 'Bienkowski M, Feldkord B, Schmidt P. A Nearly Optimal Deterministic Online
Algorithm for Non-Metric Facility Location. In: Proceedings of the 38th Symposium
on Theoretical Aspects of Computer Science (STACS). ; 2021:14:1-14:17. doi:10.4230/LIPIcs.STACS.2021.14'
apa: Bienkowski, M., Feldkord, B., & Schmidt, P. (2021). A Nearly Optimal Deterministic
Online Algorithm for Non-Metric Facility Location. In Proceedings of the 38th
Symposium on Theoretical Aspects of Computer Science (STACS) (pp. 14:1-14:17).
https://doi.org/10.4230/LIPIcs.STACS.2021.14
bibtex: '@inproceedings{Bienkowski_Feldkord_Schmidt_2021, title={A Nearly Optimal
Deterministic Online Algorithm for Non-Metric Facility Location}, DOI={10.4230/LIPIcs.STACS.2021.14},
booktitle={Proceedings of the 38th Symposium on Theoretical Aspects of Computer
Science (STACS)}, author={Bienkowski, Marcin and Feldkord, Björn and Schmidt,
Pawel}, year={2021}, pages={14:1-14:17} }'
chicago: Bienkowski, Marcin, Björn Feldkord, and Pawel Schmidt. “A Nearly Optimal
Deterministic Online Algorithm for Non-Metric Facility Location.” In Proceedings
of the 38th Symposium on Theoretical Aspects of Computer Science (STACS),
14:1-14:17, 2021. https://doi.org/10.4230/LIPIcs.STACS.2021.14.
ieee: M. Bienkowski, B. Feldkord, and P. Schmidt, “A Nearly Optimal Deterministic
Online Algorithm for Non-Metric Facility Location,” in Proceedings of the 38th
Symposium on Theoretical Aspects of Computer Science (STACS), 2021, pp. 14:1-14:17.
mla: Bienkowski, Marcin, et al. “A Nearly Optimal Deterministic Online Algorithm
for Non-Metric Facility Location.” Proceedings of the 38th Symposium on Theoretical
Aspects of Computer Science (STACS), 2021, pp. 14:1-14:17, doi:10.4230/LIPIcs.STACS.2021.14.
short: 'M. Bienkowski, B. Feldkord, P. Schmidt, in: Proceedings of the 38th Symposium
on Theoretical Aspects of Computer Science (STACS), 2021, pp. 14:1-14:17.'
date_created: 2020-12-21T13:46:16Z
date_updated: 2022-01-06T06:54:40Z
department:
- _id: '63'
doi: 10.4230/LIPIcs.STACS.2021.14
language:
- iso: eng
page: 14:1 - 14:17
project:
- _id: '1'
name: SFB 901
- _id: '2'
name: SFB 901 - Project Area A
- _id: '5'
name: SFB 901 - Subproject A1
publication: Proceedings of the 38th Symposium on Theoretical Aspects of Computer
Science (STACS)
publication_status: published
status: public
title: A Nearly Optimal Deterministic Online Algorithm for Non-Metric Facility Location
type: conference
user_id: '22704'
year: '2021'
...
---
_id: '22510'
abstract:
- lang: eng
text: 'Over the past decades, the Gathering problem, which asks to gather a group
of robots in finite time given some restrictions, has been intensively studied.
In this paper, we are given a group of n autonomous, dimensionless, deterministic,
and anonymous robots, with bounded viewing range. Assuming a continuous time model,
the goal is to gather these robots into one point in finite time. We introduce
a simple convergence criterion that defines a new class of algorithms which perform
gathering in O(nd) time, where d is the diameter of the initial robot configuration.
We show that some gathering algorithms in the literature belong to this class
and propose two new algorithms that belong to this class and have quadratic running
time, namely, Go-To-The-Relative-Center algorithm (GTRC) and Safe-Go-To-The-Relative-Center
algorithm (S-GTRC). We prove that the latter can perform gathering without collision
by using a slightly more complex robot model: non oblivious, chiral, and luminous
(i.e. robots have observable external memory, as in [8]). We also consider a variant
of the Gathering problem, the Near-Gathering problem, in which robots must get
close to each other without colliding. We show that S-GTRC solves the Near-Gathering
problem in quadratic time and assumes a weaker robot model than the one assumed
in the current state-of-the-art.'
author:
- first_name: Shouwei
full_name: Li, Shouwei
last_name: Li
- first_name: Christine
full_name: Markarian, Christine
last_name: Markarian
- first_name: Friedhelm
full_name: Meyer auf der Heide, Friedhelm
id: '15523'
last_name: Meyer auf der Heide
- first_name: Pavel
full_name: Podlipyan, Pavel
last_name: Podlipyan
citation:
ama: Li S, Markarian C, Meyer auf der Heide F, Podlipyan P. A continuous strategy
for collisionless gathering. Theoretical Computer Science. 2021;852:41-60.
doi:10.1016/j.tcs.2020.10.037
apa: Li, S., Markarian, C., Meyer auf der Heide, F., & Podlipyan, P. (2021).
A continuous strategy for collisionless gathering. Theoretical Computer Science,
852, 41–60. https://doi.org/10.1016/j.tcs.2020.10.037
bibtex: '@article{Li_Markarian_Meyer auf der Heide_Podlipyan_2021, title={A continuous
strategy for collisionless gathering}, volume={852}, DOI={10.1016/j.tcs.2020.10.037},
journal={Theoretical Computer Science}, author={Li, Shouwei and Markarian, Christine
and Meyer auf der Heide, Friedhelm and Podlipyan, Pavel}, year={2021}, pages={41–60}
}'
chicago: 'Li, Shouwei, Christine Markarian, Friedhelm Meyer auf der Heide, and Pavel
Podlipyan. “A Continuous Strategy for Collisionless Gathering.” Theoretical
Computer Science 852 (2021): 41–60. https://doi.org/10.1016/j.tcs.2020.10.037.'
ieee: S. Li, C. Markarian, F. Meyer auf der Heide, and P. Podlipyan, “A continuous
strategy for collisionless gathering,” Theoretical Computer Science, vol.
852, pp. 41–60, 2021.
mla: Li, Shouwei, et al. “A Continuous Strategy for Collisionless Gathering.” Theoretical
Computer Science, vol. 852, 2021, pp. 41–60, doi:10.1016/j.tcs.2020.10.037.
short: S. Li, C. Markarian, F. Meyer auf der Heide, P. Podlipyan, Theoretical Computer
Science 852 (2021) 41–60.
date_created: 2021-06-28T09:24:15Z
date_updated: 2022-01-06T06:55:35Z
department:
- _id: '63'
doi: 10.1016/j.tcs.2020.10.037
intvolume: ' 852'
keyword:
- Local algorithms
- Distributed algorithms
- Collisionless gathering
- Mobile robots
- Multiagent system
language:
- iso: eng
page: 41-60
publication: Theoretical Computer Science
publication_identifier:
issn:
- 0304-3975
publication_status: published
status: public
title: A continuous strategy for collisionless gathering
type: journal_article
user_id: '15415'
volume: 852
year: '2021'
...
---
_id: '22511'
abstract:
- lang: eng
text: "In this paper, we reconsider the well-known discrete, round-based Go-To-The-Center
algorithm due to Ando, Suzuki, and Yamashita [2] for gathering n autonomous mobile
robots with limited viewing range in the plane. Remarquably, this algorithm exploits
the fact that during its execution, many collisions of robots occur. Such collisions
are interpreted as a success because it is assumed that such collided robots behave
the same from now on. This is acceptable under the assumption that each robot
is represented by a single point. Otherwise, collisions should be avoided. In
this paper, we consider a continuous Go-To-The-Center algorithm in which the robots
continuously observe the positions of their neighbors and adapt their speed (assuming
a speed limit) and direction. Our first results are time bounds of O(n2) for gathering
in two dimensions Euclidean space, and Θ(n) for the one dimension. Our main contribution
is the introduction and evaluation of a continuous algorithm which performs Go-To-The-Center
considering only the neighbors of a robot with respect to the Gabriel subgraph
of the visibility graph, i.e. Go-To-The-Gabriel-Center algorithm. We show that
this modification still correctly executes gathering in one and two dimensions,
with the same time bounds as above. Simulations exhibit a severe difference of
the behavior of the Go-To-The-Center and the Go-To-The-Gabriel-Center algorithms:
Whereas lots of collisions occur during a run of the Go-To-The-Center algorithm,
typically only one, namely the final collision occurs during a run of the Go-To-The-Gabriel-Center
algorithm. We can prove this “collisionless property” of the Go-To-The-Gabriel-Center
algorithm for one dimension. In two-dimensional Euclidean space, we conjecture
that the “collisionless property” holds for almost every initial configuration.
We support our conjecture with measurements obtained from the simulation where
robots execute both continuous Go-To-The-Center and Go-To-The-Gabriel-Center algorithms.\r\n"
author:
- first_name: Shouwei
full_name: Li, Shouwei
last_name: Li
- first_name: Friedhelm
full_name: Meyer auf der Heide, Friedhelm
id: '15523'
last_name: Meyer auf der Heide
- first_name: Pavel
full_name: Podlipyan, Pavel
last_name: Podlipyan
citation:
ama: Li S, Meyer auf der Heide F, Podlipyan P. The impact of the Gabriel subgraph
of the visibility graph on the gathering of mobile autonomous robots. Theoretical
Computer Science. 2021;852:29-40. doi:10.1016/j.tcs.2020.11.009
apa: Li, S., Meyer auf der Heide, F., & Podlipyan, P. (2021). The impact of
the Gabriel subgraph of the visibility graph on the gathering of mobile autonomous
robots. Theoretical Computer Science, 852, 29–40. https://doi.org/10.1016/j.tcs.2020.11.009
bibtex: '@article{Li_Meyer auf der Heide_Podlipyan_2021, title={The impact of the
Gabriel subgraph of the visibility graph on the gathering of mobile autonomous
robots}, volume={852}, DOI={10.1016/j.tcs.2020.11.009},
journal={Theoretical Computer Science}, author={Li, Shouwei and Meyer auf der
Heide, Friedhelm and Podlipyan, Pavel}, year={2021}, pages={29–40} }'
chicago: 'Li, Shouwei, Friedhelm Meyer auf der Heide, and Pavel Podlipyan. “The
Impact of the Gabriel Subgraph of the Visibility Graph on the Gathering of Mobile
Autonomous Robots.” Theoretical Computer Science 852 (2021): 29–40. https://doi.org/10.1016/j.tcs.2020.11.009.'
ieee: S. Li, F. Meyer auf der Heide, and P. Podlipyan, “The impact of the Gabriel
subgraph of the visibility graph on the gathering of mobile autonomous robots,”
Theoretical Computer Science, vol. 852, pp. 29–40, 2021.
mla: Li, Shouwei, et al. “The Impact of the Gabriel Subgraph of the Visibility Graph
on the Gathering of Mobile Autonomous Robots.” Theoretical Computer Science,
vol. 852, 2021, pp. 29–40, doi:10.1016/j.tcs.2020.11.009.
short: S. Li, F. Meyer auf der Heide, P. Podlipyan, Theoretical Computer Science
852 (2021) 29–40.
date_created: 2021-06-28T09:34:45Z
date_updated: 2022-01-06T06:55:35Z
department:
- _id: '63'
doi: 10.1016/j.tcs.2020.11.009
intvolume: ' 852'
keyword:
- Local algorithms
- Distributed algorithms
- Collisionless gathering
- Mobile robots
- Multiagent system
language:
- iso: eng
page: 29-40
publication: Theoretical Computer Science
publication_identifier:
issn:
- 0304-3975
publication_status: published
status: public
title: The impact of the Gabriel subgraph of the visibility graph on the gathering
of mobile autonomous robots
type: journal_article
user_id: '15415'
volume: 852
year: '2021'
...
---
_id: '26986'
author:
- first_name: Jannik
full_name: Castenow, Jannik
id: '38705'
last_name: Castenow
- first_name: Thorsten
full_name: Götte, Thorsten
id: '34727'
last_name: Götte
- first_name: Till
full_name: Knollmann, Till
id: '39241'
last_name: Knollmann
orcid: 0000-0003-2014-4696
- first_name: Friedhelm
full_name: Meyer auf der Heide, Friedhelm
id: '15523'
last_name: Meyer auf der Heide
citation:
ama: 'Castenow J, Götte T, Knollmann T, Meyer auf der Heide F. The Max-Line-Formation
Problem – And New Insights for Gathering and Chain-Formation. In: Johnen C, Schiller
EM, Schmid S, eds. Proceedings of the 23rd International Symposium on Stabilization,
Safety, and Security of Distributed Systems, SSS 2021. Vol 13046. LNCS. Springer;
2021:289-304. doi:10.1007/978-3-030-91081-5_19'
apa: Castenow, J., Götte, T., Knollmann, T., & Meyer auf der Heide, F. (2021).
The Max-Line-Formation Problem – And New Insights for Gathering and Chain-Formation.
In C. Johnen, E. M. Schiller, & S. Schmid (Eds.), Proceedings of the 23rd
International Symposium on Stabilization, Safety, and Security of Distributed
Systems, SSS 2021 (Vol. 13046, pp. 289–304). Springer. https://doi.org/10.1007/978-3-030-91081-5_19
bibtex: '@inproceedings{Castenow_Götte_Knollmann_Meyer auf der Heide_2021, series={LNCS},
title={The Max-Line-Formation Problem – And New Insights for Gathering and Chain-Formation},
volume={13046}, DOI={10.1007/978-3-030-91081-5_19},
booktitle={Proceedings of the 23rd International Symposium on Stabilization, Safety,
and Security of Distributed Systems, SSS 2021}, publisher={Springer}, author={Castenow,
Jannik and Götte, Thorsten and Knollmann, Till and Meyer auf der Heide, Friedhelm},
editor={Johnen, C. and Schiller, E.M. and Schmid, S.}, year={2021}, pages={289–304},
collection={LNCS} }'
chicago: Castenow, Jannik, Thorsten Götte, Till Knollmann, and Friedhelm Meyer auf
der Heide. “The Max-Line-Formation Problem – And New Insights for Gathering and
Chain-Formation.” In Proceedings of the 23rd International Symposium on Stabilization,
Safety, and Security of Distributed Systems, SSS 2021, edited by C. Johnen,
E.M. Schiller, and S. Schmid, 13046:289–304. LNCS. Springer, 2021. https://doi.org/10.1007/978-3-030-91081-5_19.
ieee: 'J. Castenow, T. Götte, T. Knollmann, and F. Meyer auf der Heide, “The Max-Line-Formation
Problem – And New Insights for Gathering and Chain-Formation,” in Proceedings
of the 23rd International Symposium on Stabilization, Safety, and Security of
Distributed Systems, SSS 2021, Online, 2021, vol. 13046, pp. 289–304, doi:
10.1007/978-3-030-91081-5_19.'
mla: Castenow, Jannik, et al. “The Max-Line-Formation Problem – And New Insights
for Gathering and Chain-Formation.” Proceedings of the 23rd International Symposium
on Stabilization, Safety, and Security of Distributed Systems, SSS 2021, edited
by C. Johnen et al., vol. 13046, Springer, 2021, pp. 289–304, doi:10.1007/978-3-030-91081-5_19.
short: 'J. Castenow, T. Götte, T. Knollmann, F. Meyer auf der Heide, in: C. Johnen,
E.M. Schiller, S. Schmid (Eds.), Proceedings of the 23rd International Symposium
on Stabilization, Safety, and Security of Distributed Systems, SSS 2021, Springer,
2021, pp. 289–304.'
conference:
end_date: 2021-11-20
location: Online
name: 23rd International Symposium on Stabilization, Safety, and Security of Distributed
Systems
start_date: 2021-11-17
date_created: 2021-10-28T07:01:30Z
date_updated: 2022-01-07T15:24:10Z
department:
- _id: '63'
doi: 10.1007/978-3-030-91081-5_19
editor:
- first_name: C.
full_name: Johnen, C.
last_name: Johnen
- first_name: E.M.
full_name: Schiller, E.M.
last_name: Schiller
- first_name: S.
full_name: Schmid, S.
last_name: Schmid
external_id:
arxiv:
- '2109.11856'
intvolume: ' 13046'
language:
- iso: eng
page: '289-304 '
project:
- _id: '106'
name: 'Algorithmen für Schwarmrobotik: Verteiltes Rechnen trifft Dynamische Systeme'
publication: Proceedings of the 23rd International Symposium on Stabilization, Safety,
and Security of Distributed Systems, SSS 2021
publication_status: published
publisher: Springer
series_title: LNCS
status: public
title: The Max-Line-Formation Problem – And New Insights for Gathering and Chain-Formation
type: conference
user_id: '38705'
volume: 13046
year: '2021'
...
---
_id: '27778'
abstract:
- lang: eng
text: "Consider a set of jobs connected to a directed acyclic task graph with a\r\nfixed
source and sink. The edges of this graph model precedence constraints and\r\nthe
jobs have to be scheduled with respect to those. We introduce the Server\r\nCloud
Scheduling problem, in which the jobs have to be processed either on a\r\nsingle
local machine or on one of many cloud machines. Both the source and the\r\nsink
have to be scheduled on the local machine. For each job, processing times\r\nboth
on the server and in the cloud are given. Furthermore, for each edge in\r\nthe
task graph, a communication delay is included in the input and has to be\r\ntaken
into account if one of the two jobs is scheduled on the server, the other\r\nin
the cloud. The server can process jobs sequentially, whereas the cloud can\r\nserve
as many as needed in parallel, but induces costs. We consider both\r\nmakespan
and cost minimization. The main results are an FPTAS with respect for\r\nthe makespan
objective for a fairly general case and strong hardness for the\r\ncase with unit
processing times and delays."
author:
- first_name: Marten
full_name: Maack, Marten
id: '88252'
last_name: Maack
- first_name: Friedhelm
full_name: Meyer auf der Heide, Friedhelm
id: '15523'
last_name: Meyer auf der Heide
- first_name: Simon
full_name: Pukrop, Simon
id: '44428'
last_name: Pukrop
citation:
ama: Maack M, Meyer auf der Heide F, Pukrop S. Full Version -- Server Cloud Scheduling.
arXiv:210802109. Published online 2021.
apa: Maack, M., Meyer auf der Heide, F., & Pukrop, S. (2021). Full Version --
Server Cloud Scheduling. In arXiv:2108.02109.
bibtex: '@article{Maack_Meyer auf der Heide_Pukrop_2021, title={Full Version --
Server Cloud Scheduling}, journal={arXiv:2108.02109}, author={Maack, Marten and
Meyer auf der Heide, Friedhelm and Pukrop, Simon}, year={2021} }'
chicago: Maack, Marten, Friedhelm Meyer auf der Heide, and Simon Pukrop. “Full Version
-- Server Cloud Scheduling.” ArXiv:2108.02109, 2021.
ieee: M. Maack, F. Meyer auf der Heide, and S. Pukrop, “Full Version -- Server Cloud
Scheduling,” arXiv:2108.02109. 2021.
mla: Maack, Marten, et al. “Full Version -- Server Cloud Scheduling.” ArXiv:2108.02109,
2021.
short: M. Maack, F. Meyer auf der Heide, S. Pukrop, ArXiv:2108.02109 (2021).
date_created: 2021-11-24T13:23:58Z
date_updated: 2022-09-27T15:03:19Z
department:
- _id: '63'
- _id: '26'
language:
- iso: eng
publication: arXiv:2108.02109
status: public
title: Full Version -- Server Cloud Scheduling
type: preprint
user_id: '44428'
year: '2021'
...
---
_id: '44234'
author:
- first_name: Thilo Frederik
full_name: Berger, Thilo Frederik
last_name: Berger
citation:
ama: Berger TF. Combining Mobility, Heterogeneity, and Leasing Approaches for
Online Resource Allocation.; 2021.
apa: Berger, T. F. (2021). Combining Mobility, Heterogeneity, and Leasing Approaches
for Online Resource Allocation.
bibtex: '@book{Berger_2021, title={Combining Mobility, Heterogeneity, and Leasing
Approaches for Online Resource Allocation}, author={Berger, Thilo Frederik}, year={2021}
}'
chicago: Berger, Thilo Frederik. Combining Mobility, Heterogeneity, and Leasing
Approaches for Online Resource Allocation, 2021.
ieee: T. F. Berger, Combining Mobility, Heterogeneity, and Leasing Approaches
for Online Resource Allocation. 2021.
mla: Berger, Thilo Frederik. Combining Mobility, Heterogeneity, and Leasing Approaches
for Online Resource Allocation. 2021.
short: T.F. Berger, Combining Mobility, Heterogeneity, and Leasing Approaches for
Online Resource Allocation, 2021.
date_created: 2023-04-27T15:34:07Z
date_updated: 2023-04-27T15:34:17Z
department:
- _id: '63'
language:
- iso: eng
project:
- _id: '1'
name: 'SFB 901: SFB 901'
- _id: '2'
name: 'SFB 901 - A: SFB 901 - Project Area A'
- _id: '5'
name: 'SFB 901 - A1: SFB 901 - Subproject A1'
status: public
supervisor:
- first_name: Friedhelm
full_name: Meyer auf der Heide, Friedhelm
id: '15523'
last_name: Meyer auf der Heide
title: Combining Mobility, Heterogeneity, and Leasing Approaches for Online Resource
Allocation
type: bachelorsthesis
user_id: '39241'
year: '2021'
...
---
_id: '44233'
author:
- first_name: Sebastian
full_name: Pranger, Sebastian
last_name: Pranger
citation:
ama: Pranger S. Online K-Facility Reallocation Using k-Server Algorithms.;
2021.
apa: Pranger, S. (2021). Online k-Facility Reallocation using k-Server Algorithms.
bibtex: '@book{Pranger_2021, title={Online k-Facility Reallocation using k-Server
Algorithms}, author={Pranger, Sebastian}, year={2021} }'
chicago: Pranger, Sebastian. Online K-Facility Reallocation Using k-Server Algorithms,
2021.
ieee: S. Pranger, Online k-Facility Reallocation using k-Server Algorithms.
2021.
mla: Pranger, Sebastian. Online K-Facility Reallocation Using k-Server Algorithms.
2021.
short: S. Pranger, Online K-Facility Reallocation Using k-Server Algorithms, 2021.
date_created: 2023-04-27T15:31:26Z
date_updated: 2023-04-27T15:31:57Z
department:
- _id: '63'
language:
- iso: eng
project:
- _id: '1'
name: 'SFB 901: SFB 901'
- _id: '2'
name: 'SFB 901 - A: SFB 901 - Project Area A'
- _id: '5'
name: 'SFB 901 - A1: SFB 901 - Subproject A1'
status: public
supervisor:
- first_name: Friedhelm
full_name: Meyer auf der Heide, Friedhelm
id: '15523'
last_name: Meyer auf der Heide
title: Online k-Facility Reallocation using k-Server Algorithms
type: bachelorsthesis
user_id: '39241'
year: '2021'
...
---
_id: '19899'
abstract:
- lang: eng
text: "Most existing robot formation problems seek a target formation of a certain\r\nminimal
and, thus, efficient structure. Examples include the Gathering\r\nand the Chain-Formation
problem. In this work, we study formation problems that\r\ntry to reach a maximal
structure, supporting for example an efficient\r\ncoverage in exploration scenarios.
A recent example is the NASA Shapeshifter\r\nproject, which describes how the
robots form a relay chain along which gathered\r\ndata from extraterrestrial cave
explorations may be sent to a home base.\r\n As a first step towards understanding
such maximization tasks, we introduce\r\nand study the Max-Chain-Formation problem,
where $n$ robots are ordered along a\r\nwinding, potentially self-intersecting
chain and must form a connected,\r\nstraight line of maximal length connecting
its two endpoints. We propose and\r\nanalyze strategies in a discrete and in a
continuous time model. In the\r\ndiscrete case, we give a complete analysis if
all robots are initially\r\ncollinear, showing that the worst-case time to reach
an\r\n$\\varepsilon$-approximation is upper bounded by $\\mathcal{O}(n^2 \\cdot
\\log\r\n(n/\\varepsilon))$ and lower bounded by $\\Omega(n^2 \\cdot~\\log\r\n(1/\\varepsilon))$.
If one endpoint of the chain remains stationary, this result\r\ncan be extended
to the non-collinear case. If both endpoints move, we identify\r\na family of
instances whose runtime is unbounded. For the continuous model, we\r\ngive a strategy
with an optimal runtime bound of $\\Theta(n)$. Avoiding an\r\nunbounded runtime
similar to the discrete case relies crucially on a\r\ncounter-intuitive aspect
of the strategy: slowing down the endpoints while all\r\nother robots move at
full speed. Surprisingly, we can show that a similar trick\r\ndoes not work in
the discrete model."
author:
- first_name: Jannik
full_name: Castenow, Jannik
id: '38705'
last_name: Castenow
- first_name: Peter
full_name: Kling, Peter
last_name: Kling
- first_name: Till
full_name: Knollmann, Till
id: '39241'
last_name: Knollmann
orcid: 0000-0003-2014-4696
- first_name: Friedhelm
full_name: Meyer auf der Heide, Friedhelm
id: '15523'
last_name: Meyer auf der Heide
citation:
ama: 'Castenow J, Kling P, Knollmann T, Meyer auf der Heide F. A Discrete and Continuous
Study of the Max-Chain-Formation Problem – Slow Down to Speed Up. In: Devismes S,
Mittal N, eds. Stabilization, Safety, and Security of Distributed Systems -
22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020,
Proceedings. Vol 12514. Lecture Notes in Computer Science (LNCS). Springer;
2020:65-80. doi:10.1007/978-3-030-64348-5_6'
apa: Castenow, J., Kling, P., Knollmann, T., & Meyer auf der Heide, F. (2020).
A Discrete and Continuous Study of the Max-Chain-Formation Problem – Slow Down
to Speed Up. In S. Devismes & N. Mittal (Eds.), Stabilization, Safety,
and Security of Distributed Systems - 22nd International Symposium, SSS 2020,
Austin, Texas, USA, November 18-21, 2020, Proceedings (Vol. 12514, pp. 65–80).
Springer. https://doi.org/10.1007/978-3-030-64348-5_6
bibtex: '@inproceedings{Castenow_Kling_Knollmann_Meyer auf der Heide_2020, series={Lecture
Notes in Computer Science (LNCS)}, title={A Discrete and Continuous Study of the
Max-Chain-Formation Problem – Slow Down to Speed Up}, volume={12514}, DOI={10.1007/978-3-030-64348-5_6},
booktitle={Stabilization, Safety, and Security of Distributed Systems - 22nd International
Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings}, publisher={Springer},
author={Castenow, Jannik and Kling, Peter and Knollmann, Till and Meyer auf der
Heide, Friedhelm}, editor={Devismes , Stéphane and Mittal, Neeraj Editors}, year={2020},
pages={65–80}, collection={Lecture Notes in Computer Science (LNCS)} }'
chicago: Castenow, Jannik, Peter Kling, Till Knollmann, and Friedhelm Meyer auf
der Heide. “A Discrete and Continuous Study of the Max-Chain-Formation Problem
– Slow Down to Speed Up.” In Stabilization, Safety, and Security of Distributed
Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November
18-21, 2020, Proceedings, edited by Stéphane Devismes and Neeraj Mittal,
12514:65–80. Lecture Notes in Computer Science (LNCS). Springer, 2020. https://doi.org/10.1007/978-3-030-64348-5_6.
ieee: J. Castenow, P. Kling, T. Knollmann, and F. Meyer auf der Heide, “A Discrete
and Continuous Study of the Max-Chain-Formation Problem – Slow Down to Speed Up,”
in Stabilization, Safety, and Security of Distributed Systems - 22nd International
Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings,
2020, vol. 12514, pp. 65–80.
mla: Castenow, Jannik, et al. “A Discrete and Continuous Study of the Max-Chain-Formation
Problem – Slow Down to Speed Up.” Stabilization, Safety, and Security of Distributed
Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November
18-21, 2020, Proceedings, edited by Stéphane Devismes and Neeraj Mittal,
vol. 12514, Springer, 2020, pp. 65–80, doi:10.1007/978-3-030-64348-5_6.
short: 'J. Castenow, P. Kling, T. Knollmann, F. Meyer auf der Heide, in: S. Devismes
, N. Mittal (Eds.), Stabilization, Safety, and Security of Distributed Systems
- 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21,
2020, Proceedings, Springer, 2020, pp. 65–80.'
date_created: 2020-10-06T07:27:10Z
date_updated: 2022-01-06T06:54:14Z
department:
- _id: '63'
doi: 10.1007/978-3-030-64348-5_6
editor:
- first_name: 'Stéphane '
full_name: 'Devismes , Stéphane '
last_name: 'Devismes '
- first_name: 'Neeraj '
full_name: 'Mittal, Neeraj '
last_name: Mittal
external_id:
arxiv:
- '2010.02043 '
intvolume: ' 12514'
language:
- iso: eng
page: 65-80
publication: Stabilization, Safety, and Security of Distributed Systems - 22nd International
Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings
publication_identifier:
isbn:
- 978-3-030-64347-8
publication_status: published
publisher: Springer
series_title: Lecture Notes in Computer Science (LNCS)
status: public
title: A Discrete and Continuous Study of the Max-Chain-Formation Problem – Slow Down
to Speed Up
type: conference
user_id: '38705'
volume: 12514
year: '2020'
...
---
_id: '20159'
abstract:
- lang: eng
text: "Let G = (V,E) be an undirected graph on n vertices with non-negative capacities
on its edges. The mincut sensitivity problem for the insertion of an edge is defined
as follows. Build a compact data structure for G and a given set S ⊆ V of vertices
that, on receiving any edge (x,y) ∈ S×S of positive capacity as query input, can
efficiently report the set of all pairs from S× S whose mincut value increases
upon insertion of the edge (x,y) to G. The only result that exists for this problem
is for a single pair of vertices (Picard and Queyranne, Mathematical Programming
Study, 13 (1980), 8-16). We present the following results for the single source
and the all-pairs versions of this problem. \r\n1) Single source: Given any designated
source vertex s, there exists a data structure of size \U0001D4AA(|S|) that can
output all those vertices from S whose mincut value to s increases upon insertion
of any given edge. The time taken by the data structure to answer any query is
\U0001D4AA(|S|). \r\n2) All-pairs: There exists an \U0001D4AA(|S|²) size data
structure that can output all those pairs of vertices from S× S whose mincut value
gets increased upon insertion of any given edge. The time taken by the data structure
to answer any query is \U0001D4AA(k), where k is the number of pairs of vertices
whose mincut increases. \r\nFor both these versions, we also address the problem
of reporting the values of the mincuts upon insertion of any given edge. To derive
our results, we use interesting insights into the nearest and the farthest mincuts
for a pair of vertices. In addition, a crucial result, that we establish and use
in our data structures, is that there exists a directed acyclic graph of \U0001D4AA(n)
size that compactly stores the farthest mincuts from all vertices of V to a designated
vertex s in the graph. We believe that this result is of independent interest,
especially, because it also complements a previously existing result by Hariharan
et al. (STOC 2007) that the nearest mincuts from all vertices of V to s is a laminar
family, and hence, can be stored compactly in a tree of \U0001D4AA(n) size."
author:
- first_name: Surender
full_name: Baswana, Surender
last_name: Baswana
- first_name: Shiv
full_name: Gupta, Shiv
last_name: Gupta
- first_name: Till
full_name: Knollmann, Till
id: '39241'
last_name: Knollmann
orcid: 0000-0003-2014-4696
citation:
ama: 'Baswana S, Gupta S, Knollmann T. Mincut Sensitivity Data Structures for the
Insertion of an Edge. In: Grandoni F, Herman G, Sanders P, eds. 28th Annual
European Symposium on Algorithms (ESA 2020). Vol 173. Leibniz International
Proceedings in Informatics (LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl -- Leibniz-Zentrum
für Informatik; 2020:12:1-12:14. doi:10.4230/LIPIcs.ESA.2020.12'
apa: 'Baswana, S., Gupta, S., & Knollmann, T. (2020). Mincut Sensitivity Data
Structures for the Insertion of an Edge. In F. Grandoni, G. Herman, & P. Sanders
(Eds.), 28th Annual European Symposium on Algorithms (ESA 2020) (Vol. 173,
pp. 12:1-12:14). Dagstuhl, Germany: Schloss Dagstuhl -- Leibniz-Zentrum für Informatik.
https://doi.org/10.4230/LIPIcs.ESA.2020.12'
bibtex: '@inproceedings{Baswana_Gupta_Knollmann_2020, place={Dagstuhl, Germany},
series={Leibniz International Proceedings in Informatics (LIPIcs)}, title={Mincut
Sensitivity Data Structures for the Insertion of an Edge}, volume={173}, DOI={10.4230/LIPIcs.ESA.2020.12},
booktitle={28th Annual European Symposium on Algorithms (ESA 2020)}, publisher={Schloss
Dagstuhl -- Leibniz-Zentrum für Informatik}, author={Baswana, Surender and Gupta,
Shiv and Knollmann, Till}, editor={Grandoni, Fabrizio and Herman, Grzegorz and
Sanders, PeterEditors}, year={2020}, pages={12:1-12:14}, collection={Leibniz International
Proceedings in Informatics (LIPIcs)} }'
chicago: 'Baswana, Surender, Shiv Gupta, and Till Knollmann. “Mincut Sensitivity
Data Structures for the Insertion of an Edge.” In 28th Annual European Symposium
on Algorithms (ESA 2020), edited by Fabrizio Grandoni, Grzegorz Herman, and
Peter Sanders, 173:12:1-12:14. Leibniz International Proceedings in Informatics
(LIPIcs). Dagstuhl, Germany: Schloss Dagstuhl -- Leibniz-Zentrum für Informatik,
2020. https://doi.org/10.4230/LIPIcs.ESA.2020.12.'
ieee: S. Baswana, S. Gupta, and T. Knollmann, “Mincut Sensitivity Data Structures
for the Insertion of an Edge,” in 28th Annual European Symposium on Algorithms
(ESA 2020), 2020, vol. 173, pp. 12:1-12:14.
mla: Baswana, Surender, et al. “Mincut Sensitivity Data Structures for the Insertion
of an Edge.” 28th Annual European Symposium on Algorithms (ESA 2020), edited
by Fabrizio Grandoni et al., vol. 173, Schloss Dagstuhl -- Leibniz-Zentrum für
Informatik, 2020, pp. 12:1-12:14, doi:10.4230/LIPIcs.ESA.2020.12.
short: 'S. Baswana, S. Gupta, T. Knollmann, in: F. Grandoni, G. Herman, P. Sanders
(Eds.), 28th Annual European Symposium on Algorithms (ESA 2020), Schloss Dagstuhl
-- Leibniz-Zentrum für Informatik, Dagstuhl, Germany, 2020, pp. 12:1-12:14.'
date_created: 2020-10-21T12:00:20Z
date_updated: 2022-01-06T06:54:20Z
department:
- _id: '63'
doi: 10.4230/LIPIcs.ESA.2020.12
editor:
- first_name: Fabrizio
full_name: Grandoni, Fabrizio
last_name: Grandoni
- first_name: Grzegorz
full_name: Herman, Grzegorz
last_name: Herman
- first_name: Peter
full_name: Sanders, Peter
last_name: Sanders
intvolume: ' 173'
keyword:
- Mincut
- Sensitivity
- Data Structure
language:
- iso: eng
page: 12:1-12:14
place: Dagstuhl, Germany
publication: 28th Annual European Symposium on Algorithms (ESA 2020)
publication_identifier:
isbn:
- 978-3-95977-162-7
issn:
- 1868-8969
publisher: Schloss Dagstuhl -- Leibniz-Zentrum für Informatik
series_title: Leibniz International Proceedings in Informatics (LIPIcs)
status: public
title: Mincut Sensitivity Data Structures for the Insertion of an Edge
type: conference
user_id: '39241'
volume: 173
year: '2020'
...
---
_id: '20185'
author:
- first_name: Jannik
full_name: Castenow, Jannik
id: '38705'
last_name: Castenow
- first_name: Jonas
full_name: Harbig, Jonas
id: '47213'
last_name: Harbig
- first_name: Daniel
full_name: Jung, Daniel
id: '37827'
last_name: Jung
- first_name: Till
full_name: Knollmann, Till
id: '39241'
last_name: Knollmann
orcid: 0000-0003-2014-4696
- first_name: Friedhelm
full_name: Meyer auf der Heide, Friedhelm
id: '15523'
last_name: Meyer auf der Heide
citation:
ama: 'Castenow J, Harbig J, Jung D, Knollmann T, Meyer auf der Heide F. Brief Announcement:
Gathering in Linear Time: A Closed Chain of Disoriented & Luminous Robots
with Limited Visibility . In: Devismes S, Mittal N, eds. Stabilization, Safety,
and Security of Distributed Systems - 22nd International Symposium, SSS 2020,
Austin, Texas, USA, November 18-21, 2020, Proceedings . Vol 12514. Lecture
Notes in Computer Science (LNCS). Springer; 2020:60-64. doi:10.1007/978-3-030-64348-5_5'
apa: 'Castenow, J., Harbig, J., Jung, D., Knollmann, T., & Meyer auf der Heide,
F. (2020). Brief Announcement: Gathering in Linear Time: A Closed Chain of Disoriented
& Luminous Robots with Limited Visibility . In S. Devismes & N. Mittal
(Eds.), Stabilization, Safety, and Security of Distributed Systems - 22nd International
Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings
(Vol. 12514, pp. 60–64). Springer. https://doi.org/10.1007/978-3-030-64348-5_5'
bibtex: '@inproceedings{Castenow_Harbig_Jung_Knollmann_Meyer auf der Heide_2020,
series={Lecture Notes in Computer Science (LNCS)}, title={Brief Announcement:
Gathering in Linear Time: A Closed Chain of Disoriented & Luminous Robots
with Limited Visibility }, volume={12514}, DOI={10.1007/978-3-030-64348-5_5},
booktitle={Stabilization, Safety, and Security of Distributed Systems - 22nd International
Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings },
publisher={Springer}, author={Castenow, Jannik and Harbig, Jonas and Jung, Daniel
and Knollmann, Till and Meyer auf der Heide, Friedhelm}, editor={Devismes, Stéphane and Mittal,
NeerajEditors}, year={2020}, pages={60–64}, collection={Lecture Notes in Computer
Science (LNCS)} }'
chicago: 'Castenow, Jannik, Jonas Harbig, Daniel Jung, Till Knollmann, and Friedhelm
Meyer auf der Heide. “Brief Announcement: Gathering in Linear Time: A Closed Chain
of Disoriented & Luminous Robots with Limited Visibility .” In Stabilization,
Safety, and Security of Distributed Systems - 22nd International Symposium, SSS
2020, Austin, Texas, USA, November 18-21, 2020, Proceedings , edited by Stéphane Devismes
and Neeraj Mittal, 12514:60–64. Lecture Notes in Computer Science (LNCS). Springer,
2020. https://doi.org/10.1007/978-3-030-64348-5_5.'
ieee: 'J. Castenow, J. Harbig, D. Jung, T. Knollmann, and F. Meyer auf der Heide,
“Brief Announcement: Gathering in Linear Time: A Closed Chain of Disoriented &
Luminous Robots with Limited Visibility ,” in Stabilization, Safety, and Security
of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas,
USA, November 18-21, 2020, Proceedings , 2020, vol. 12514, pp. 60–64.'
mla: 'Castenow, Jannik, et al. “Brief Announcement: Gathering in Linear Time: A
Closed Chain of Disoriented & Luminous Robots with Limited Visibility .” Stabilization,
Safety, and Security of Distributed Systems - 22nd International Symposium, SSS
2020, Austin, Texas, USA, November 18-21, 2020, Proceedings , edited by Stéphane Devismes
and Neeraj Mittal, vol. 12514, Springer, 2020, pp. 60–64, doi:10.1007/978-3-030-64348-5_5.'
short: 'J. Castenow, J. Harbig, D. Jung, T. Knollmann, F. Meyer auf der Heide, in:
S. Devismes, N. Mittal (Eds.), Stabilization, Safety, and Security of Distributed
Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November
18-21, 2020, Proceedings , Springer, 2020, pp. 60–64.'
date_created: 2020-10-23T08:50:28Z
date_updated: 2022-01-06T06:54:21Z
department:
- _id: '63'
doi: 10.1007/978-3-030-64348-5_5
editor:
- first_name: 'Stéphane '
full_name: 'Devismes, Stéphane '
last_name: Devismes
- first_name: Neeraj
full_name: ' Mittal, Neeraj'
last_name: ' Mittal'
external_id:
arxiv:
- '2010.04424 '
intvolume: ' 12514'
language:
- iso: eng
page: 60-64
publication: 'Stabilization, Safety, and Security of Distributed Systems - 22nd International
Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings '
publication_identifier:
isbn:
- 978-3-030-64347-8
publication_status: published
publisher: Springer
series_title: Lecture Notes in Computer Science (LNCS)
status: public
title: 'Brief Announcement: Gathering in Linear Time: A Closed Chain of Disoriented
& Luminous Robots with Limited Visibility '
type: conference
user_id: '38705'
volume: 12514
year: '2020'
...