@article{31479,
author = {{Baswana, Surender and Gupta, Shiv and Knollmann, Till}},
issn = {{0178-4617}},
journal = {{Algorithmica}},
keywords = {{Applied Mathematics, Computer Science Applications, General Computer Science}},
publisher = {{Springer Science and Business Media LLC}},
title = {{{Mincut Sensitivity Data Structures for the Insertion of an Edge}}},
doi = {{10.1007/s00453-022-00978-0}},
year = {{2022}},
}
@article{29843,
author = {{Castenow, Jannik and Kling, Peter and Knollmann, Till and Meyer auf der Heide, Friedhelm}},
issn = {{0890-5401}},
journal = {{Information and Computation}},
keywords = {{Computational Theory and Mathematics, Computer Science Applications, Information Systems, Theoretical Computer Science}},
publisher = {{Elsevier BV}},
title = {{{A Discrete and Continuous Study of the Max-Chain-Formation Problem}}},
doi = {{10.1016/j.ic.2022.104877}},
year = {{2022}},
}
@inbook{29872,
author = {{Maack, Marten and Meyer auf der Heide, Friedhelm and Pukrop, Simon}},
booktitle = {{Approximation and Online Algorithms}},
isbn = {{9783030927011}},
issn = {{0302-9743}},
publisher = {{Springer International Publishing}},
title = {{{Server Cloud Scheduling}}},
doi = {{10.1007/978-3-030-92702-8_10}},
year = {{2022}},
}
@inproceedings{31847,
abstract = {{The famous $k$-Server Problem covers plenty of resource allocation scenarios, and several variations have been studied extensively for decades. However, to the best of our knowledge, no research has considered the problem if the servers are not identical and requests can express which specific servers should serve them. Therefore, we present a new model generalizing the $k$-Server Problem by *preferences* of the requests and proceed to study it in a uniform metric space for deterministic online algorithms (the special case of paging).
In our model, requests can either demand to be answered by any server (*general requests*) or by a specific one (*specific requests*). If only general requests appear, the instance is one of the original $k$-Server Problem, and a lower bound for the competitive ratio of $k$ applies. If only specific requests appear, a solution with a competitive ratio of $1$ becomes trivial since there is no freedom regarding the servers' movements. Perhaps counter-intuitively, we show that if both kinds of requests appear, the lower bound raises to $2k-1$.
We study deterministic online algorithms in uniform metrics and present two algorithms. The first one has an adaptive competitive ratio dependent on the frequency of specific requests. It achieves a worst-case competitive ratio of $3k-2$ while it is optimal when only general or only specific requests appear (competitive ratio of $k$ and $1$, respectively). The second has a fixed close-to-optimal worst-case competitive ratio of $2k+14$. For the first algorithm, we show a lower bound of $3k-2$, while the second algorithm has a lower bound of $2k-1$ when only general requests appear.
The two algorithms differ in only one behavioral rule for each server that significantly influences the competitive ratio. Each server acting according to the rule allows approaching the worst-case lower bound, while it implies an increased lower bound for $k$-Server instances. In other words, there is a trade-off between performing well against instances of the $k$-Server Problem and instances containing specific requests. We also show that no deterministic online algorithm can be optimal for both kinds of instances simultaneously.}},
author = {{Castenow, Jannik and Feldkord, Björn and Knollmann, Till and Malatyali, Manuel and Meyer auf der Heide, Friedhelm}},
booktitle = {{Proceedings of the 34th ACM Symposium on Parallelism in Algorithms and Architectures}},
isbn = {{9781450391467}},
keywords = {{K-Server Problem, Heterogeneity, Online Caching}},
pages = {{345--356}},
publisher = {{Association for Computing Machinery}},
title = {{{The k-Server with Preferences Problem}}},
doi = {{10.1145/3490148.3538595}},
year = {{2022}},
}
@unpublished{27778,
abstract = {{Consider a set of jobs connected to a directed acyclic task graph with a
fixed source and sink. The edges of this graph model precedence constraints and
the jobs have to be scheduled with respect to those. We introduce the Server
Cloud Scheduling problem, in which the jobs have to be processed either on a
single local machine or on one of many cloud machines. Both the source and the
sink have to be scheduled on the local machine. For each job, processing times
both on the server and in the cloud are given. Furthermore, for each edge in
the task graph, a communication delay is included in the input and has to be
taken into account if one of the two jobs is scheduled on the server, the other
in the cloud. The server can process jobs sequentially, whereas the cloud can
serve as many as needed in parallel, but induces costs. We consider both
makespan and cost minimization. The main results are an FPTAS with respect for
the makespan objective for a fairly general case and strong hardness for the
case with unit processing times and delays.}},
author = {{Maack, Marten and Meyer auf der Heide, Friedhelm and Pukrop, Simon}},
booktitle = {{arXiv:2108.02109}},
title = {{{Full Version -- Server Cloud Scheduling}}},
year = {{2021}},
}
@article{21096,
abstract = {{While many research in distributed computing has covered solutions for self-stabilizing computing and topologies, there is far less work on self-stabilization for distributed data structures. However, when peers in peer-to-peer networks crash, a distributed data structure may not remain intact. We present a self-stabilizing protocol for a distributed data structure called the Hashed Patricia Trie (Kniesburges and Scheideler WALCOM'11) that enables efficient prefix search on a set of keys. The data structure has many applications while offering low overhead and efficient operations when embedded on top of a Distributed Hash Table. Especially, longest prefix matching for x can be done in O(log |x|) hash table read accesses. We show how to maintain the structure in a self-stabilizing way, while assuring a low overhead in a legal state and an asymptotically optimal memory demand of O(d) bits, where d is the number of bits needed for storing all keys.}},
author = {{Knollmann, Till and Scheideler, Christian}},
issn = {{0890-5401}},
journal = {{Information and Computation}},
title = {{{A self-stabilizing Hashed Patricia Trie}}},
doi = {{10.1016/j.ic.2021.104697}},
year = {{2021}},
}
@inproceedings{23730,
author = {{Castenow, Jannik and Harbig, Jonas and Jung, Daniel and Knollmann, Till and Meyer auf der Heide, Friedhelm}},
booktitle = {{Proceedings of the 17th International Symposium on Algorithms and Experiments for Wireless Sensor Networks (ALGOSENSORS)}},
editor = {{Gasieniec, Leszek and Klasing, Ralf and Radzik, Tomasz}},
location = {{Lissabon}},
pages = {{29 -- 44}},
publisher = {{Springer}},
title = {{{Gathering a Euclidean Closed Chain of Robots in Linear Time}}},
doi = {{10.1007/978-3-030-89240-1_3}},
volume = {{12961}},
year = {{2021}},
}
@inproceedings{23779,
abstract = {{Produktentstehung (PE) bezieht sich auf den Prozess der Planung und Entwicklung eines Produkts sowie der damit verbundenen Dienstleistungen von der ersten Idee bis zur Herstellung und zum Vertrieb. Während dieses Prozesses gibt es zahlreiche Aufgaben, die von menschlichem Fachwissen abhängen und typischerweise von erfahrenen Experten übernommen werden. Da sich das Feld der Künstlichen Intelligenz (KI) immer weiterentwickelt und seinen Weg in den Fertigungssektor findet, gibt es viele Möglichkeiten für eine Anwendung von KI, um bei der Lösung der oben genannten Aufgaben zu helfen. In diesem Paper geben wir einen umfassenden Überblick über den aktuellen Stand der Technik des Einsatzes von KI in der PE.
Im Detail analysieren wir 40 bestehende Surveys zu KI in der PE und 94 Case Studies, um herauszufinden, welche Bereiche der PE von der aktuellen Forschung in diesem Bereich vorrangig adressiert werden, wie ausgereift die diskutierten KI-Methoden sind und inwieweit datenzentrierte Ansätze in der aktuellen Forschung genutzt werden.}},
author = {{Bernijazov, Ruslan and Dicks, Alexander and Dumitrescu, Roman and Foullois, Marc and Hanselle, Jonas Manuel and Hüllermeier, Eyke and Karakaya, Gökce and Ködding, Patrick and Lohweg, Volker and Malatyali, Manuel and Meyer auf der Heide, Friedhelm and Panzner, Melina and Soltenborn, Christian}},
booktitle = {{Proceedings of the 30th International Joint Conference on Artificial Intelligence (IJCAI-21)}},
keywords = {{Artificial Intelligence Product Creation Literature Review}},
location = {{Montreal, Kanada}},
title = {{{A Meta-Review on Artiﬁcial Intelligence in Product Creation}}},
year = {{2021}},
}
@article{20683,
author = {{Feldkord, Björn and Knollmann, Till and Malatyali, Manuel and Meyer auf der Heide, Friedhelm}},
journal = {{Theory of Computing Systems}},
pages = {{943–984}},
title = {{{Managing Multiple Mobile Resources}}},
doi = {{10.1007/s00224-020-10023-8}},
volume = {{65}},
year = {{2021}},
}
@inproceedings{20817,
author = {{Bienkowski, Marcin and Feldkord, Björn and Schmidt, Pawel}},
booktitle = {{Proceedings of the 38th Symposium on Theoretical Aspects of Computer Science (STACS)}},
pages = {{14:1 -- 14:17}},
title = {{{A Nearly Optimal Deterministic Online Algorithm for Non-Metric Facility Location}}},
doi = {{10.4230/LIPIcs.STACS.2021.14}},
year = {{2021}},
}
@article{22510,
abstract = {{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 = {{Li, Shouwei and Markarian, Christine and Meyer auf der Heide, Friedhelm and Podlipyan, Pavel}},
issn = {{0304-3975}},
journal = {{Theoretical Computer Science}},
keywords = {{Local algorithms, Distributed algorithms, Collisionless gathering, Mobile robots, Multiagent system}},
pages = {{41--60}},
title = {{{A continuous strategy for collisionless gathering}}},
doi = {{10.1016/j.tcs.2020.10.037}},
volume = {{852}},
year = {{2021}},
}
@article{22511,
abstract = {{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.
}},
author = {{Li, Shouwei and Meyer auf der Heide, Friedhelm and Podlipyan, Pavel}},
issn = {{0304-3975}},
journal = {{Theoretical Computer Science}},
keywords = {{Local algorithms, Distributed algorithms, Collisionless gathering, Mobile robots, Multiagent system}},
pages = {{29--40}},
title = {{{The impact of the Gabriel subgraph of the visibility graph on the gathering of mobile autonomous robots}}},
doi = {{10.1016/j.tcs.2020.11.009}},
volume = {{852}},
year = {{2021}},
}
@inproceedings{26986,
author = {{Castenow, Jannik and Götte, Thorsten and Knollmann, Till and Meyer auf der Heide, Friedhelm}},
booktitle = {{Proceedings of the 23rd International Symposium on Stabilization, Safety, and Security of Distributed Systems, SSS 2021}},
editor = {{Johnen, C. and Schiller, E.M. and Schmid, S.}},
location = {{Online}},
pages = {{289--304 }},
publisher = {{Springer}},
title = {{{The Max-Line-Formation Problem – And New Insights for Gathering and Chain-Formation}}},
doi = {{10.1007/978-3-030-91081-5_19}},
volume = {{13046}},
year = {{2021}},
}
@inproceedings{19899,
abstract = {{Most existing robot formation problems seek a target formation of a certain
minimal and, thus, efficient structure. Examples include the Gathering
and the Chain-Formation problem. In this work, we study formation problems that
try to reach a maximal structure, supporting for example an efficient
coverage in exploration scenarios. A recent example is the NASA Shapeshifter
project, which describes how the robots form a relay chain along which gathered
data from extraterrestrial cave explorations may be sent to a home base.
As a first step towards understanding such maximization tasks, we introduce
and study the Max-Chain-Formation problem, where $n$ robots are ordered along a
winding, potentially self-intersecting chain and must form a connected,
straight line of maximal length connecting its two endpoints. We propose and
analyze strategies in a discrete and in a continuous time model. In the
discrete case, we give a complete analysis if all robots are initially
collinear, showing that the worst-case time to reach an
$\varepsilon$-approximation is upper bounded by $\mathcal{O}(n^2 \cdot \log
(n/\varepsilon))$ and lower bounded by $\Omega(n^2 \cdot~\log
(1/\varepsilon))$. If one endpoint of the chain remains stationary, this result
can be extended to the non-collinear case. If both endpoints move, we identify
a family of instances whose runtime is unbounded. For the continuous model, we
give a strategy with an optimal runtime bound of $\Theta(n)$. Avoiding an
unbounded runtime similar to the discrete case relies crucially on a
counter-intuitive aspect of the strategy: slowing down the endpoints while all
other robots move at full speed. Surprisingly, we can show that a similar trick
does not work in the discrete model.}},
author = {{Castenow, Jannik and Kling, Peter and Knollmann, Till and Meyer auf der Heide, Friedhelm}},
booktitle = {{Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings}},
editor = {{Devismes , Stéphane and Mittal, Neeraj }},
isbn = {{978-3-030-64347-8}},
pages = {{65--80}},
publisher = {{Springer}},
title = {{{A Discrete and Continuous Study of the Max-Chain-Formation Problem – Slow Down to Speed Up}}},
doi = {{10.1007/978-3-030-64348-5_6}},
volume = {{12514}},
year = {{2020}},
}
@inproceedings{20159,
abstract = {{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.
1) Single source: Given any designated source vertex s, there exists a data structure of size 𝒪(|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 𝒪(|S|).
2) All-pairs: There exists an 𝒪(|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 𝒪(k), where k is the number of pairs of vertices whose mincut increases.
For 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 𝒪(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 𝒪(n) size.}},
author = {{Baswana, Surender and Gupta, Shiv and Knollmann, Till}},
booktitle = {{28th Annual European Symposium on Algorithms (ESA 2020)}},
editor = {{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter}},
isbn = {{978-3-95977-162-7}},
issn = {{1868-8969}},
keywords = {{Mincut, Sensitivity, Data Structure}},
pages = {{12:1--12:14}},
publisher = {{Schloss Dagstuhl -- Leibniz-Zentrum für Informatik}},
title = {{{Mincut Sensitivity Data Structures for the Insertion of an Edge}}},
doi = {{10.4230/LIPIcs.ESA.2020.12}},
volume = {{173}},
year = {{2020}},
}
@inproceedings{20185,
author = {{Castenow, Jannik and Harbig, Jonas and Jung, Daniel and Knollmann, Till and Meyer auf der Heide, Friedhelm}},
booktitle = {{Stabilization, Safety, and Security of Distributed Systems - 22nd International Symposium, SSS 2020, Austin, Texas, USA, November 18-21, 2020, Proceedings }},
editor = {{Devismes, Stéphane and Mittal, Neeraj}},
isbn = {{978-3-030-64347-8}},
pages = {{60--64}},
publisher = {{Springer}},
title = {{{Brief Announcement: Gathering in Linear Time: A Closed Chain of Disoriented & Luminous Robots with Limited Visibility }}},
doi = {{10.1007/978-3-030-64348-5_5}},
volume = {{12514}},
year = {{2020}},
}
@inproceedings{17370,
abstract = {{ We consider a natural extension to the metric uncapacitated Facility Location Problem (FLP) in which requests ask for different commodities out of a finite set \( S \) of commodities.
Ravi and Sinha (SODA 2004) introduced the model as the \emph{Multi-Commodity Facility Location Problem} (MFLP) and considered it an offline optimization problem.
The model itself is similar to the FLP: i.e., requests are located at points of a finite metric space and the task of an algorithm is to construct facilities and assign requests to facilities while minimizing the construction cost and the sum over all assignment distances.
In addition, requests and facilities are heterogeneous; they request or offer multiple commodities out of $S$.
A request has to be connected to a set of facilities jointly offering the commodities demanded by it.
In comparison to the FLP, an algorithm has to decide not only if and where to place facilities, but also which commodities to offer at each.
To the best of our knowledge we are the first to study the problem in its online variant in which requests, their positions and their commodities are not known beforehand but revealed over time.
We present results regarding the competitive ratio.
On the one hand, we show that heterogeneity influences the competitive ratio by developing a lower bound on the competitive ratio for any randomized online algorithm of \( \Omega ( \sqrt{|S|} + \frac{\log n}{\log \log n} ) \) that already holds for simple line metrics.
Here, \( n \) is the number of requests.
On the other side, we establish a deterministic \( \mathcal{O}(\sqrt{|S|} \cdot \log n) \)-competitive algorithm and a randomized \( \mathcal{O}(\sqrt{|S|} \cdot \frac{\log n}{\log \log n} ) \)-competitive algorithm.
Further, we show that when considering a more special class of cost functions for the construction cost of a facility, the competitive ratio decreases given by our deterministic algorithm depending on the function.}},
author = {{Castenow, Jannik and Feldkord, Björn and Knollmann, Till and Malatyali, Manuel and Meyer auf der Heide, Friedhelm}},
booktitle = {{Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures}},
isbn = {{9781450369350}},
keywords = {{Online Multi-Commodity Facility Location, Competitive Ratio, Online Optimization, Facility Location Problem}},
title = {{{The Online Multi-Commodity Facility Location Problem}}},
doi = {{10.1145/3350755.3400281}},
year = {{2020}},
}
@inproceedings{17371,
author = {{Castenow, Jannik and Kling, Peter and Knollmann, Till and Meyer auf der Heide, Friedhelm}},
booktitle = {{Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures}},
isbn = {{9781450369350}},
title = {{{Brief Announcement: A Discrete and Continuous Study of the Max-Chain-Formation Problem: Slow Down to Speed up}}},
doi = {{10.1145/3350755.3400263}},
year = {{2020}},
}
@inproceedings{16968,
abstract = {{In this work, we initiate the research about the Gathering problem for robots
with limited viewing range in the three-dimensional Euclidean space. In the
Gathering problem, a set of initially scattered robots is required to gather at
the same position. The robots' capabilities are very restricted -- they do not
agree on any coordinate system or compass, have a limited viewing range, have
no memory of the past and cannot communicate. We study the problem in two
different time models, in FSYNC (fully synchronized discrete rounds) and the
continuous time model. For FSYNC, we introduce the 3D-Go-To-The-Center-strategy
and prove a runtime of $\Theta(n^2)$ that matches the currently best runtime
bound for the same model in the Euclidean plane [SPAA'11]. Our main result is
the generalization of contracting strategies (continuous time) from
[Algosensors'17] to three dimensions. In contracting strategies, every robot
that is located on the global convex hull of all robots' positions moves with
full speed towards the inside of the convex hull. We prove a runtime bound of
$O(\Delta \cdot n^{3/2})$ for any three-dimensional contracting strategy, where
$\Delta$ denotes the diameter of the initial configuration. This comes up to a
factor of $\sqrt{n}$ close to the lower bound of $\Omega (\Delta \cdot n)$
which is already true in two dimensions. In general, it might be hard for
robots with limited viewing range to decide whether they are located on the
global convex hull and which movement maintains the connectivity of the swarm,
rendering the design of concrete contracting strategies a challenging task. We
prove that the continuous variant of 3D-Go-To-The-Center is contracting and
keeps the swarm connected. Moreover, we give a simple design criterion for
three-dimensional contracting strategies that maintains the connectivity of the
swarm and introduce an exemplary strategy based on this criterion.}},
author = {{Braun, Michael and Castenow, Jannik and Meyer auf der Heide, Friedhelm}},
booktitle = {{Proceedings of the 27th Conference on Structural Information and Communication Complexity (SIROCCO)}},
location = {{Paderborn}},
publisher = {{Springer}},
title = {{{Local Gathering of Mobile Robots in Three Dimensions}}},
doi = {{10.1007/978-3-030-54921-3_4}},
year = {{2020}},
}
@phdthesis{15631,
author = {{Feldkord, Björn}},
title = {{{Mobile Resource Allocation}}},
doi = {{10.17619/UNIPB/1-869}},
year = {{2020}},
}