@article{33947, author = {{Castenow, Jannik and Harbig, Jonas and Jung, Daniel and Knollmann, Till and Meyer auf der Heide, Friedhelm}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, keywords = {{General Computer Science, Theoretical Computer Science}}, pages = {{261--291}}, publisher = {{Elsevier BV}}, title = {{{Gathering a Euclidean Closed Chain of Robots in Linear Time and Improved Algorithms for Chain-Formation}}}, doi = {{10.1016/j.tcs.2022.10.031}}, volume = {{939}}, year = {{2023}}, } @inproceedings{34008, author = {{Castenow, Jannik and Harbig, Jonas and Jung, Daniel and Kling, Peter and Knollmann, Till and Meyer auf der Heide, Friedhelm}}, booktitle = {{Proceedings of the 26th International Conference on Principles of Distributed Systems (OPODIS) }}, editor = {{Hillel, Eshcar and Palmieri, Roberto and Riviére, Etienne}}, isbn = {{978-3-95977-265-5}}, issn = {{1868-8969}}, location = {{Brussels}}, pages = {{15:1–15:25}}, publisher = {{Schloss Dagstuhl – Leibniz Zentrum für Informatik}}, title = {{{A Unifying Approach to Efficient (Near-)Gathering of Disoriented Robots with Limited Visibility }}}, doi = {{10.4230/LIPIcs.OPODIS.2022.15}}, volume = {{253}}, year = {{2023}}, } @inbook{44769, author = {{Castenow, Jannik and Harbig, Jonas and Meyer auf der Heide, Friedhelm}}, booktitle = {{Lecture Notes in Computer Science}}, isbn = {{9783031304477}}, issn = {{0302-9743}}, publisher = {{Springer International Publishing}}, title = {{{Unifying Gathering Protocols for Swarms of Mobile Robots}}}, doi = {{10.1007/978-3-031-30448-4_1}}, year = {{2023}}, } @phdthesis{45580, author = {{Castenow, Jannik}}, title = {{{Local Protocols for Contracting and Expanding Robot Formation Problems}}}, doi = {{10.17619/UNIPB/1-1750}}, year = {{2023}}, } @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}}, } @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}}, } @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{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{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}}, } @inproceedings{15169, author = {{Castenow, Jannik and Kolb, Christina and Scheideler, Christian}}, booktitle = {{Proceedings of the 21st International Conference on Distributed Computing and Networking (ICDCN)}}, location = {{Kolkata, Indien}}, publisher = {{ACM}}, title = {{{A Bounding Box Overlay for Competitive Routing in Hybrid Communication Networks}}}, year = {{2020}}, } @article{16299, author = {{Castenow, Jannik and Fischer, Matthias and Harbig, Jonas and Jung, Daniel and Meyer auf der Heide, Friedhelm}}, issn = {{0304-3975}}, journal = {{Theoretical Computer Science}}, pages = {{289--309}}, title = {{{Gathering Anonymous, Oblivious Robots on a Grid}}}, doi = {{10.1016/j.tcs.2020.02.018}}, volume = {{815}}, year = {{2020}}, } @inproceedings{14539, author = {{Castenow, Jannik and Kolb, Christina and Scheideler, Christian}}, booktitle = {{Proceedings of the 26th International Colloquium on Structural Information and Communication Complexity (SIROCCO)}}, location = {{L'Aquila, Italy}}, pages = {{345--348}}, title = {{{A Bounding Box Overlay for Competitive Routing in Hybrid Communication Networks}}}, doi = {{10.1007/978-3-030-24922-9\_26}}, year = {{2019}}, } @inproceedings{4563, abstract = {{Routing is a challenging problem for wireless ad hoc networks, especially when the nodes are mobile and spread so widely that in most cases multiple hops are needed to route a message from one node to another. In fact, it is known that any online routing protocol has a poor performance in the worst case, in a sense that there is a distribution of nodes resulting in bad routing paths for that protocol, even if the nodes know their geographic positions and the geographic position of the destination of a message is known. The reason for that is that radio holes in the ad hoc network may require messages to take long detours in order to get to a destination, which are hard to find in an online fashion. In this paper, we assume that the wireless ad hoc network can make limited use of long-range links provided by a global communication infrastructure like a cellular infrastructure or a satellite in order to compute an abstraction of the wireless ad hoc network that allows the messages to be sent along near-shortest paths in the ad hoc network. We present distributed algorithms that compute an abstraction of the ad hoc network in $\mathcal{O}\left(\log ^2 n\right)$ time using long-range links, which results in $c$-competitive routing paths between any two nodes of the ad hoc network for some constant $c$ if the convex hulls of the radio holes do not intersect. We also show that the storage needed for the abstraction just depends on the number and size of the radio holes in the wireless ad hoc network and is independent on the total number of nodes, and this information just has to be known to a few nodes for the routing to work. }}, author = {{Jung, Daniel and Kolb, Christina and Scheideler, Christian and Sundermeier, Jannik}}, booktitle = {{Proceedings of the 14th International Symposium on Algorithms and Experiments for Wireless Networks (ALGOSENSORS) }}, keywords = {{greedy routing, ad hoc networks, convex hulls, c-competitiveness}}, location = {{Helsinki}}, publisher = {{Springer}}, title = {{{Competitive Routing in Hybrid Communication Networks}}}, year = {{2018}}, } @inproceedings{4565, author = {{Jung, Daniel and Kolb, Christina and Scheideler, Christian and Sundermeier, Jannik}}, booktitle = {{Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures (SPAA)}}, isbn = {{9781450357999}}, location = {{Wien}}, publisher = {{ACM Press}}, title = {{{Brief Announcement: Competitive Routing in Hybrid Communication Networks}}}, doi = {{10.1145/3210377.3210663}}, year = {{2018}}, } @inproceedings{4375, abstract = {{We present a peer-to-peer network that supports the efficient processing of orthogonal range queries $R=\bigtimes_{i=1}^{d}[a_i,\,b_i]$ in a $d$-dimensional point space.\\ The network is the same for each dimension, namely a distance halving network like the one introduced by Naor and Wieder (ACM TALG'07). We show how to execute such range queries using $\mathcal{O}\left(2^{d'}d\,\log m + d\,|R|\right)$ hops (and the same number of messages) in total. Here $[m]^d$ is the ground set, $|R|$ is the size and $d'$ the dimension of the queried range. Furthermore, if the peers form a distributed network, the query can be answered in $\mathcal{O}\left(d\,\log m + d\,\sum_{i=1}^{d}(b_i-a_i+1)\right)$ communication rounds. Our algorithms are based on a mapping of the Hilbert Curve through $[m]^d$ to the peers.}}, author = {{Benter, Markus and Knollmann, Till and Meyer auf der Heide, Friedhelm and Setzer, Alexander and Sundermeier, Jannik}}, booktitle = {{Proceedings of the 4th International Symposium on Algorithmic Aspects of Cloud Computing (ALGOCLOUD)}}, keywords = {{Distributed Storage, Multi-Dimensional Range Queries, Peer-to-Peer, Hilbert Curve}}, location = {{Helsinki}}, title = {{{A Peer-to-Peer based Cloud Storage supporting orthogonal Range Queries of arbitrary Dimension}}}, doi = {{10.1007/978-3-030-19759-9_4}}, year = {{2018}}, } @misc{699, author = {{Sundermeier, Jannik}}, publisher = {{Universität Paderborn}}, title = {{{Routing in Hybrid Communication Networks with Holes - Considering Bounding Boxes as Hole Abstractions}}}, year = {{2017}}, }