@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}}, } @phdthesis{45579, author = {{Knollmann, Till}}, title = {{{Online Algorithms for Allocating Heterogeneous Resources}}}, doi = {{10.17619/UNIPB/1-1751}}, year = {{2023}}, } @inbook{45875, author = {{Götte, Thorsten and Knollmann, Till and Meyer auf der Heide, Friedhelm and Scheideler, Christian and Werthmann, Julian}}, booktitle = {{On-The-Fly Computing -- Individualized IT-services in dynamic markets}}, editor = {{Haake, Claus-Jochen and Meyer auf der Heide, Friedhelm and Platzner, Marco and Wachsmuth, Henning and Wehrheim, Heike}}, pages = {{1----20}}, publisher = {{Heinz Nixdorf Institut, Universität Paderborn}}, title = {{{Capabilities and Limitations of Local Strategies in Dynamic Networks}}}, doi = {{10.5281/zenodo.8060372}}, volume = {{412}}, 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}}, } @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{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 = {{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}}, } @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{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{12870, author = {{Feldkord, Björn and Knollmann, Till and Malatyali, Manuel and Meyer auf der Heide, Friedhelm}}, booktitle = {{Proceedings of the 17th Workshop on Approximation and Online Algorithms (WAOA)}}, pages = {{120 -- 137}}, publisher = {{Springer}}, title = {{{Managing Multiple Mobile Resources}}}, doi = {{10.1007/978-3-030-39479-0_9}}, year = {{2019}}, } @inproceedings{4411, abstract = {{While a lot of 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. Considering crashing peers in peer-to-peer networks, it should not be taken for granted that a distributed data structure remains intact. In this work, 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 a wide area of applications including string matching problems 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 $\mathcal{O}(\log |x|)$ hash table read accesses. We show how to maintain the structure in a self-stabilizing way. Our protocol assures low overhead in a legal state and a total (asymptotically optimal) memory demand of $\Theta(d)$ bits, where $d$ is the number of bits needed for storing all keys.}}, author = {{Knollmann, Till and Scheideler, Christian}}, booktitle = {{Proceedings of the 20th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS)}}, editor = {{Izumi, Taisuke and Kuznetsov, Petr}}, keywords = {{Self-Stabilizing, Prefix Search, Distributed Data Structure}}, location = {{Tokyo}}, publisher = {{Springer, Cham}}, title = {{{A Self-Stabilizing Hashed Patricia Trie}}}, doi = {{10.1007/978-3-030-03232-6_1}}, volume = {{11201}}, 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}}, } @inbook{16461, author = {{Bemmann, Pascal and Biermeier, Felix and Bürmann, Jan and Kemper, Arne and Knollmann, Till and Knorr, Steffen and Kothe, Nils and Mäcker, Alexander and Malatyali, Manuel and Meyer auf der Heide, Friedhelm and Riechers, Sören and Schaefer, Johannes Sebastian and Sundermeier, Jannik}}, booktitle = {{Structural Information and Communication Complexity}}, isbn = {{9783319720494}}, issn = {{0302-9743}}, title = {{{Monitoring of Domain-Related Problems in Distributed Data Streams}}}, doi = {{10.1007/978-3-319-72050-0_13}}, year = {{2017}}, }