@inproceedings{8534, abstract = {{We propose two protocols for distributed priority queues (denoted by 'heap' for simplicity in this paper) called SKEAP and SEAP. SKEAP realizes a distributed heap for a constant amount of priorities and SEAP one for an arbitrary amount. Both protocols build on an overlay, which induces an aggregation tree on which heap operations are aggregated in batches, ensuring that our protocols scale even for a high rate of incoming requests. As part of SEAP we provide a novel distributed protocol for the k-selection problem that runs in time O(log n) w.h.p. SKEAP guarantees sequential consistency for its heap operations, while SEAP guarantees serializability. SKEAP and SEAP provide logarithmic runtimes w.h.p. on all their operations. SKEAP and SEAP provide logarithmic runtimes w.h.p. on all their operations with SEAP having to use only O(log n) bit messages.}}, author = {{Feldmann, Michael and Scheideler, Christian}}, booktitle = {{Proceedings of the 31st ACM Symposium on Parallelism in Algorithms and Architectures (SPAA)}}, pages = {{287----296}}, publisher = {{ACM}}, title = {{{Skeap & Seap: Scalable Distributed Priority Queues for Constant and Arbitrary Priorities}}}, doi = {{10.1145/3323165.3323193}}, year = {{2019}}, } @inproceedings{8871, author = {{Augustine, John and Ghaffari, Mohsen and Gmyr, Robert and Hinnenthal, Kristian and Kuhn, Fabian and Li, Jason and Scheideler, Christian}}, booktitle = {{Proceedings of the 31st ACM Symposium on Parallelism in Algorithms and Architectures}}, pages = {{69----79}}, publisher = {{ACM}}, title = {{{Distributed Computation in Node-Capacitated Networks}}}, doi = {{10.1145/3323165.3323195}}, year = {{2019}}, } @inbook{9599, author = {{Daymude, Joshua J. and Hinnenthal, Kristian and Richa, Andréa W. and Scheideler, Christian}}, booktitle = {{Distributed Computing by Mobile Entities, Current Research in Moving and Computing.}}, pages = {{615--681}}, publisher = {{Springer, Cham}}, title = {{{Computing by Programmable Particles}}}, doi = {{https://doi.org/10.1007/978-3-030-11072-7_22}}, year = {{2019}}, } @inproceedings{6976, abstract = {{We investigate the maintenance of overlay networks under massive churn, i.e. nodes joining and leaving the network. We assume an adversary that may churn a constant fraction $\alpha n$ of nodes over the course of $\mathcal{O}(\log n)$ rounds. In particular, the adversary has an almost up-to-date information of the network topology as it can observe an only slightly outdated topology that is at least $2$ rounds old. Other than that, we only have the provably minimal restriction that new nodes can only join the network via nodes that have taken part in the network for at least one round. Our contributions are as follows: First, we show that it is impossible to maintain a connected topology if adversary has up-to-date information about the nodes' connections. Further, we show that our restriction concerning the join is also necessary. As our main result present an algorithm that constructs a new overlay- completely independent of all previous overlays - every $2$ rounds. Furthermore, each node sends and receives only $\mathcal{O}(\log^3 n)$ messages each round. As part of our solution we propose the Linearized DeBruijn Swarm (LDS), a highly churn resistant overlay, which will be maintained by the algorithm. However, our approaches can be transferred to a variety of classical P2P Topologies where nodes are mapped into the $[0,1)$-interval.}}, author = {{Götte, Thorsten and Vijayalakshmi, Vipin Ravindran and Scheideler, Christian}}, booktitle = {{Proceedings of the 2019 IEEE 33rd International Parallel and Distributed Processing Symposium (IPDPS '19)}}, location = {{Rio de Janeiro, Brazil}}, publisher = {{IEEE}}, title = {{{Always be Two Steps Ahead of Your Enemy - Maintaining a Routable Overlay under Massive Churn with an Almost Up-to-date Adversary}}}, year = {{2019}}, } @inproceedings{10586, abstract = {{We consider the problem of transforming a given graph G_s into a desired graph G_t by applying a minimum number of primitives from a particular set of local graph transformation primitives. These primitives are local in the sense that each node can apply them based on local knowledge and by affecting only its 1-neighborhood. Although the specific set of primitives we consider makes it possible to transform any (weakly) connected graph into any other (weakly) connected graph consisting of the same nodes, they cannot disconnect the graph or introduce new nodes into the graph, making them ideal in the context of supervised overlay network transformations. We prove that computing a minimum sequence of primitive applications (even centralized) for arbitrary G_s and G_t is NP-hard, which we conjecture to hold for any set of local graph transformation primitives satisfying the aforementioned properties. On the other hand, we show that this problem admits a polynomial time algorithm with a constant approximation ratio.}}, author = {{Scheideler, Christian and Setzer, Alexander}}, booktitle = {{Proceedings of the 46th International Colloquium on Automata, Languages, and Programming}}, keywords = {{Graphs transformations, NP-hardness, approximation algorithms}}, location = {{Patras, Greece}}, pages = {{150:1----150:14}}, publisher = {{Dagstuhl Publishing}}, title = {{{On the Complexity of Local Graph Transformations}}}, doi = {{10.4230/LIPICS.ICALP.2019.150}}, volume = {{132}}, year = {{2019}}, } @inproceedings{12944, author = {{Götte, Thorsten and Hinnenthal, Kristian and Scheideler, Christian}}, booktitle = {{Structural Information and Communication Complexity}}, title = {{{Faster Construction of Overlay Networks}}}, doi = {{10.1007/978-3-030-24922-9_18}}, year = {{2019}}, } @inproceedings{15627, author = {{Augustine, John and Hinnenthal, Kristian and Kuhn, Fabian and Scheideler, Christian and Schneider, Philipp}}, booktitle = {{Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms}}, isbn = {{9781611975994}}, pages = {{1280--1299}}, title = {{{Shortest Paths in a Hybrid Network Model}}}, doi = {{10.1137/1.9781611975994.78}}, year = {{2019}}, } @article{14830, author = {{Gmyr, Robert and Lefevre, Jonas and Scheideler, Christian}}, journal = {{Theory Comput. Syst.}}, number = {{2}}, pages = {{177--199}}, title = {{{Self-Stabilizing Metric Graphs}}}, doi = {{10.1007/s00224-017-9823-4}}, volume = {{63}}, year = {{2019}}, } @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{13182, abstract = {{We consider congestion control in peer-to-peer distributed systems. The problem can be reduced to the following scenario: Consider a set $V$ of $n$ peers (called \emph{clients} in this paper) that want to send messages to a fixed common peer (called \emph{server} in this paper). We assume that each client $v \in V$ sends a message with probability $p(v) \in [0,1)$ and the server has a capacity of $\sigma \in \mathbb{N}$, i.e., it can recieve at most $\sigma$ messages per round and excess messages are dropped. The server can modify these probabilities when clients send messages. Ideally, we wish to converge to a state with $\sum p(v) = \sigma$ and $p(v) = p(w)$ for all $v,w \in V$. We propose a \emph{loosely} self-stabilizing protocol with a slightly relaxed legitimate state. Our protocol lets the system converge from \emph{any} initial state to a state where $\sum p(v) \in \left[\sigma \pm \epsilon\right]$ and $|p(v)-p(w)| \in O(\frac{1}{n})$. This property is then maintained for $\Omega(n^{\mathfrak{c}})$ rounds in expectation. In particular, the initial client probabilities and server variables are not necessarily well-defined, i.e., they may have arbitrary values. Our protocol uses only $O(W + \log n)$ bits of memory where $W$ is length of node identifiers, making it very lightweight. Finally we state a lower bound on the convergence time an see that our protocol performs asymptotically optimal (up to some polylogarithmic factor). }}, author = {{Feldmann, Michael and Götte, Thorsten and Scheideler, Christian}}, booktitle = {{Proceedings of the 21st International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS)}}, pages = {{149--164}}, publisher = {{Springer, Cham}}, title = {{{A Loosely Self-stabilizing Protocol for Randomized Congestion Control with Logarithmic Memory}}}, doi = {{https://doi.org/10.1007/978-3-030-34992-9_13}}, year = {{2019}}, } @inproceedings{13652, author = {{Hinnenthal, Kristian and Scheideler, Christian and Struijs, Martijn}}, booktitle = {{33rd International Symposium on Distributed Computing (DISC 2019)}}, title = {{{Fast Distributed Algorithms for LP-Type Problems of Low Dimension}}}, doi = {{10.4230/LIPICS.DISC.2019.23}}, year = {{2019}}, } @inproceedings{27051, author = {{Augustine, John and Hinnenthal, Kristian and Kuhn, Fabian and Scheideler, Christian and Schneider, Philipp}}, booktitle = {{Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms, SODA 2020, Salt Lake City, UT, USA, January 5-8, 2020}}, editor = {{Chawla, Shuchi}}, pages = {{1280--1299}}, publisher = {{SIAM}}, title = {{{Shortest Paths in a Hybrid Network Model}}}, doi = {{10.1137/1.9781611975994.78}}, year = {{2020}}, } @article{17808, author = {{Gmyr, Robert and Hinnenthal, Kristian and Kostitsyna, Irina and Kuhn, Fabian and Rudolph, Dorian and Scheideler, Christian and Strothmann, Thim}}, journal = {{Nat. Comput.}}, number = {{2}}, pages = {{375--390}}, title = {{{Forming tile shapes with simple robots}}}, doi = {{10.1007/s11047-019-09774-2}}, volume = {{19}}, year = {{2020}}, } @inproceedings{20755, abstract = {{We consider the problem of computing shortest paths in \emph{hybrid networks}, in which nodes can make use of different communication modes. For example, mobile phones may use ad-hoc connections via Bluetooth or Wi-Fi in addition to the cellular network to solve tasks more efficiently. Like in this case, the different communication modes may differ considerably in range, bandwidth, and flexibility. We build upon the model of Augustine et al. [SODA '20], which captures these differences by a \emph{local} and a \emph{global} mode. Specifically, the local edges model a fixed communication network in which $O(1)$ messages of size $O(\log n)$ can be sent over every edge in each synchronous round. The global edges form a clique, but nodes are only allowed to send and receive a total of at most $O(\log n)$ messages over global edges, which restricts the nodes to use these edges only very sparsely. We demonstrate the power of hybrid networks by presenting algorithms to compute Single-Source Shortest Paths and the diameter very efficiently in \emph{sparse graphs}. Specifically, we present exact $O(\log n)$ time algorithms for cactus graphs (i.e., graphs in which each edge is contained in at most one cycle), and $3$-approximations for graphs that have at most $n + O(n^{1/3})$ edges and arboricity $O(\log n)$. For these graph classes, our algorithms provide exponentially faster solutions than the best known algorithms for general graphs in this model. Beyond shortest paths, we also provide a variety of useful tools and techniques for hybrid networks, which may be of independent interest. }}, author = {{Feldmann, Michael and Hinnenthal, Kristian and Scheideler, Christian}}, booktitle = {{Proceedings of the 24th International Conference on Principles of Distributed Systems (OPODIS)}}, publisher = {{Schloss Dagstuhl - Leibniz-Zentrum für Informatik}}, title = {{{Fast Hybrid Network Algorithms for Shortest Paths in Sparse Graphs}}}, doi = {{10.4230/LIPIcs.OPODIS.2020.31}}, year = {{2020}}, } @article{16902, abstract = {{The maintenance of efficient and robust overlay networks is one of the most fundamental and reoccurring themes in networking. This paper presents a survey of state-of-the-art algorithms to design and repair overlay networks in a distributed manner. In particular, we discuss basic algorithmic primitives to preserve connectivity, review algorithms for the fundamental problem of graph linearization, and then survey self-stabilizing algorithms for metric and scalable topologies. We also identify open problems and avenues for future research. }}, author = {{Feldmann, Michael and Scheideler, Christian and Schmid, Stefan}}, journal = {{ACM Computing Surveys}}, publisher = {{ACM}}, title = {{{Survey on Algorithms for Self-Stabilizing Overlay Networks}}}, doi = {{10.1145/3397190}}, year = {{2020}}, } @inproceedings{16903, abstract = {{We consider the clock synchronization problem in the (discrete) beeping model: Given a network of $n$ nodes with each node having a clock value $\delta(v) \in \{0,\ldots T-1\}$, the goal is to synchronize the clock values of all nodes such that they have the same value in any round. As is standard in clock synchronization, we assume \emph{arbitrary activations} for all nodes, i.e., the nodes start their protocol at an arbitrary round (not limited to $\{0,\ldots,T-1\}$). We give an asymptotically optimal algorithm that runs in $4D + \Bigl\lfloor \frac{D}{\lfloor T/4 \rfloor} \Bigr \rfloor \cdot (T \mod 4) = O(D)$ rounds, where $D$ is the diameter of the network. Once all nodes are in sync, they beep at the same round every $T$ rounds. The algorithm drastically improves on the $O(T D)$-bound of \cite{firefly_sync} (where $T$ is required to be at least $4n$, so the bound is no better than $O(nD)$). Our algorithm is very simple as nodes only have to maintain $3$ bits in addition to the $\lceil \log T \rceil$ bits needed to maintain the clock. Furthermore we investigate the complexity of \emph{self-stabilizing} solutions for the clock synchronization problem: We first show lower bounds of $\Omega(\max\{T,n\})$ rounds on the runtime and $\Omega(\log(\max\{T,n\}))$ bits of memory required for any such protocol. Afterwards we present a protocol that runs in $O(\max\{T,n\})$ rounds using at most $O(\log(\max\{T,n\}))$ bits at each node, which is asymptotically optimal with regards to both, runtime and memory requirements.}}, author = {{Feldmann, Michael and Khazraei, Ardalan and Scheideler, Christian}}, booktitle = {{Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA)}}, publisher = {{ACM}}, title = {{{Time- and Space-Optimal Discrete Clock Synchronization in the Beeping Model}}}, doi = {{10.1145/3350755.3400246}}, 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}}, } @inproceedings{16346, author = {{Daymude, Joshua J. and Gmyr, Robert and Hinnenthal, Kristian and Kostitsyna, Irina and Scheideler, Christian and Richa, Andréa W.}}, booktitle = {{Proceedings of the 21st International Conference on Distributed Computing and Networking}}, isbn = {{9781450377515}}, title = {{{Convex Hull Formation for Programmable Matter}}}, doi = {{10.1145/3369740.3372916}}, year = {{2020}}, } @inproceedings{25105, author = {{Dolev, Shlomi and Prasadh Narayanan, Ram and Scheideler, Christian and Schindelhauer, Christian}}, booktitle = {{NANOCOM '21: The Eighth Annual ACM International Conference on Nanoscale Computing and Communication, Virtual Event, Italy, September 7 - 9, 2021}}, editor = {{Galluccio, Laura and Mitra, Urbashi and Magarini, Maurizio and Abada, Sergi and Taynnan Barros, Michael and Krishnaswamy, Bhuvana}}, pages = {{30:1--30:2}}, publisher = {{ACM}}, title = {{{Logarithmic Time MIMO Based Self-Stabilizing Clock Synchronization}}}, doi = {{10.1145/3477206.3477471}}, year = {{2021}}, } @inproceedings{28917, author = {{Feldmann, Michael and Padalkin, Andreas and Scheideler, Christian and Dolev, Shlomi}}, booktitle = {{Stabilization, Safety, and Security of Distributed Systems - 23rd International Symposium, (SSS) 2021, Virtual Event, November 17-20, 2021, Proceedings}}, editor = {{Johnen, Colette and Michael Schiller, Elad and Schmid, Stefan}}, pages = {{484--488}}, publisher = {{Springer}}, title = {{{Coordinating Amoebots via Reconfigurable Circuits}}}, doi = {{10.1007/978-3-030-91081-5\_34}}, volume = {{13046}}, year = {{2021}}, }