TY - CHAP AU - Götte, Thorsten AU - Kolb, Christina AU - Scheideler, Christian AU - Werthmann, Julian ID - 26888 SN - 0302-9743 T2 - Algorithms for Sensor Systems (ALGOSENSORS '21) TI - Beep-And-Sleep: Message and Energy Efficient Set Cover ER - TY - CONF AU - Augustine, John AU - Hinnenthal, Kristian AU - Kuhn, Fabian AU - Scheideler, Christian AU - Schneider, Philipp ED - Chawla, Shuchi ID - 27051 T2 - Proceedings of the 2020 ACM-SIAM Symposium on Discrete Algorithms, SODA 2020, Salt Lake City, UT, USA, January 5-8, 2020 TI - Shortest Paths in a Hybrid Network Model ER - TY - JOUR AU - Gmyr, Robert AU - Hinnenthal, Kristian AU - Kostitsyna, Irina AU - Kuhn, Fabian AU - Rudolph, Dorian AU - Scheideler, Christian AU - Strothmann, Thim ID - 17808 IS - 2 JF - Nat. Comput. TI - Forming tile shapes with simple robots VL - 19 ER - TY - CONF AB - 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. AU - Feldmann, Michael AU - Hinnenthal, Kristian AU - Scheideler, Christian ID - 20755 T2 - Proceedings of the 24th International Conference on Principles of Distributed Systems (OPODIS) TI - Fast Hybrid Network Algorithms for Shortest Paths in Sparse Graphs ER - TY - JOUR AB - 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. AU - Feldmann, Michael AU - Scheideler, Christian AU - Schmid, Stefan ID - 16902 JF - ACM Computing Surveys TI - Survey on Algorithms for Self-Stabilizing Overlay Networks ER - TY - CONF AB - 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. AU - Feldmann, Michael AU - Khazraei, Ardalan AU - Scheideler, Christian ID - 16903 T2 - Proceedings of the 32nd ACM Symposium on Parallelism in Algorithms and Architectures (SPAA) TI - Time- and Space-Optimal Discrete Clock Synchronization in the Beeping Model ER - TY - CONF AU - Castenow, Jannik AU - Kolb, Christina AU - Scheideler, Christian ID - 15169 T2 - Proceedings of the 21st International Conference on Distributed Computing and Networking (ICDCN) TI - A Bounding Box Overlay for Competitive Routing in Hybrid Communication Networks ER - TY - CONF AU - Daymude, Joshua J. AU - Gmyr, Robert AU - Hinnenthal, Kristian AU - Kostitsyna, Irina AU - Scheideler, Christian AU - Richa, Andréa W. ID - 16346 SN - 9781450377515 T2 - Proceedings of the 21st International Conference on Distributed Computing and Networking TI - Convex Hull Formation for Programmable Matter ER - TY - CONF AB - Self-stabilizing overlay networks have the advantage of being able to recover from illegal states and faults. However, the majority of these networks cannot give any guarantees on their functionality while the recovery process is going on. We are especially interested in searchability, i.e., the functionality that search messages for a specific node are answered successfully if a node exists in the network. In this paper we investigate overlay networks that ensure the maintenance of monotonic searchability while the self-stabilization is going on. More precisely, once a search message from node u to another node v is successfully delivered, all future search messages from u to v succeed as well. We extend the existing research by focusing on skip graphs and present a solution for two scenarios: (i) the goal topology is a super graph of the perfect skip graph and (ii) the goal topology is exactly the perfect skip graph. AU - Luo, Linghui AU - Scheideler, Christian AU - Strothmann, Thim Frederik ID - 7636 T2 - Proceedings of the 2019 IEEE 33rd International Parallel and Distributed Processing Symposium (IPDPS '19) TI - MultiSkipGraph: A Self-stabilizing Overlay Network that Maintains Monotonic Searchability ER - TY - CONF AB - 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. AU - Feldmann, Michael AU - Scheideler, Christian ID - 8534 T2 - Proceedings of the 31st ACM Symposium on Parallelism in Algorithms and Architectures (SPAA) TI - Skeap & Seap: Scalable Distributed Priority Queues for Constant and Arbitrary Priorities ER -