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 - TY - CONF AU - Augustine, John AU - Ghaffari, Mohsen AU - Gmyr, Robert AU - Hinnenthal, Kristian AU - Kuhn, Fabian AU - Li, Jason AU - Scheideler, Christian ID - 8871 T2 - Proceedings of the 31st ACM Symposium on Parallelism in Algorithms and Architectures TI - Distributed Computation in Node-Capacitated Networks ER - TY - CHAP AU - Daymude, Joshua J. AU - Hinnenthal, Kristian AU - Richa, Andréa W. AU - Scheideler, Christian ID - 9599 T2 - Distributed Computing by Mobile Entities, Current Research in Moving and Computing. TI - Computing by Programmable Particles ER - TY - CONF AB - 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the adversary has an almost up-to-date information of the network topology as it can observe an only slightly outdated topology that is at least $2$ rounds old.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. AU - Götte, Thorsten AU - Vijayalakshmi, Vipin Ravindran AU - Scheideler, Christian ID - 6976 T2 - Proceedings of the 2019 IEEE 33rd International Parallel and Distributed Processing Symposium (IPDPS '19) TI - Always be Two Steps Ahead of Your Enemy - Maintaining a Routable Overlay under Massive Churn with an Almost Up-to-date Adversary ER - TY - CONF AB - 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. AU - Scheideler, Christian AU - Setzer, Alexander ID - 10586 KW - Graphs transformations KW - NP-hardness KW - approximation algorithms T2 - Proceedings of the 46th International Colloquium on Automata, Languages, and Programming TI - On the Complexity of Local Graph Transformations VL - 132 ER - TY - CONF AU - Götte, Thorsten AU - Hinnenthal, Kristian AU - Scheideler, Christian ID - 12944 T2 - Structural Information and Communication Complexity TI - Faster Construction of Overlay Networks ER - TY - CONF AU - Augustine, John AU - Hinnenthal, Kristian AU - Kuhn, Fabian AU - Scheideler, Christian AU - Schneider, Philipp ID - 15627 SN - 9781611975994 T2 - Proceedings of the Fourteenth Annual ACM-SIAM Symposium on Discrete Algorithms TI - Shortest Paths in a Hybrid Network Model ER - TY - JOUR AU - Gmyr, Robert AU - Lefevre, Jonas AU - Scheideler, Christian ID - 14830 IS - 2 JF - Theory Comput. Syst. TI - Self-Stabilizing Metric Graphs VL - 63 ER - TY - CONF AU - Castenow, Jannik AU - Kolb, Christina AU - Scheideler, Christian ID - 14539 T2 - Proceedings of the 26th International Colloquium on Structural Information and Communication Complexity (SIROCCO) TI - A Bounding Box Overlay for Competitive Routing in Hybrid Communication Networks ER - TY - CONF AB - 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). AU - Feldmann, Michael AU - Götte, Thorsten AU - Scheideler, Christian ID - 13182 T2 - Proceedings of the 21st International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS) TI - A Loosely Self-stabilizing Protocol for Randomized Congestion Control with Logarithmic Memory ER -