@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{7636,
abstract = {{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.
}},
author = {{Luo, Linghui and Scheideler, Christian and Strothmann, Thim Frederik}},
booktitle = {{Proceedings of the 2019 IEEE 33rd International Parallel and Distributed Processing Symposium (IPDPS '19)}},
location = {{Rio de Janeiro, Brazil}},
title = {{{MultiSkipGraph: A Self-stabilizing Overlay Network that Maintains Monotonic Searchability}}},
year = {{2019}},
}
@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}},
}