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the network topology as it can observe an only slightly outdated topology that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
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 - 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
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
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 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 -
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 - 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 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 - 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 study the consensus problem in a synchronous distributed system of n nodes under an adaptive adversary that has a slightly outdated view of the system and can block all incoming and outgoing communication of a constant fraction of the nodes in each round. Motivated by a result of Ben-Or and Bar-Joseph (1998), showing that any consensus algorithm that is resilient against a linear number of crash faults requires $\tilde \Omega(\sqrt n)$ rounds in an n-node network against an adaptive adversary, we consider a late adaptive adversary, who has full knowledge of the network state at the beginning of the previous round and unlimited computational power, but is oblivious to the current state of the nodes.
Our main contributions are randomized distributed algorithms that achieve consensus with high probability among all except a small constant fraction of the nodes (i.e., "almost-everywhere'') against a late adaptive adversary who can block up to ε n$ nodes in each round, for a small constant ε >0$. Our first protocol achieves binary almost-everywhere consensus and also guarantees a decision on the majority input value, thus ensuring plurality consensus. We also present an algorithm that achieves the same time complexity for multi-value consensus. Both of our algorithms succeed in $O(log n)$ rounds with high probability, thus showing an exponential gap to the $\tilde\Omega(\sqrt n)$ lower bound of Ben-Or and Bar-Joseph for strongly adaptive crash-failure adversaries, which can be strengthened to $\Omega(n)$ when allowing the adversary to block nodes instead of permanently crashing them. Our algorithms are scalable to large systems as each node contacts only an (amortized) constant number of peers in each communication round. We show that our algorithms are optimal up to constant (resp.\ sub-logarithmic) factors by proving that every almost-everywhere consensus protocol takes $\Omega(log_d n)$ rounds in the worst case, where d is an upper bound on the number of communication requests initiated per node in each round. We complement our theoretical results with an experimental evaluation of the binary almost-everywhere consensus protocol revealing a short convergence time even against an adversary blocking a large fraction of nodes.
AU - Robinson, Peter
AU - Scheideler, Christian
AU - Setzer, Alexander
ID - 3422
KW - distributed consensus
KW - randomized algorithm
KW - adaptive adversary
KW - complexity lower bound
SN - 978-1-4503-5799-9/18/07
T2 - Proceedings of the 30th ACM Symposium on Parallelism in Algorithms and Architectures (SPAA)
TI - Breaking the $\tilde\Omega(\sqrt{n})$ Barrier: Fast Consensus under a Late Adversary
ER -
TY - CONF
AU - Gmyr, Robert
AU - Hinnenthal, Kristian
AU - Kostitsyna, Irina
AU - Kuhn, Fabian
AU - Rudolph, Dorian
AU - Scheideler, Christian
AU - Strothmann, Thim Frederik
ID - 5764
T2 - Proceedings of the 24th International Conference on DNA Computing and Molecular Programming
TI - Forming Tile Shapes with Simple Robots
ER -
TY - CONF
AU - Scheideler, Christian
ID - 5985
T2 - Proceedings of the 2018 Workshop on Theory and Practice for Integrated Cloud, Fog and Edge Computing Paradigms, TOPIC@PODC 2018, Egham, United Kingdom, July 27, 2018
TI - Relays: Towards a Link Layer for Robust and Secure Fog Computing
ER -
TY - CONF
AB - We extend the concept of monotonic searchability~\cite{DBLP:conf/opodis/ScheidelerSS15}~\cite{DBLP:conf/wdag/ScheidelerSS16} for self-stabilizing systems from one to multiple dimensions.
A system is self-stabilizing if it can recover to a legitimate state from any initial illegal state.
These kind of systems are most often used in distributed applications.
Monotonic searchability provides guarantees when searching for nodes while the recovery process is going on.
More precisely, if a search request started at some node $u$ succeeds in reaching its destination $v$, then all future search requests from $u$ to $v$ succeed as well.
Although there already exists a self-stabilizing protocol for a two-dimensional topology~\cite{DBLP:journals/tcs/JacobRSS12} and an universal approach for monotonic searchability~\cite{DBLP:conf/wdag/ScheidelerSS16}, it is not clear how both of these concepts fit together effectively.
The latter concept even comes with some restrictive assumptions on messages, which is not the case for our protocol.
We propose a simple novel protocol for a self-stabilizing two-dimensional quadtree that satisfies monotonic searchability.
Our protocol can easily be extended to higher dimensions and offers routing in $\mathcal O(\log n)$ hops for any search request.
AU - Feldmann, Michael
AU - Kolb, Christina
AU - Scheideler, Christian
ID - 4351
T2 - Proceedings of the 20th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS)
TI - Self-stabilizing Overlays for high-dimensional Monotonic Searchability
VL - 11201
ER -
TY - CONF
AB - We present a self-stabilizing protocol for an overlay network that constructs the Minimum Spanning Tree (MST) for an underlay that is modeled by a weighted tree. The weight of an overlay edge between two nodes is the weighted length of their shortest path in the tree. We rigorously prove that our protocol works correctly under asynchronous and non-FIFO message delivery. Further, the protocol stabilizes after O(N^2) asynchronous rounds where N is the number of nodes in the overlay.
AU - Götte, Thorsten
AU - Scheideler, Christian
AU - Setzer, Alexander
ID - 5222
T2 - Proceedings of the 20th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS 2018)
TI - On Underlay-Aware Self-Stabilizing Overlay Networks
VL - 11201
ER -
TY - CONF
AU - Gmyr, Robert
AU - Hinnenthal, Kristian
AU - Kostitsyna, Irina
AU - Kuhn, Fabian
AU - Rudolph, Dorian
AU - Scheideler, Christian
ID - 5986
T2 - 43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018, August 27-31, 2018, Liverpool, UK
TI - Shape Recognition by a Finite Automaton Robot
ER -
TY - CONF
AU - Jung, Daniel
AU - Kolb, Christina
AU - Scheideler, Christian
AU - Sundermeier, Jannik
ID - 4565
SN - 9781450357999
T2 - Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures (SPAA)
TI - Brief Announcement: Competitive Routing in Hybrid Communication Networks
ER -
TY - CONF
AB - In this paper we present two major results:
First, we introduce the first self-stabilizing version of a supervised overlay network (as introduced in~\cite{DBLP:conf/ispan/KothapalliS05}) by presenting a self-stabilizing supervised skip ring.
Secondly, we show how to use the self-stabilizing supervised skip ring to construct an efficient self-stabilizing publish-subscribe system.
That is, in addition to stabilizing the overlay network, every subscriber of a topic will eventually know all of the publications that have been issued so far for that topic. The communication work needed to processes a subscribe or unsubscribe operation is just a constant in a legitimate state, and the communication work of checking whether the system is still in a legitimate state is just a constant on expectation for the supervisor as well as any process in the system.
AU - Feldmann, Michael
AU - Kolb, Christina
AU - Scheideler, Christian
AU - Strothmann, Thim Frederik
ID - 1163
KW - Topological Self-stabilization
KW - Supervised Overlay
KW - Publish-Subscribe System
T2 - Proceedings of the 32nd IEEE International Parallel & Distributed Processing Symposium (IPDPS)
TI - Self-Stabilizing Supervised Publish-Subscribe Systems
ER -
TY - CONF
AB - A fundamental problem for overlay networks is to safely exclude leaving nodes, i.e., the nodes requesting to leave the overlay network are excluded from it without affecting its connectivity. To rigorously study self-stabilizing solutions to this problem, the Finite Departure Problem (FDP) has been proposed [9]. In the FDP we are given a network of processes in an arbitrary state, and the goal is to eventually arrive at (and stay in) a state in which all leaving processes irrevocably decided to leave the system while for all weakly-connected components in the initial overlay network, all staying processes in that component will still form a weakly connected component. In the standard interconnection model, the FDP is known to be unsolvable by local control protocols, so oracles have been investigated that allow the problem to be solved [9]. To avoid the use of oracles, we introduce a new interconnection model based on relays. Despite the relay model appearing to be rather restrictive, we show that it is universal, i.e., it is possible to transform any weakly-connected topology into any other weakly-connected topology, which is important for being a useful interconnection model for overlay networks. Apart from this, our model allows processes to grant and revoke access rights, which is why we believe it to be of interest beyond the scope of this paper. We show how to implement the relay layer in a self-stabilizing way and identify properties protocols need to satisfy so that the relay layer can recover while serving protocol requests.
AU - Scheideler, Christian
AU - Setzer, Alexander
ID - 5216
T2 - Proceedings of the 20th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS 2018)
TI - Relays: A New Approach for the Finite Departure Problem in Overlay Networks
ER -
TY - CONF
AB - We propose a distributed protocol for a queue, called Skueue, which spreads its data fairly onto multiple processes, avoiding bottlenecks in high throughput scenarios.
Skueuecan be used in highly dynamic environments, through the addition of join and leave requests to the standard queue operations enqueue and dequeue.
Furthermore Skueue satisfies sequential consistency in the asynchronous message passing model.
Scalability is achieved by aggregating multiple requests to a batch, which can then be processed in a distributed fashion without hurting the queue semantics.
Operations in Skueue need a logarithmic number of rounds w.h.p. until they are processed, even under a high rate of incoming requests.
AU - Feldmann, Michael
AU - Scheideler, Christian
AU - Setzer, Alexander
ID - 1164
T2 - Proceedings of the 32nd IEEE International Parallel & Distributed Processing Symposium (IPDPS)
TI - Skueue: A Scalable and Sequentially Consistent Distributed Queue
ER -