Shape Recognition by a Finite Automaton Robot - Gmyr, Robert; Hinnenthal, Kristian; Kostitsyna, Irina; Kuhn, Fabian; Rudolph, Dorian; Scheideler, Christian (43rd International Symposium on Mathematical Foundations of Computer Science, MFCS 2018, August 27-31, 2018, Liverpool, UK)

A Self-Stabilizing Hashed Patricia Trie - Knollmann, Till; Scheideler, Christian (Proceedings of the 20th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS))
While a lot of research in distributed computing has covered solutions for self-stabilizing computing and topologies, there is far less work on self-stabilization for distributed data structures. Considering crashing peers in peer-to-peer networks, it should not be taken for granted that a distributed data structure remains intact. In this work, we present a self-stabilizing protocol for a distributed data structure called the hashed Patricia Trie (Kniesburges and Scheideler WALCOM'11) that enables efficient prefix search on a set of keys. The data structure has a wide area of applications including string matching problems while offering low overhead and efficient operations when embedded on top of a distributed hash table. Especially, longest prefix matching for $x$ can be done in $\mathcal{O}(\log |x|)$ hash table read accesses. We show how to maintain the structure in a self-stabilizing way. Our protocol assures low overhead in a legal state and a total (asymptotically optimal) memory demand of $Θ(d)$ bits, where $d$ is the number of bits needed for storing all keys.
Keywords: Self-Stabilizing; Prefix Search; Distributed Data Structure

Competitive Routing in Hybrid Communication Networks - Jung, Daniel; Kolb, Christina; Scheideler, Christian; Sundermeier, Jannik (Proceedings of the 14th International Symposium on Algorithms and Experiments for Wireless Networks (ALGOSENSORS))
Routing is a challenging problem for wireless ad hoc networks, especially when the nodes are mobile and spread so widely that in most cases multiple hops are needed to route a message from one node to another. In fact, it is known that any online routing protocol has a poor performance in the worst case, in a sense that there is a distribution of nodes resulting in bad routing paths for that protocol, even if the nodes know their geographic positions and the geographic position of the destination of a message is known. The reason for that is that radio holes in the ad hoc network may require messages to take long detours in order to get to a destination, which are hard to find in an online fashion. In this paper, we assume that the wireless ad hoc network can make limited use of long-range links provided by a global communication infrastructure like a cellular infrastructure or a satellite in order to compute an abstraction of the wireless ad hoc network that allows the messages to be sent along near-shortest paths in the ad hoc network. We present distributed algorithms that compute an abstraction of the ad hoc network in $\mathcal{O}\left(\log ^2 n\right)$ time using long-range links, which results in $c$-competitive routing paths between any two nodes of the ad hoc network for some constant $c$ if the convex hulls of the radio holes do not intersect. We also show that the storage needed for the abstraction just depends on the number and size of the radio holes in the wireless ad hoc network and is independent on the total number of nodes, and this information just has to be known to a few nodes for the routing to work.
Keywords: greedy routing; ad hoc networks; convex hulls; c-competitiveness

Brief Announcement: Competitive Routing in Hybrid Communication Networks - Jung, Daniel; Kolb, Christina; Scheideler, Christian; Sundermeier, Jannik (Proceedings of the 30th on Symposium on Parallelism in Algorithms and Architectures (SPAA))

Self-stabilizing Overlays for high-dimensional Monotonic Searchability - Feldmann, Michael; Kolb, Christina; Scheideler, Christian (Proceedings of the 20th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS))
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.

A Peer-to-Peer based Cloud Storage supporting orthogonal Range Queries of arbitrary Dimension - Benter, Markus; Knollmann, Till; Meyer auf der Heide, Friedhelm; Setzer, Alexander; Sundermeier, Jannik (Proceedings of the 4th International Symposium on Algorithmic Aspects of Cloud Computing (ALGOCLOUD))
We present a peer-to-peer network that supports the efficient processing of orthogonal range queries $R=\bigtimes_{i=1}^{d}[a_i,\,b_i]$ in a $d$-dimensional point space.\\ The network is the same for each dimension, namely a distance halving network like the one introduced by Naor and Wieder (ACM TALG'07). We show how to execute such range queries using $\mathcal{O}\left(2^{d'}d\,\log m + d\,|R|\right)$ hops (and the same number of messages) in total. Here $[m]^d$ is the ground set, $|R|$ is the size and $d'$ the dimension of the queried range. Furthermore, if the peers form a distributed network, the query can be answered in $\mathcal{O}\left(d\,\log m + d\,\sum_{i=1}^{d}(b_i-a_i+1)\right)$ communication rounds. Our algorithms are based on a mapping of the Hilbert Curve through $[m]^d$ to the peers.
Keywords: Distributed Storage; Multi-Dimensional Range Queries; Peer-to-Peer; Hilbert Curve

Relays: A New Approach for the Finite Departure Problem in Overlay Networks - Scheideler, Christian; Setzer, Alexander (Proceedings of the 20th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS 2018))
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.

On Underlay-Aware Self-Stabilizing Overlay Networks - Götte, Thorsten; Scheideler, Christian; Setzer, Alexander (Proceedings of the 20th International Symposium on Stabilization, Safety, and Security of Distributed Systems (SSS 2018))
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.

Monotone Suchbarkeit bei den selbststabilisierenden Protokollen Build-List und Build-Multilist mit systemverlassenden Knoten - Jochmaring, Moritz

Sade: competitive MAC under adversarial SINR - Ogierman, Adrian; Richa, Andrea; Scheideler, Christian; Schmid, Stefan; Zhang, Jin (Distributed Computing)
This paper considers the problem of how to efficiently share a wireless medium which is subject to harsh external interference or even jamming. So far, this problem is understood only in simplistic single-hop or unit disk graph models. We in this paper initiate the study of MAC protocols for the SINR interference model (a.k.a. physical model). This paper makes two contributions. First, we introduce a new adversarial SINR model which captures a wide range of interference phenomena. Concretely, we consider a powerful, adaptive adversary which can jam nodes at arbitrary times and which is only limited by some energy budget. Our second contribution is a distributed MAC protocol called Sade which provably achieves a constant competitive throughput in this environment: we show that, with high probability, the protocol ensures that a constant fraction of the non-blocked time periods is used for successful transmissions.