TY - CONF
AB - We show how to construct an overlay network of constant degree and diameter $O(\log n)$ in time $O(\log n)$ starting from an arbitrary weakly connected graph.
We assume a synchronous communication network in which nodes can send messages to nodes they know the identifier of and establish new connections by sending node identifiers.
If the initial network's graph is weakly connected and has constant degree, then our algorithm constructs the desired topology with each node sending and receiving only $O(\log n)$ messages in each round in time $O(\log n)$, w.h.p., which beats the currently best $O(\log^{3/2} n)$ time algorithm of [Götte et al., SIROCCO'19].
Since the problem cannot be solved faster than by using pointer jumping for $O(\log n)$ rounds (which would even require each node to communicate $\Omega(n)$ bits), our algorithm is asymptotically optimal.
We achieve this speedup by using short random walks to repeatedly establish random connections between the nodes that quickly reduce the conductance of the graph using an observation of [Kwok and Lau, APPROX'14].
Additionally, we show how our algorithm can be used to efficiently solve graph problems in \emph{hybrid networks} [Augustine et al., SODA'20].
Motivated by the idea that nodes possess two different modes of communication, we assume that communication of the \emph{initial} edges is unrestricted. In contrast, only polylogarithmically many messages can be communicated over edges that have been established throughout an algorithm's execution.
For an (undirected) graph $G$ with arbitrary degree, we show how to compute connected components, a spanning tree, and biconnected components in time $O(\log n)$, w.h.p.
Furthermore, we show how to compute an MIS in time $O(\log d + \log \log n)$, w.h.p., where $d$ is the initial degree of $G$.
AU - Götte, Thorsten
AU - Hinnenthal, Kristian
AU - Scheideler, Christian
AU - Werthmann, Julian
ED - Censor-Hillel, Keren
ID - 22283
T2 - Proc. of the 40th ACM Symposium on Principles of Distributed Computing (PODC '21)
TI - Time-Optimal Construction of Overlays
ER -
TY - JOUR
AB - While many 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. However, when peers in peer-to-peer networks crash, a distributed data structure may not remain intact. 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 many applications 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 O(log |x|) hash table read accesses. We show how to maintain the structure in a self-stabilizing way, while assuring a low overhead in a legal state and an asymptotically optimal memory demand of O(d) bits, where d is the number of bits needed for storing all keys.
AU - Knollmann, Till
AU - Scheideler, Christian
ID - 21096
JF - Information and Computation
SN - 0890-5401
TI - A self-stabilizing Hashed Patricia Trie
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 - 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
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
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 - Hinnenthal, Kristian
AU - Scheideler, Christian
AU - Struijs, Martijn
ID - 13652
T2 - 33rd International Symposium on Distributed Computing (DISC 2019)
TI - Fast Distributed Algorithms for LP-Type Problems of Low Dimension
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 -