Self-Stabilizing Supervised Publish-Subscribe Systems

In this paper we present two major results: First, we introduce the first self-stabilizing version of a supervised overlay network 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

Towards Establishing Monotonic Searchability in Self-Stabilizing Data Structures

Distributed applications are commonly based on overlay networks interconnecting their sites so that they can exchange information. For these overlay networks to preserve their functionality, they should be able to recover from various problems like membership changes or faults. Various self-stabilizing overlay networks have already been proposed in recent years, which have the advantage of being able to recover from any illegal state, but none of these networks can give any guarantees on its functionality while the recovery process is going on. We initiate research on overlay networks that are not only self-stabilizing but that also ensure that searchability is maintained while the recovery process is going on, as long as there are no corrupted messages in the system. 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 call this property monotonic searchability. We show that in general it is impossible to provide monotonic searchability if corrupted messages are present in the system, which justifies the restriction to system states without corrupted messages. Furthermore, we provide a self-stabilizing protocol for the line for which we can also show monotonic searchability. It turns out that even for the line it is non-trivial to achieve this property. Additionally, we extend our protocol to deal with node departures in terms of the Finite Departure Problem of Foreback et al. (SSS 2014). This makes our protocol even capable of handling node dynamics

Self-* Algorithms for distributed systems : programmable matter & overlay networks

In dieser Doktorarbeit werden zwei Szenarien für Self-* Algorithmen in verteilten Systemen betrachtet: selbst-organisierende programmierbare Materie und monotone Suchbarkeit für selbst-stabilisierende Overlaytopologien. Das erste Thema betrachtet programmierbare Materie, welche aus kleinen, in ihren rechnerischen Fähigkeiten beschränkten Einheiten besteht, die Partikel genannt werden. Programmierbare Materie solcher Art kann im amoebot Model betrachtet werden. Es wird eruiert ob programmierbare Materie zwei grundlegende Probleme in diesem Model lösen kann: Coating und Shape Formation. Im Coating sind die Partikel mit einem unbekannten Objekt verbunden und es ist das Ziel dieses gleichmäßig zu ummanteln. Bei der Shape Formation soll die Materie einfache Formen konstruieren, wobei die Größe der Form mit der Anzahl der Partikel skaliert. Dazu ergänzend wird die Fähigkeit von programmierbarer Materie konstanter Größe betrachtet, die zu einem unbekannten Objekt verbunden ist. Das zweite Thema fokussiert sich auf das Problem Suchbarkeit monoton in einer Overlaytopologie aufrecht zu erhalten, während sich diese stabilisiert. Konkret werden selbst-stabilisierende Protokolle für die Linientopologie betrachtet. Zusätzlich zu der Konvergenz sollen die Protokolle auch die Eigenschaft der Suchbarkeit monoton aufrechterhalten. Das Problem wird in zwei Varianten betrachtet: die strikten Linie und die Super-Linie. In der ersten Variante ist die Liste über alle Knoten die Zieltopologie. In der zweiten Variante werden mehrere Nachbarn in der Zieltopologie erlaubt, aber die Linie muss ein Subgraph sein. Für beide Szenarien wird: (i) ein selbst-stabilisierendes Protokoll präsentiert, (ii) ein Routing Protokoll für Suchnachrichten angegeben, (iii) die Selbst-Stabilisierung bewiesen und (iv) der Erhalt der monotonen Suchbarkeit bewiesen.This thesis considers two scenarios for self-* algorithms in distributed computing: self-organizing programmable matter and monotonic searchability for self-stabilizing overlay topologies. The former topic considers programmable matter that consists of tiny computationally limited units called particles, which can move in two-dimensional space, bond and communicate with each other. This kind of matter is studied in the recently introduced amoebot model and we investigate the feasibility of solving fundamental problems for programmable matter in that model. More precisely, the focus is on two major problems: coating and shape formation.In coating, the particles are connected to an unknown object and the ultimate goal is to coat the object as evenly as possible. In shape formation, we focus on building basic shapes out of programmable matter where the size of the constructed shape scales with the number of particles. Supplementary to these two central problems we investigate the ability of constant-size programmable matter that is connected to an unknown object. The latter topic focuses on the problem of maintaining searchability in an overlay topology while that topology is stabilizing. More specifically, we investigate self-stabilizing protocols for the line topology. In addition to the convergence process, the protocols should also monotonically maintain a property called searchability. We study this problem in two variants: the strict line topology and the super-line topology. In the first variant the ultimate goal topology is a line over all nodes. In the second variant, we allow the goal topology to have more edges, but the line has to be a subgraph of it. In both scenarios we present: (i) a protocol that stabilizes to the desired protocol, (ii) a routing protocol that is able to route search messages, (iii) a self-stabilization proof and (iv) a monotonic searc++Thim Frederik Strothmann ; reviewers: Prof. Dr. Christian Scheideler, Paderborn University, Prof. Dr. Andréa W. Richa, Arizona State University, Prof. Dr. Friedhelm Meyer auf der Heide, Paderborn UniversityTag der Verteidigung: 18.07.2017Universität Paderborn, Dissertation, 201

Forming tile shapes with simple robots

Motivated by the problem of manipulating nanoscale materials, we investigate the problem of reconfiguring a set of tiles into certain shapes by robots with limited computational capabilities. As a first step towards developing a general framework for these problems, we consider the problem of rearranging a connected set of hexagonal tiles by a single deterministic finite automaton. After investigating some limitations of a single-robot system, we show that a feasible approach to build a particular shape is to first rearrange the tiles into an intermediate structure by performing very simple tile movements. We introduce three types of such intermediate structures, each having certain advantages and disadvantages. Each of these structures can be built in asymptotically optimal O(n2) rounds, where n is the number of tiles. As a proof of concept, we give an algorithm for reconfiguring a set of tiles into an equilateral triangle through one of the intermediate structures. Finally, we experimentally show that the algorithm for building the simplest of the three intermediate structures can be modified to be executed by multiple robots in a distributed manner, achieving an almost linear speedup in the case where the number of robots is reasonably small, and explain how the algorithm can be used to construct a triangle distributedly

Forming tile shapes with simple robots

Motivated by the problem of manipulating nanoscale materials, we investigate the problem of reconfiguring a set of tiles into certain shapes by robots with limited computational capabilities. As a first step towards developing a general framework for these problems, we consider the problem of rearranging a connected set of hexagonal tiles by a single deterministic finite automaton. After investigating some limitations of a single-robot system, we show that a feasible approach to build a particular shape is to first rearrange the tiles into an intermediate structure by performing very simple tile movements. We introduce three types of such intermediate structures, each having certain advantages and disadvantages. Each of these structures can be built in asymptotically optimal O(n2) rounds, where n is the number of tiles. As a proof of concept, we give an algorithm for reconfiguring a set of tiles into an equilateral triangle through one of the intermediate structures. Finally, we experimentally show that the algorithm for building the simplest of the three intermediate structures can be modified to be executed by multiple robots in a distributed manner, achieving an almost linear speedup in the case where the number of robots is reasonably small