Self-* Algorithms for Distributed Systems

TL;DR: This thesis presents an algorithmic framework that solves the coating problem in a worst-case runtime that is linear in the number of particles, which is shown to be best-case optimal and investigates the ability of constant-size programmable matter that is connected to an unknown object.

Abstract: 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 (e.g., it can be convex or concave) and the ultimate goal is to coat the object as evenly as possible. We present an algorithmic framework that solves the coating problem in a worst-case runtime that is linear in the number of particles, which is shown to be worst-case optimal. 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. We introduce an algorithmic framework to construct various simple geometric shapes, which again has a linear worst-case runtime. 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: i.e., protocols that are guaranteed to converge from any possible initial state to a desired state in which the overlay constitutes a line. In addition to the convergence process, the protocols should also monotonically maintain a property called searchability: i.e., once a node a can send a search message to another node b in the topology, it is always able to do so in the future. We study this problem in two variants: the strict line topology and the super-line topology. In the first variant the