Survey of Distributed Decision

We survey the recent distributed computing literature on checking whether a given distributed system configuration satisfies a given boolean predicate, i.e., whether the configuration is legal or illegal w.r.t. that predicate. We consider classical distributed computing environments, including mostly synchronous fault-free network computing (LOCAL and CONGEST models), but also asynchronous crash-prone shared-memory computing (WAIT-FREE model), and mobile computing (FSYNC model)

Three Notes on Distributed Property Testing

In this paper we present distributed property-testing algorithms for graph properties in the CONGEST model, with emphasis on testing subgraph-freeness. Testing a graph property P means distinguishing graphs G = (V,E) having property P from graphs that are epsilon-far from having it, meaning that epsilon|E| edges must be added or removed from G to obtain a graph satisfying P. We present a series of results, including: - Testing H-freeness in O(1/epsilon) rounds, for any constant-sized graph H containing an edge (u,v) such that any cycle in H contain either u or v (or both). This includes all connected graphs over five vertices except K_5. For triangles, we can do even better when epsilon is not too small. - A deterministic CONGEST protocol determining whether a graph contains a given tree as a subgraph in constant time. - For cliques K_s with s >= 5, we show that K_s-freeness can be tested in O(m^(1/2-1/(s-2)) epsilon^(-1/2-1/(s-2))) rounds, where m is the number of edges in the network graph. - We describe a general procedure for converting epsilon-testers with f(D) rounds, where D denotes the diameter of the graph, to work in O((log n)/epsilon)+f((log n)/epsilon) rounds, where n is the number of processors of the network. We then apply this procedure to obtain an epsilon-tester for testing whether a graph is bipartite and testing whether a graph is cycle-free. Moreover, for cycle-freeness, we obtain a corrector of the graph that locally corrects the graph so that the corrected graph is acyclic. Note that, unlike a tester, a corrector needs to mend the graph in many places in the case that the graph is far from having the property. These protocols extend and improve previous results of [Censor-Hillel et al. 2016] and [Fraigniaud et al. 2016]

Locality of Distributed Graph Problems

Locality is one of the central themes in distributed computing. Suppose in a network each node only has direct communication with its local neighbors, how efficiently can a global task be solved? We aim to investigate the locality of fundamental distributed graph problems. Toward this goal, we consider the following three basic abstract models of distributed computing. • LOCAL: each device has direct communication links with its neighbors, there is no message size constraint. • CONGEST: each device has direct communication links with its neighbors, the size of each message is at most O(log n) bits. • CONGESTED-CLIQUE: each device has direct communication links with all other devices, the size of each message is at most O(log n) bits. A brief summary of our results is as follows. 1. Complexity Theory for the LOCAL Model: We study the spectrum of natural problem complexities that can exist in the LOCAL model. We provide answers to the following fundamental questions regarding the nature of the LOCAL model: (i) How to classify the distributed problems according to their complexities? (ii) How much does randomness help? (iii) Can we solve more problems given more time? 2. Complexity of Distributed Coloring: The coloring problem is a classical and well-studied problem in distributed computing. We devise distributed algorithms for the edge-coloring problem and the vertex-coloring problem in the LOCAL model that improve upon the previous state of the art. 3. Bandwidth Constraint: We develop a new framework for algorithm design based on expander decompositions that allows us to apply CONGESTED-CLIQUE techniques to the CONGEST model. Using this approach, we provide improved algorithms for the triangle detection and enumeration problem in CONGEST.PHDComputer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttps://deepblue.lib.umich.edu/bitstream/2027.42/149872/1/cyijun_1.pd

Airborne Directional Networking: Topology Control Protocol Design

This research identifies and evaluates the impact of several architectural design choices in relation to airborne networking in contested environments related to autonomous topology control. Using simulation, we evaluate topology reconfiguration effectiveness using classical performance metrics for different point-to-point communication architectures. Our attention is focused on the design choices which have the greatest impact on reliability, scalability, and performance. In this work, we discuss the impact of several practical considerations of airborne networking in contested environments related to autonomous topology control modeling. Using simulation, we derive multiple classical performance metrics to evaluate topology reconfiguration effectiveness for different point-to-point communication architecture attributes for the purpose of qualifying protocol design elements

Building Robust Distributed Infrastructure Networks

Many competing designs for Distributed Hash Tables exist exploring multiple models of addressing, routing and network maintenance. Designing a general theoretical model and implementation of a Distributed Hash Table allows exploration of the possible properties of Distributed Hash Tables. We will propose a generalized model of DHT behavior, centered on utilizing Delaunay triangulation in a given metric space to maintain the networks topology. We will show that utilizing this model we can produce network topologies that approximate existing DHT methods and provide a starting point for further exploration. We will use our generalized model of DHT construction to design and implement more efficient Distributed Hash Table protocols, and discuss the qualities of potential successors to existing DHT technologies

On Flows, Paths, Roots, and Zeros

This thesis has two parts; in the first of which we give new results for various network flow problems. (1) We present a novel dual ascent algorithm for min-cost flow and show that an implementation of it is very efficient on certain instance classes. (2) We approach the problem of numerical stability of interior point network flow algorithms by giving a path following method that works with integer arithmetic solely and is thus guaranteed to be free of any nu-merical instabilities. (3) We present a gradient descent approach for the undirected transship-ment problem and its special case, the single source shortest path problem (SSSP). For distrib-uted computation models this yields the first SSSP-algorithm with near-optimal number of communication rounds. The second part deals with fundamental topics from algebraic computation. (1) We give an algorithm for computing the complex roots of a complex polynomial. While achieving a com-parable bit complexity as previous best results, our algorithm is simple and promising to be of practical impact. It uses a test for counting the roots of a polynomial in a region that is based on Pellet's theorem. (2) We extend this test to polynomial systems, i.e., we develop an algorithm that can certify the existence of a k-fold zero of a zero-dimensional polynomial system within a given region. For bivariate systems, we show experimentally that this approach yields signifi-cant improvements when used as inclusion predicate in an elimination method.Im ersten Teil dieser Dissertation präsentieren wir neue Resultate für verschiedene Netzwerkflussprobleme. (1)Wir geben eine neue Duale-Aufstiegsmethode für das Min-Cost-Flow- Problem an und zeigen, dass eine Implementierung dieser Methode sehr effizient auf gewissen Instanzklassen ist. (2)Wir behandeln numerische Stabilität von Innere-Punkte-Methoden fürNetwerkflüsse, indem wir eine solche Methode angeben die mit ganzzahliger Arithmetik arbeitet und daher garantiert frei von numerischen Instabilitäten ist. (3) Wir präsentieren ein Gradienten-Abstiegsverfahren für das ungerichtete Transshipment-Problem, und seinen Spezialfall, das Single-Source-Shortest-Problem (SSSP), die für SSSP in verteilten Rechenmodellen die erste mit nahe-optimaler Anzahl von Kommunikationsrunden ist. Der zweite Teil handelt von fundamentalen Problemen der Computeralgebra. (1) Wir geben einen Algorithmus zum Berechnen der komplexen Nullstellen eines komplexen Polynoms an, der eine vergleichbare Bitkomplexität zu vorherigen besten Resultaten hat, aber vergleichsweise einfach und daher vielversprechend für die Praxis ist. (2)Wir erweitern den darin verwendeten Pellet-Test zum Zählen der Nullstellen eines Polynoms auf Polynomsysteme, sodass wir die Existenz einer k-fachen Nullstelle eines Systems in einer gegebenen Region zertifizieren können. Für bivariate Systeme zeigen wir experimentell, dass eine Integration dieses Ansatzes in eine Eliminationsmethode zu einer signifikanten Verbesserung führt