Hypertiling -- a high performance Python library for the generation and visualization of hyperbolic lattices

Hypertiling is a high-performance Python library for the generation and visualization of regular hyperbolic lattices embedded in the Poincar\'e disk model. Using highly optimized, efficient algorithms, hyperbolic tilings with millions of vertices can be created in a matter of minutes on a single workstation computer. Facilities including computation of adjacent vertices, dynamic lattice manipulation, refinements, as well as powerful plotting and animation capabilities are provided to support advanced uses of hyperbolic graphs. In this manuscript, we present a comprehensive exploration of the package, encompassing its mathematical foundations, usage examples, applications, and a detailed description of its implementation.Comment: 52 pages, 20 figure

Irreducibility and Galois Properties of Lifts of Supersingular Polynomials

It has recently been shown that a rational specialization of Jacobi polynomials, when reduced modulo a prime number p, has roots which coincide with the supersingular j- invariants of elliptic curves in characteristic p. These supersingular lifts are conjectured to be irreducible with maximal Galois groups. Using the theory of p-adic Newton Polygons, we provide a new infinite class of irreducibility and, assuming a conjecture of Hardy and Littlewood, give strong evidence for their Galois groups being as large as possible

VLSI Routing for Advanced Technology

Routing is a major step in VLSI design, the design process of complex integrated circuits (commonly known as chips). The basic task in routing is to connect predetermined locations on a chip (pins) with wires which serve as electrical connections. One main challenge in routing for advanced chip technology is the increasing complexity of design rules which reflect manufacturing requirements. In this thesis we investigate various aspects of this challenge. First, we consider polygon decomposition problems in the context of VLSI design rules. We introduce different width notions for polygons which are important for width-dependent design rules in VLSI routing, and we present efficient algorithms for computing width-preserving decompositions of rectilinear polygons into rectangles. Such decompositions are used in routing to allow for fast design rule checking. A main contribution of this thesis is an O(n) time algorithm for computing a decomposition of a simple rectilinear polygon with n vertices into O(n) rectangles, preseverving two-dimensional width. Here the two-dimensional width at a point of the polygon is defined as the edge length of a largest square that contains the point and is contained in the polygon. In order to obtain these results we establish a connection between such decompositions and Voronoi diagrams. Furthermore, we consider implications of multiple patterning and other advanced design rules for VLSI routing. The main contribution in this context is the detailed description of a routing approach which is able to manage such advanced design rules. As a main algorithmic concept we use multi-label shortest paths where certain path properties (which model design rules) can be enforced by defining labels assigned to path vertices and allowing only certain label transitions. The described approach has been implemented in BonnRoute, a VLSI routing tool developed at the Research Institute for Discrete Mathematics, University of Bonn, in cooperation with IBM. We present experimental results confirming that a flow combining BonnRoute and an external cleanup step produces far superior results compared to an industry standard router. In particular, our proposed flow runs more than twice as fast, reduces the via count by more than 20%, the wiring length by more than 10%, and the number of remaining design rule errors by more than 60%. These results obtained by applying our multiple patterning approach to real-world chip instances provided by IBM are another main contribution of this thesis. We note that IBM uses our proposed combined BonnRoute flow as the default tool for signal routing

A Geofencing Algorithm Fit for Supply Chain Management

Location Based Services play an important role in decision-making processes, company activities or in any control and policy system in modern computer organizations. Usually LBS applications provide location-specific information only when user requests it. However, Supply Chain Management applications require to push geolocalized information directly to the user. The most discussed and requested application is Geofencing, which allows to determine the topological relation between a moving object and a set of delimited geographical areas. This paper describes the design of an innovative solution for implementing proactive location-based services suitable for application scenarios with strong time constraints, such as realtime systems, called Proactive Fast and Low Resource Geofencing Algorithm

Weiterentwicklung analytischer Datenbanksysteme

This thesis contributes to the state of the art in analytical database systems. First, we identify and explore extensions to better support analytics on event streams. Second, we propose a novel polygon index to enable efficient geospatial data processing in main memory. Third, we contribute a new deep learning approach to cardinality estimation, which is the core problem in cost-based query optimization.Diese Arbeit trägt zum aktuellen Forschungsstand von analytischen Datenbanksystemen bei. Wir identifizieren und explorieren Erweiterungen um Analysen auf Eventströmen besser zu unterstützen. Wir stellen eine neue Indexstruktur für Polygone vor, die eine effiziente Verarbeitung von Geodaten im Hauptspeicher ermöglicht. Zudem präsentieren wir einen neuen Ansatz für Kardinalitätsschätzungen mittels maschinellen Lernens

LUMIS: Land Use Management and Information Systems; coordinate oriented program documentation

An integrated geographic information system to assist program managers and planning groups in metropolitan regions is presented. The series of computer software programs and procedures involved in data base construction uses the census DIME file and point-in-polygon architectures. The system is described in two parts: (1) instructions to operators with regard to digitizing and editing procedures, and (2) application of data base construction algorithms to achieve map registration, assure the topological integrity of polygon files, and tabulate land use acreages within administrative districts

Applying Airspace Capacity Estimation Models to the Airspace of Hungary

Estimation of airspace capacity in order to keep air traffic controller workload at an optimal level is essential for the safety of air traffic. In the past, several different methods were developed for airspace capacity estimation with different benefits and drawbacks. In our research we studied the applicability of one of these methods (based on a neural network model) in the airspace of Hungary. This paper presents a possible way of gathering and processing data and validating the results given by the model