Memory-Adjustable Navigation Piles with Applications to Sorting and Convex Hulls

We consider space-bounded computations on a random-access machine (RAM) where the input is given on a read-only random-access medium, the output is to be produced to a write-only sequential-access medium, and the available workspace allows random reads and writes but is of limited capacity. The length of the input is $N$ elements, the length of the output is limited by the computation, and the capacity of the workspace is $O(S)$ bits for some predetermined parameter $S$. We present a state-of-the-art priority queue---called an adjustable navigation pile---for this restricted RAM model. Under some reasonable assumptions, our priority queue supports $\mathit{minimum}$ and $\mathit{insert}$ in $O(1)$ worst-case time and $\mathit{extract}$ in $O(N/S + \lg{} S)$ worst-case time for any $S \geq \lg{} N$. We show how to use this data structure to sort $N$ elements and to compute the convex hull of $N$ points in the two-dimensional Euclidean space in $O(N^2/S + N \lg{} S)$ worst-case time for any $S \geq \lg{} N$. Following a known lower bound for the space-time product of any branching program for finding unique elements, both our sorting and convex-hull algorithms are optimal. The adjustable navigation pile has turned out to be useful when designing other space-efficient algorithms, and we expect that it will find its way to yet other applications.Comment: 21 page

The Limited Workspace Model for Geometric Algorithms

Space usage has been a concern since the very early days of algorithm design. The increased availability of devices with limited memory or power supply – such as smartphones, drones, or small sensors – as well as the proliferation of new storage media for which write access is comparatively slow and may have negative effects on the lifetime – such as flash drives – have led to renewed interest in the subject. As a result, the design of algorithms for the limited workspace model has seen a significant rise in popularity in computational geometry over the last decade. In this setting, we typically have a large amount of data that needs to be processed. Although we may access the data in any way and as often as we like, write-access to the main storage is limited and/or slow. Thus, we opt to use only higher level memory for intermediate data (e.g., CPU registers). Since the application areas of the devices mentioned above – sensors, smartphones, and drones – often handle a large amount of geographic (i.e., geometric) data, the scenario becomes particularly interesting from the viewpoint of computational geometry. Motivated by these considerations, we investigate geometric problems in the limited workspace model. In this model the input of size n resides in read-only memory, an algorithm may use a workspace of size s = {1, . . . , n} to read and write the intermediate data during its execution, and it reports the output to a write-only stream. The goal is to design algorithms whose running time decreases as s increases, which provides a time-space trade-off. In this thesis, we consider three fundamental geometric problems, namely, computing different types of Voronoi diagrams of a planar point set, computing the Euclidean minimum spanning tree of a planar point set, and computing the k-visibility region of a point inside a polygonal domain. Using several innovative techniques, we either achieve the first time-space trade-offs for those problems or improve the previous results.Der Speicherplatzbedarf ist seit den Anfängen des Algorithmenentwurfs von Interesse. Die erhöhte Verfügbarkeit von Geräten mit begrenztem Speicherplatz oder begrenzter Stromversorgung – wie Smartphones, Drohnen oder kleine Sensoren – sowie die Verbreitung neuer Speichermedien, bei denen der Schreibzugriff vergleichsweise langsam ist und negative Auswirkungen auf die Lebensdauer haben kann – wie beispielsweise Flash-Laufwerken – haben zu erneuter Aufmerksamkeit für dieses Thema geführt. In der Folge hat der Entwurf von Algorithmen für das Limited Workspace Model (Modell mit begrenztem Arbeitsspeicher) in den letzten zehn Jahren einen signifikanten Anstieg an Popularität in der algorithmischen Geometrie erfahren. In diesem Setting haben wir in der Regel eine große Menge an Daten, die verarbeitet werden müssen. Obwohl wir auf die Daten beliebig oft und in beliebiger Weise zugreifen können, ist der Schreibzugriff auf den Hauptspeicher begrenzt und/oder langsam. Zwischenergebnisse werden daher nur in einem kleineren, übergeordneten Speicher (z. B. CPU-Register) abgelegt. Da die Anwendungsbereiche der oben genannten Geräte – Sensoren, Smartphones und Drohnen – oft mit einer großen Menge an geografischen (d. h., geometrischen) Daten umgehen, ist dieses Szenario aus Sicht der algorithmischen Geometrie besonders interessant. Motiviert durch diese Überlegungen haben wir geometrische Probleme im Limited Workspace Model untersucht. In diesem Modell befindet sich die Eingabe der Größe n in einem schreibgeschützten Speicher, ein Algorithmus kann einen Arbeitsspeicher der Größe s = {1, . . . , n} verwenden, um die Zwischendaten während der Ausführung zu lesen und zu schreiben. Die Ausgabe sendet er an einen lesegeschützten Stream. Ziel ist es, Algorithmen zu entwickeln, deren Laufzeit mit zunehmender Verfügbarkeit an Arbeitsspeicher abnimmt, was einen Time-Space Trade-Off (Laufzeit-Speicher-Abwägung) darstellt. In dieser Arbeit betrachten wir drei grundlegende geometrische Probleme, nämlich die Berechnung verschiedener Arten von Voronoi-Diagrammen einer Punktmenge in der Ebene, die Berechnung des euklidischen minimalen Spannbaums einer ebenen Punktmenge und die Bestimmung der k-Sichtbarkeitsregion (k-visibility region) eines Punkts innerhalb eines polygonalen Gebiets. Mit mehreren innovativen Techniken entwickeln wir entweder die ersten Time-Space Trade-Offs für diese Probleme oder verbessern die bisherigen Ergebnisse

Defense Technical Information Center thesaurus

This DTIC Thesaurus provides a basic multidisciplinary subject term vocabulary used by DTIC to index and retrieve scientific and technical information from its various data bases and to aid DTIC`s users in their information storage and retrieval operations. It includes an alphabetical posting term display, a hierarchy display, and a Keywork Out of Context (KWOC) display

ReSCon '12, Research Student Conference: Book of Abstracts

The fifth SED Research Student Conference (ReSCon2012) was hosted over three days, 18-20 June 2012, in the Hamilton Centre at Brunel University. The conference consisted of 130 oral and 70 poster presentations, based on the high quality and diverse research being conducted within the School of Engineering and Design by postgraduate research students. The conference is held annually, and ReSCon plays a key role in contributing to research and innovations within the School

The Siren of Cirebon: a tenth-century trading vessel lost in the Java Sea

This thesis examines data collected during the salvage of the cargo of a merchant ves-sel foundered in the Java Sea, by a short inscription in a fragment of a bowl and coins dat-ed to around 970 CE. The wreck’s position indicates that the ship was on her way to the island of Java; the verssel herself belongs into the so called ‘lashed-lug and doweled’, Western Austronesian (‘Malayo-Indonesian’) tradition of boat-building. The surviving cargo ranges from Chinese stonewares and Southeast Asian ceramics to Middle Eastern glassware, tin and lead from –proposedly– the Malay Archipelago, and a wide variety of “smaller finds”, most of which can be attributed to the broader area of the western Indian Ocean. The find palpably demonstrates the far-reaching and well-institutionalised trade rela-tions throughout early medieval Asia. It is often assumed that pre-modern Asian com-merce was largely organised in small-scale ventures, the so called “pedlar trade”, and a number of sources indicate structural features of the ships facilitating this commerce that could have supported such a “particularised” exchange. However, a critical assessment of the composition and distribution of the ship’s payload and a virtual reconstruction of the ship and her initial loading pattern reveal that the vessel’s ceramic cargo in all probability was not acquired, handled, and bound to be marketed as a particularised “peddling” ven-ture, but managed by a single authority. The huge amount of ceramics carried on the ves-sel raises questions regarding frequency, volume and modus operandi of maritime ex-changes in tenth-century Southeast Asia, implying that the ship’s tragic voyage was but an attempt at instituting a virtual monopoly in such trade

Fabricate 2020

Fabricate 2020 is the fourth title in the FABRICATE series on the theme of digital fabrication and published in conjunction with a triennial conference (London, April 2020). The book features cutting-edge built projects and work-in-progress from both academia and practice. It brings together pioneers in design and making from across the fields of architecture, construction, engineering, manufacturing, materials technology and computation. Fabricate 2020 includes 32 illustrated articles punctuated by four conversations between world-leading experts from design to engineering, discussing themes such as drawing-to-production, behavioural composites, robotic assembly, and digital craft