Geometric optimization and querying : exact & approximate

This thesis has two main parts. The first part deals with the stage illumination problem. Given a stage represented by a line segment L and a set of lightsources represented by a set of points S in the plane, assign powers to the lightsources such that every point on the stage receives a sufficient amount, e.g. one unit, of light while minimizing the overall power consumption. By assuming that the amount of light arriving from a fixed lightsource decreases rapidly with the distance from the lightsource, this becomes an interesting geometric optimization problem. We present different solutions, based on convex optimization, discretization and linear programming, as well as a purely combinatorial approximation algorithm. Some experimental results are also provided. In the second part of this thesis, we are concerned with two different geometric problems whose solutions are based on the construction of a data structure that would allow for efficient queries. The central idea of our data structures is the well-separated pair decomposition. The first problem we address is the k-hop restricted shortest path under the power-euclidean distance function. Given a set P of n points in the plane and the distance function jpqjd +Cp for some constant d > 1, nonnegative offset cost Cp and p;q 2 P, where jpqj denotes the Euclidean distance between p and q, we consider the problem of finding paths between any pair of points that minimize the lenght of the path and do not use more than some constant number k of hops. Known exact algorithms for this problem required W(nlogn) per query pair (p;q). We relax the exactness requirement and only require approximate (1+e) solutions which allows us to derive schemes which guarantee constant query time using linear space and O(nlogn) preprocessing time. The dependence on e is polynomial in 1=e. We also develop a tool that might be of independent interest: For any pair of points p;q 2 P report in constant time the cluster pair (A;B) representing (p;q) in a well-separated pair decomposition of P. The second problem in this part is so-called cone-restricted nearest neighbor. For a given point set in Euclidean space we consider the problem of finding (approximate) nearest neighbors of a query point but restricting only to points that lie within a fixed cone with apex at the query point. We investigate the structure of the Voronoi diagram induced by this notion of proximity and present approximate and exact data structures for answering cone-restricted nearest neighbor queries. In particular, we develop an approximate Voronoi diagram of size O((n=ed) log(1=e)) that can be used to answer cone-restricted nearest neighbor queries in O(log(n=e)) time.Diese Arbeit besteht aus zwei Teilen. Der erste Teil behandelt das Stage Illumination Problem. Hierbei möchte man eine Bühne, die durch ein Geradenstück repräsentiert ist, durch Lichtquellen, die durch Punkte in der Ebene repräsentiert sind, so beleuchten, dass jeder Punkt der Bühne genügend Licht erhält und dabei möglichst wenig Energie verbrauchen. Wenn man annimmt, dass die Lichtintensität stark mit der Entfernung zur Lichtquelle abnimmt, so stellt dies ein interesanntes geometrisches Optimierungsproblem dar. Wir geben verschiedene Lösungen an, die sowohl auf konvexer Optimierung, Diskretisierung und Linearer Programmierung basieren, als auch einen kombinatorischen Approximationsalgorithmus. Es werden auch experimentelle Resultate angegeben. Im zweiten Teil dieser Arbeit behandeln wir zwei verschiedene geometrische Probleme, deren Lösungen auf einer Datenstruktur basieren, die effiziente Anfragen beantworten kann. Die zentrale Idee unserer Datenstruktur ist die well-separated pair decomposition WSPD. Das erste Problem, das wir ansprechen ist das k-hop restricted shortest path under the power-euclidean distance function. Für n Punkte in der Ebene möchte man den kürzesten Pfad zwischen zwei beliebigen Punkten finden, der nicht mehr als k Kanten benötigt. Bekannte exakte Algorithmen für dieses Problem benötigen W(nlogn) Zeit pro Anfrage (p;q). Wir lockern die Exaktheitsforderung und verlangen nur eine (1+e)-Approximation. Dies erlaubt uns eine Methode zu entwickeln, die konstante Zeit pro Anfrage garaniert und nur linearen Platz benötigt bei einer Vorverarbeitungszeit von O(nlogn). Die Abhängigkeit von e ist polynomiell in 1=e. Außerdem entwickeln wir eine Methode, die davon unabhängig von Interesse ist. Für ein Punktepaar p;q 2 P bestimmen wir in konstanter Zeit das Cluster-paar (A;B), das (p;q) in einer WSPD von P bestimmt. Das zweite Problem in diesem Teil ist das sogenannte cone-restricted nearest neighbor problem. Für eine gegebene Menge von Punkten im Euklidischen Raum betrachten wir das Problem den nächsten Nachbarpunkt zu bestimmen, der in einem Kegel liegt, dessen Spitze ein beliebiger Anfragepunkt ist. Wir untersuchen das dazugehörige Voronoi- Diagramm und entwickeln effiziente Datenstrukturen sowohl für exakte als auch für approximative cone-restricted nearest neighbor-Anfragen. Im speziellen entwickeln wir ein approximatives Voronoi-Diagramm der Größe O((n=ed) log(1=e)), das dazu benutzt werden kann, Anfragen in der Zeit O(log(n=e)) zu beantworten

Geometric optimization and querying : exact & approximate

This thesis has two main parts. The first part deals with the stage illumination problem. Given a stage represented by a line segment L and a set of lightsources represented by a set of points S in the plane, assign powers to the lightsources such that every point on the stage receives a sufficient amount, e.g. one unit, of light while minimizing the overall power consumption. By assuming that the amount of light arriving from a fixed lightsource decreases rapidly with the distance from the lightsource, this becomes an interesting geometric optimization problem. We present different solutions, based on convex optimization, discretization and linear programming, as well as a purely combinatorial approximation algorithm. Some experimental results are also provided. In the second part of this thesis, we are concerned with two different geometric problems whose solutions are based on the construction of a data structure that would allow for efficient queries. The central idea of our data structures is the well-separated pair decomposition. The first problem we address is the k-hop restricted shortest path under the power-euclidean distance function. Given a set P of n points in the plane and the distance function jpqjd +Cp for some constant d > 1, nonnegative offset cost Cp and p;q 2 P, where jpqj denotes the Euclidean distance between p and q, we consider the problem of finding paths between any pair of points that minimize the lenght of the path and do not use more than some constant number k of hops. Known exact algorithms for this problem required W(nlogn) per query pair (p;q). We relax the exactness requirement and only require approximate (1+e) solutions which allows us to derive schemes which guarantee constant query time using linear space and O(nlogn) preprocessing time. The dependence on e is polynomial in 1=e. We also develop a tool that might be of independent interest: For any pair of points p;q 2 P report in constant time the cluster pair (A;B) representing (p;q) in a well-separated pair decomposition of P. The second problem in this part is so-called cone-restricted nearest neighbor. For a given point set in Euclidean space we consider the problem of finding (approximate) nearest neighbors of a query point but restricting only to points that lie within a fixed cone with apex at the query point. We investigate the structure of the Voronoi diagram induced by this notion of proximity and present approximate and exact data structures for answering cone-restricted nearest neighbor queries. In particular, we develop an approximate Voronoi diagram of size O((n=ed) log(1=e)) that can be used to answer cone-restricted nearest neighbor queries in O(log(n=e)) time.Diese Arbeit besteht aus zwei Teilen. Der erste Teil behandelt das Stage Illumination Problem. Hierbei möchte man eine Bühne, die durch ein Geradenstück repräsentiert ist, durch Lichtquellen, die durch Punkte in der Ebene repräsentiert sind, so beleuchten, dass jeder Punkt der Bühne genügend Licht erhält und dabei möglichst wenig Energie verbrauchen. Wenn man annimmt, dass die Lichtintensität stark mit der Entfernung zur Lichtquelle abnimmt, so stellt dies ein interesanntes geometrisches Optimierungsproblem dar. Wir geben verschiedene Lösungen an, die sowohl auf konvexer Optimierung, Diskretisierung und Linearer Programmierung basieren, als auch einen kombinatorischen Approximationsalgorithmus. Es werden auch experimentelle Resultate angegeben. Im zweiten Teil dieser Arbeit behandeln wir zwei verschiedene geometrische Probleme, deren Lösungen auf einer Datenstruktur basieren, die effiziente Anfragen beantworten kann. Die zentrale Idee unserer Datenstruktur ist die well-separated pair decomposition WSPD. Das erste Problem, das wir ansprechen ist das k-hop restricted shortest path under the power-euclidean distance function. Für n Punkte in der Ebene möchte man den kürzesten Pfad zwischen zwei beliebigen Punkten finden, der nicht mehr als k Kanten benötigt. Bekannte exakte Algorithmen für dieses Problem benötigen W(nlogn) Zeit pro Anfrage (p;q). Wir lockern die Exaktheitsforderung und verlangen nur eine (1+e)-Approximation. Dies erlaubt uns eine Methode zu entwickeln, die konstante Zeit pro Anfrage garaniert und nur linearen Platz benötigt bei einer Vorverarbeitungszeit von O(nlogn). Die Abhängigkeit von e ist polynomiell in 1=e. Außerdem entwickeln wir eine Methode, die davon unabhängig von Interesse ist. Für ein Punktepaar p;q 2 P bestimmen wir in konstanter Zeit das Cluster-paar (A;B), das (p;q) in einer WSPD von P bestimmt. Das zweite Problem in diesem Teil ist das sogenannte cone-restricted nearest neighbor problem. Für eine gegebene Menge von Punkten im Euklidischen Raum betrachten wir das Problem den nächsten Nachbarpunkt zu bestimmen, der in einem Kegel liegt, dessen Spitze ein beliebiger Anfragepunkt ist. Wir untersuchen das dazugehörige Voronoi- Diagramm und entwickeln effiziente Datenstrukturen sowohl für exakte als auch für approximative cone-restricted nearest neighbor-Anfragen. Im speziellen entwickeln wir ein approximatives Voronoi-Diagramm der Größe O((n=ed) log(1=e)), das dazu benutzt werden kann, Anfragen in der Zeit O(log(n=e)) zu beantworten

Sonic Histories of Occupation

This open access book examines how auditory environments in different contexts have contributed to understanding foreign occupation and colonialism, and how they have given rise to historical music cultures. How are sound and music implicated in the control and discipline of people under occupation? Exploring case studies of foreign occupation and colonialism from around the world, Sonic Histories of Occupation seeks to answer these questions and more. Examining how an emphasis on auditory culture adds complexity and nuance to understanding the relationship between occupation and the bodily senses, this book is structured around three conceptual themes: voice and occupation; memory, sound and occupation; and auditory responses to occupation and colonialism. Highlighting case studies in Asia, North Africa, North America and Europe, contributors employ a range of theoretical approaches to examine histories of imperialism and foreign occupation, and the auditory legacies they created, and contribute to a wider dialogue about the relationship between sound and imperial projects across political and temporal boundaries. The open access edition of this book is available under a CC-BY-NC-ND 4.0 license on www.bloomsburycollections.com. Open access was funded by the European Research Council (Horizon 2020, Grant Number 682081)

MY AUSCHWITZ STATE OF MIND: A study of the nature of emergence of a text in relation to Auschwitz

While this thesis is presented as divided into two parts (a creative, Knowing Auschwitz, and a critical, The Other Auschwitz), I ask the reader to read it as two movements that intersect in one hybrid-inclined text, a text that can only exist when the two parts are interpenetrated. Both parts are equally a documentation of my research by practice and the outcome of my research by practice. They are not so much de Certeau’s crossword decoding stencil, but a puzzle filled out in response to the question that I set myself at the start.This thesis uses practice-based research to ask how I can write a textual deep map from an investigation of Auschwitz-Birkenau. As a key part of the research, I made repeated visits to the environs of Auschwitz-Birkenau, walking and cycling extensively around the area in a search for contemporary fragments in the landscape, for example buildings, routes, sites, landmarks, place names, signposts and found objects. I used my own collection of guides, documents, textual, cartographic and photographic fragments and other ephemera related to the town and the Auschwitz museum in addition to support from the Auschwitz Museum itself and external archives such as the Arolsen Archives (“International Center on the Nazi Era - Arolsen Archives,” n.d.) and the Weiner Holocaust Library (“Home - The Wiener Holocaust Library” n.d.) in London. These all acted as points of departure as I embarked on making my deep map. The research translates into a complex textual map of my subject combining autoethnographic stories with tales from psychogeographical drift, non-fiction examinations of place and semi-fictionalised histories. The research is presented as two conjoined texts, one a form of creative non-fiction and the other a critical reflexion, which between them constitute an examination of how a place as imbued with meaning as Auschwitz can be written about in a new way. I refer to the writings of a variety of writers, philosophers and theorists, including Giorgio Agamben’s spatial grey area, or soglia , Walter Benjamin’s ‘alternative model for organising things in the field of knowledge’ and Charlotte Delbo‘s entrances, exits, boundaries and markers that delineate Birkenau. My process is deeply personal and predicated on a form of personal exposure to the landscape with few specific notions or processes of exploration. A process of constant sorting is fundamental to my production as I examine place as a series of complex, palimpsestic texts