Sharp Bounds on Davenport-Schinzel Sequences of Every Order

One of the longest-standing open problems in computational geometry is to bound the lower envelope of $n$ univariate functions, each pair of which crosses at most $s$ times, for some fixed $s$. This problem is known to be equivalent to bounding the length of an order-$s$ Davenport-Schinzel sequence, namely a sequence over an $n$-letter alphabet that avoids alternating subsequences of the form $a \cdots b \cdots a \cdots b \cdots$ with length $s+2$. These sequences were introduced by Davenport and Schinzel in 1965 to model a certain problem in differential equations and have since been applied to bounding the running times of geometric algorithms, data structures, and the combinatorial complexity of geometric arrangements. Let $\lambda_s(n)$ be the maximum length of an order-$s$ DS sequence over $n$ letters. What is $\lambda_s$ asymptotically? This question has been answered satisfactorily (by Hart and Sharir, Agarwal, Sharir, and Shor, Klazar, and Nivasch) when $s$ is even or $s\le 3$. However, since the work of Agarwal, Sharir, and Shor in the mid-1980s there has been a persistent gap in our understanding of the odd orders. In this work we effectively close the problem by establishing sharp bounds on Davenport-Schinzel sequences of every order $s$. Our results reveal that, contrary to one's intuition, $\lambda_s(n)$ behaves essentially like $\lambda_{s-1}(n)$ when $s$ is odd. This refutes conjectures due to Alon et al. (2008) and Nivasch (2010).Comment: A 10-page extended abstract will appear in the Proceedings of the Symposium on Computational Geometry, 201

Morphological characterization and reconstruction of fractured heat-treated glass

Fracture morphology has insightful information related to the residual effect of fractured structural glass, which is vital in assessing the post-fracture performance of glass members. This study experimentally characterized the fracture morphology of heat-treated glass and developed a novel method of morphology reconstruction, which aims to facilitate the numerical analysis of fractured structural glass. With the development of a computer-vision-based method for transparent objects, the morphology information from fragmentation tests was extracted and systematically investigated for monolithic heat-treated glass with various thicknesses, surface compressive stresses and fracture initiation locations, which are considered as the key influencing factors of heat-treated glass fracture. The geometrical features of fragments and their spatial distribution were quantitatively analysed, identifying their correlations with glass properties. The result indicates that the distribution of fragment centroids shows greater dispersion as the tempering level increases, and the fragments tend to be smaller and more rounded. The strain energy release at fracture was also assessed by fracture patterns, showing it presents high sensitivity to the glass thickness and surface compressive stress. Subsequently, a novel approach was proposed for the stochastic reconstruction of fracture morphology, combining feature points distribution and Voronoi tessellation concept. The control parameters are determined by data from the fragmentation tests and the influence of fracture load could be properly considered. The proposed method shows satisfactory outcomes and good agreement with the experimental records, which has further potential in developing refined numerical models by considering more realistic fracture morphology of glass members

Problemas de localização-distribuição de serviços semiobnóxios: aproximações e apoio à decisão

Doutoramento em Gestão IndustrialA presente tese resulta de um trabalho de investigação cujo objectivo se centrou no problema de localização-distribuição (PLD) que pretende abordar, de forma integrada, duas actividades logísticas intimamente relacionadas: a localização de equipamentos e a distribuição de produtos. O PLD, nomeadamente a sua modelação matemática, tem sido estudado na literatura, dando origem a diversas aproximações que resultam de diferentes cenários reais. Importa portanto agrupar as diferentes variantes por forma a facilitar e potenciar a sua investigação. Após fazer uma revisão e propor uma taxonomia dos modelos de localização-distribuição, este trabalho foca-se na resolução de alguns modelos considerados como mais representativos. É feita assim a análise de dois dos PLDs mais básicos (os problema capacitados com procura nos nós e nos arcos), sendo apresentadas, para ambos, propostas de resolução. Posteriormente, é abordada a localização-distribuição de serviços semiobnóxios. Este tipo de serviços, ainda que seja necessário e indispensável para o público em geral, dada a sua natureza, exerce um efeito desagradável sobre as comunidades contíguas. Assim, aos critérios tipicamente utilizados na tomada de decisão sobre a localização destes serviços (habitualmente a minimização de custo) é necessário adicionar preocupações que reflectem a manutenção da qualidade de vida das regiões que sofrem o impacto do resultado da referida decisão. A abordagem da localização-distribuição de serviços semiobnóxios requer portanto uma análise multi-objectivo. Esta análise pode ser feita com recurso a dois métodos distintos: não interactivos e interactivos. Ambos são abordados nesta tese, com novas propostas, sendo o método interactivo proposto aplicável a outros problemas de programação inteira mista multi-objectivo. Por último, é desenvolvida uma ferramenta de apoio à decisão para os problemas abordados nesta tese, sendo apresentada a metodologia adoptada e as suas principais funcionalidades. A ferramenta desenvolvida tem grandes preocupações com a interface de utilizador, visto ser direccionada para decisores que tipicamente não têm conhecimentos sobre os modelos matemáticos subjacentes a este tipo de problemas.This thesis main objective is to address the location-routing problem (LRP) which intends to tackle, using an integrated approach, two highly related logistics activities: the location of facilities and the distribution of materials. The LRP, namely its mathematical formulation, has been studied in the literature, and several approaches have emerged, corresponding to different real-world scenarios. Therefore, it is important to identify and group the different LRP variants, in order to segment current research and foster future studies. After presenting a review and a taxonomy of location-routing models, the following research focuses on solving some of its variants. Thus, a study of two of the most basic LRPs (capacitated problems with demand either on the nodes or on the arcs) is performed, and new approaches are presented. Afterwards, the location-routing of semi-obnoxious facilities is addressed. These are facilities that, although providing useful and indispensible services, given their nature, bring about an undesirable effect to adjacent communities. Consequently, to the usual objectives when considering their location (cost minimization), new ones must be added that are able to reflect concerns regarding the quality of life of the communities impacted by the outcome of these decisions. The location-routing of semi-obnoxious facilities therefore requires to be analysed using multi-objective approaches, which can be of two types: noninteractive or interactive. Both are discussed and new methods proposed in this thesis; the proposed interactive method is suitable to other multi-objective mixed integer programming problems. Finally, a newly developed decision-support tool to address the LRP is presented (being the adopted methodology discussed, and its main functionalities shown). This tool has great concerns regarding the user interface, as it is directed at decision makers who typically don’t have specific knowledge of the underlying models of this type of problems

Information Preserving Processing of Noisy Handwritten Document Images

Many pre-processing techniques that normalize artifacts and clean noise induce anomalies due to discretization of the document image. Important information that could be used at later stages may be lost. A proposed composite-model framework takes into account pre-printed information, user-added data, and digitization characteristics. Its benefits are demonstrated by experiments with statistically significant results. Separating pre-printed ruling lines from user-added handwriting shows how ruling lines impact people\u27s handwriting and how they can be exploited for identifying writers. Ruling line detection based on multi-line linear regression reduces the mean error of counting them from 0.10 to 0.03, 6.70 to 0.06, and 0.13 to 0.02, com- pared to an HMM-based approach on three standard test datasets, thereby reducing human correction time by 50%, 83%, and 72% on average. On 61 page images from 16 rule-form templates, the precision and recall of form cell recognition are increased by 2.7% and 3.7%, compared to a cross-matrix approach. Compensating for and exploiting ruling lines during feature extraction rather than pre-processing raises the writer identification accuracy from 61.2% to 67.7% on a 61-writer noisy Arabic dataset. Similarly, counteracting page-wise skew by subtracting it or transforming contours in a continuous coordinate system during feature extraction improves the writer identification accuracy. An implementation study of contour-hinge features reveals that utilizing the full probabilistic probability distribution function matrix improves the writer identification accuracy from 74.9% to 79.5%

Spatial access to healthcare: exploring the provision of local services

This thesis creates a context for exploring the provision of local healthcare services quantitatively, with particular focus on the application of spatial analysis and the use of geographic information systems (GIS). It focuses theoretically on the intersections between: health and medical geography; GIScience and spatially integrated social science; and social justice and spatial equity, elucidating the value of space and place in understanding patient registration with, and usage of, healthcare services. The practical elements of the thesis are based on patient registration data provided by Southwark primary care trust (PCT), and Hospital Episode Statistics from the NHS Information Centre. Focussing initially on primary care, registration with GP surgeries in Southwark is considered firstly from a normative perspective, and subsequently by employing a service area delineation approach. Profiling GP surgeries in this way enables an insight into patient registration behaviours, and sheds light on the challenges of implementing an agenda of patient choice as advocated by recent NHS white papers. The perspective of inpatient and outpatient care is also considered, given the increasing import of joined up provision in primary and secondary care. The thesis considers the linkage between the two service hierarchies, investigating utilisation of secondary care by patients. The value of this thesis derives from its relevance to the reform agenda that looks likely to radically reshape the NHS, the exploitation of patient registration data at individual level, novel use of classification, and the systematic application of spatial analysis across a range of scales

Automatisierte Erzeugung personalisierter ad-hoc-Karten in einem Service-basierten GIS (Mapping on Demand)

In den letzten Jahren wurden mehr und mehr raumbezogene Daten über das World Wide Web zur Verfügung gestellt. Karten und Luftbilder bekannter Anwendungen (z.B. Google Maps) lassen sich direkt nutzen oder mit Daten anderer Angebote verknüpfen und in ihrem Informationsgehalt erweitern. Ein Nutzer hat so die Möglichkeit, unabhängig von Ort und Zeit, zu einer aktuellen Fragestellung beliebige Daten zu integrieren und eigene Karten zu erstellen (Mapping on demand). Benötigte Daten werden zunehmend im Zusammenhang mit Diensten - Funktionen, die den Zugriff auf Daten und deren sachgerechte Verwendung unterstützen - zur Verfügung gestellt. Dies entspricht dem allgemeinen Trend des Internets hin zu einer Service-orientierten Architektur; deren Implementierung durch Web Services löst Daten aus dem Kontext spezifischer Anwendungen und macht sie über definierte Schnittstellen verfügbar. Herausforderung in einer Service-orientierten Architektur ist zunächst, dass die genutzten Daten weltweit verteilt sind, zu verschiedensten Zwecken erhoben wurden und in unterschiedlichen Formaten vorliegen. Diese Heterogenität wird durch den Einsatz standardisierter Dienste und Formate überwunden. In der vorliegenden Arbeit wird gezeigt, dass im World Wide Web Technologien verfügbar sind, die das notwendige Potential für ein Mapping on demand besitzen. Beim Auffinden geeigneter Dienste und der Nutzung verfügbarer Technologien wird ein Nutzer durch Webportale unterstützt. Diese bündeln Dienste, machen sie strukturiert zugänglich und ermöglichen die Erschließung durch geeignete Werkzeuge. Eine konkrete Umsetzung von Webportalen wird in dieser Arbeit anhand dreier Beispiele aus dem Bereich der Freizeitplanung gezeigt. Für das Mapping on demand ist von Bedeutung, dass Daten verfügbarer Dienste nicht nur als fertige Karten vorliegen, sondern auch als Kartenbausteine in Form raumbezogener Objekte oder thematischer Layer. Bei der Integration der graphischen Ausgaben dieser Dienste wird offensichtlich, dass die graphische Repräsentation, die jedes Angebot von sich aus mitbringt, isoliert von anderen Angeboten festgelegt ist. Die Kombination beliebiger Quellen führt damit häufig zu Darstellungen, die schon den Mindestanforderungen graphischer Gestaltungsregeln und erst recht den Erfordernissen der Prägnanz nicht genügen, so dass der Inhalt schwer erfassbar ist. Nur eine prägnante Darstellung gibt dem Nutzer die Möglichkeit, Objekte visuell zu differenzieren und effektiv Wesentliches von Unwesentlichem zu unterscheiden. Eine Voraussetzung hierfür ist der Einsatz visuell gut unterscheidbarer Farben. Kern dieser Arbeit ist der Nachweis, dass die Bestimmung gut unterscheidbarer Farben als Optimierungsproblem formuliert und mit mathematischen Methoden on demand gelöst werden kann. Dies erfordert eine objektivierte Beschreibung des subjektiven Vorgangs der Farbwahrnehmung in einem Bezugssystem (Farbraum), auf dem eine geeignete, der menschlichen Wahrnehmung entsprechende, Metrik definiert ist. Ein solches System steht bspw. mit dem CIELUV-Farbraum zur Verfügung: Wenn darin der Abstand zweier Farben ein gewisses Minimum überschreitet, ist die Verschiedenheit dieser Farben für einen (normalsichtigen) Menschen klar erkennbar. Das Optimierungsproblem besteht dann darin, die minimale Distanz in einem dreidimensionalen Raum zu maximieren. Es handelt sich dabei um ein nichtlineares Problem, das durch eine Vielzahl lokal optimaler Lösungen gekennzeichnet ist. Klassische gradientenbasierte Verfahren berechnen zwar eine lokale, in der Regel aber nicht die global optimale Lösung. Probleme der globalen Optimierung sind im Allgemeinen schwer lösbar (NP-vollständig). Effiziente Verfahren wurden für diskrete Problemstellungen entwickelt, sind aber wegen der spezifischen Randbedingungen auf das vorliegende Problem nicht übertragbar. In dieser Arbeit wird eine Methode entwickelt, die mehrere Standardverfahren und Lösungsparadigmen integriert. Ausgangspunkt ist ein randomisierter Algorithmus zur Bestimmung geeigneter Startpunkte. Dieser Algorithmus basiert auf der Beobachtung, dass sich Punkte auf dem Rand der konvexen Hülle des Farbraums in besonderer Weise als Startpunkte eignen. Die Lage dieser Punkte wird durch Anwendung eines Verfahrens der lokalen Optimierung verbessert. Ein dreidimensionales Voronoi-Diagramm wird genutzt, um eine suboptimale Nutzung des verfügbaren Farbraums zu identifizieren und Verbesserungsmöglichkeiten herzuleiten. Das skizzierte Szenario geht zunächst von einem Standardnutzer und Standardbedingungen aus. Die Methode kann aber ohne weiteres auch auf davon abweichende Randbedingungen, z.B. Farbsehschwächen eines Nutzers, Qualität der Farbwiedergabe eines Anzeigegeräts oder Umgebungsbedingungen (abgedunkelter Raum oder helles Sonnenlicht), angepasst werden. In ihrer Auswirkung führen diese Bedingungen zu einer Einschränkung des verfügbaren Farbraums.Automated Creation of personalised ad-hoc-Maps in a Service-based GIS (Mapping on Demand) Providing geospatial data over the World Wide Web has developed rapidly in recent years. Maps and aerial photographs offered by popular applications (e.g. Google Maps) can either be used directly or may be linked to data of other providers to broaden information content. Hence, a user who demands a map to answer a current question is enabled to create his own map by overlaying arbitrary data - regardless of location and time (Mapping on demand). Data is increasingly provided in connection with services - functions, which support access and appropriate use of data. Services correspond to a general trend of realising a service-oriented architecture in the internet. Web services, which implement this architecture, dissolve data from specific applications and provide them by defined interfaces. The challenge in using services consists in the worldwide distribution of data, different intentions of data collection and the large variety of available formats. This heterogeneity is overcome by applying standardised formats and services. This thesis demonstrates the potential of technologies which are available for a mapping on demand. In finding suitable services and using technologies, a user is supported by web portals. These portals make services accessible in a structured manner and support their exploration by suitable tools. This thesis presents three examples of real implementations of web portals from the domain of recreation planning. In the scope of mapping on demand it is important to note that data provided by services are not only available as complete maps but also as components (thematic layers or features). Integrating their graphical output shows that graphical representation of data from each source is defined independently and that graphical representations of different sources may conflict. Thus, the ad hoc combination of sources may lead to maps, which do not satisfy basic rules of graphical design or even requirements of a concise cartographic product. But only conciseness enables a user to identify features visually and to distinguish between essential and nonessential contents. This requires the choice of colours which are well distinguishable by human visual perception. The main contribution of this thesis is the proof that the determination of well distinguishable colours can be formulated as an optimization problem, which can be solved on demand by mathematical methods. This approach requires an objectified description of the subjective process of colour vision in a reference system (colour space), which provides an appropriate metric according to human perception. Particularly the CIELUV colour space satisfies the requirement: If the distance between two colours exceeds a certain minimum, a human with full colour vision is able to distinguish these colours clearly. Thus the optimization problem is to maximise the minimal distance in a three-dimensional space. This is a nonlinear problem, which is characterized by a large number of locally optimal solutions. Classical descend methods find a locally, but usually not the globally optimal solution. In general, global optimization problems are computationally hard to solve (NP-complete). Efficient methods have been developed for solving discrete problems. Due to specific constraints these methods are not applicable to the problem at hand. This thesis presents a method which integrates several standard methods and solution paradigms. It is based on a randomized algorithm to determine appropriate starting points. The essential observation is that points on the boundary of the convex hull of the colour space are well suited as starting points. Afterwards the location of these points is improved by a method of local optimization. A three-dimensional Voronoi-diagram is used to detect suboptimal solutions and to identify possible improvements. Initially the scenario outlined above acts on a standard user and standard conditions. The method is adaptable to incorporate further constraints, e.g. user's colour-defective vision, device-specific colour reproduction and ambient conditions (darkened room or sunlight). These constraints result in clipping the available colour space

LIPIcs, Volume 248, ISAAC 2022, Complete Volume

LIPIcs, Volume 248, ISAAC 2022, Complete Volum