Discrepancy-Sensitive Dynamic Fractional Cascading, Dominated Maxima Searching, and 2-d Nearest Neighbors in Any Minkowski Metric

This paper studies a discrepancy-sensitive approach to dynamic fractional cascading. We provide an efficient data structure for dominated maxima searching in a dynamic set of points in the plane, which in turn leads to an efficient dynamic data structure that can answer queries for nearest neighbors using any Minkowski metric

A systems approach to analyze the robustness of infrastructure networks to complex spatial hazards

Ph. D. ThesisInfrastructure networks such as water supply systems, power networks, railway networks, and road networks provide essential services that underpin modern society’s health, wealth, security, and wellbeing. However, infrastructures are susceptible to damage and disruption caused by extreme weather events such as floods and windstorms. For instance, in 2007, extensive disruption was caused by floods affecting a number of electricity substations in the United Kingdom, resulting in an estimated damage of GBP£3.18bn (US$4bn). In 2017, Hurricane Harvey hit the Southern United States, causing an approximated US$125bn (GBP£99.35bn) in damage due to the resulting floods and high winds. The magnitude of these impacts is at risk of being compounded by the effects of Climate Change, which is projected to increase the frequency of extreme weather events. As a result, it is anticipated that an estimated US$3.7tn (GBP£2.9tn) in investment will be required, per year, to meet the expected need between 2019 and 2035. A key reason for the susceptibility of infrastructure networks to extreme weather events is the wide area that needs to be covered to provide essential services. For example, in the United Kingdom alone there are over 800,000 km of overhead electricity cables, suggesting that the footprint of infrastructure networks can be as extended as that of an entire Country. These networks possess different spatial structures and attributes, as a result of their evolution over long timeframes, and respond to damage and disruption in different and complex ways. Existing approaches to understanding the impact of hazards on infrastructure networks typically either (i) use computationally expensive models, which are unable to support the investigation of enough events and scenarios to draw general insights, or (ii) use low complexity representations of hazards, with little or no consideration of their spatial properties. Consequently, this has limited the understanding of the relationship between spatial hazards, the spatial form and connectivity of infrastructure networks, and infrastructure reliability. This thesis investigates these aspects through a systemic modelling approach, applied to a synthetic and a real case study, to evaluate the response of infrastructure networks to spatially complex hazards against a series of robustness metrics. In the first case study, non-deterministic spatial hazards are generated by a fractal method which allows to control their spatial variability, resulting in spatial configurations that very closely resemble natural phenomena such as floods or windstorms. These hazards are then superimposed on a range of synthetic network layouts, which have spatial structures consistent with real infrastructure networks reported in the literature. Failure of network components is initially determined as a function of hazard intensity, and cascading failure of further components is also investigated. The performance of different infrastructure configurations is captured by an array of metrics which cover different aspects of robustness, ranging from the proneness to partitioning to the ability to process flows in the face of disruptions. Whereas analyses to date have largely adopted low complexity representations of hazards, this thesis shows that consideration of a high complexity representation which includes hazard spatial variability can reduce the robustness of the infrastructure network by nearly 40%. A “small-world” network, in which each node is within a limited number of steps from any other node, is shown to be the most robust of all the modelled networks to the different structures of spatial hazard. The second case study uses real data to assess the robustness of a power supply network operating in the Hull region in the United Kingdom, which is split in high and low voltage lines. The spatial hazard is represented by a high-resolution wind gust model and tested under current and future climate scenarios. The analysis reveals how the high and low voltage lines interact with each other in the event of faults, which lines would benefit the most from increased robustness, and which are most exposed to cascading failures. The second case study also reveals the importance of the spatial footprint of the hazard relative to the location of the infrastructure, and how particular hazard patterns can affect low voltage lines that are more often located in exposed areas at the edge of the network. The impact of Climate Change on windstorms is highly uncertain, although it could further reduce network robustness due to more severe events. Overall the two case studies provide important insights for infrastructure designers, asset managers, the academic sector, and practitioners in general. In fact, in the first case study, this thesis defines important design principles, such as the adoption of a small-world network layout, that can integrate the traditional design drivers of demand, efficiency, and cost. In the second case study, this thesis lays out a methodology that can help identify assets requiring increased robustness and protection against cascading failures, resulting in more effective prioritized infrastructure investments and adaptation plans

LIPIcs, Volume 258, SoCG 2023, Complete Volume

LIPIcs, Volume 258, SoCG 2023, Complete Volum

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

Pattern Recognition

Pattern recognition is a very wide research field. It involves factors as diverse as sensors, feature extraction, pattern classification, decision fusion, applications and others. The signals processed are commonly one, two or three dimensional, the processing is done in real- time or takes hours and days, some systems look for one narrow object class, others search huge databases for entries with at least a small amount of similarity. No single person can claim expertise across the whole field, which develops rapidly, updates its paradigms and comprehends several philosophical approaches. This book reflects this diversity by presenting a selection of recent developments within the area of pattern recognition and related fields. It covers theoretical advances in classification and feature extraction as well as application-oriented works. Authors of these 25 works present and advocate recent achievements of their research related to the field of pattern recognition

Large bichromatic point sets admit empty monochromatic 4-gons

We consider a variation of a problem stated by Erd˝os and Szekeres in 1935 about the existence of a number fES(k) such that any set S of at least fES(k) points in general position in the plane has a subset of k points that are the vertices of a convex k-gon. In our setting the points of S are colored, and we say that a (not necessarily convex) spanned polygon is monochromatic if all its vertices have the same color. Moreover, a polygon is called empty if it does not contain any points of S in its interior. We show that any bichromatic set of n ≥ 5044 points in R2 in general position determines at least one empty, monochromatic quadrilateral (and thus linearly many).Postprint (published version