Network Survivability Analysis: Coarse-Graining And Graph-Theoretic Strategies

In this dissertation, the interplay between geographic information about the network and the principal properties and structure of the underlying graph are used to quantify the structural and functional survivability of the network. This work focuses on the local aspect of survivability by studying the propagation of loss in the network as a function of the distance of the fault from a given origin-destination node pair

A graph-based mathematical morphology reader

This survey paper aims at providing a "literary" anthology of mathematical morphology on graphs. It describes in the English language many ideas stemming from a large number of different papers, hence providing a unified view of an active and diverse field of research

The characteristics of asymmetric pedestrian behavior: A preliminary study using passive smartphone location data

Understanding the movements of people is essential for the design and management of urban areas. This article presents a novel approach to understanding the asymmetry in route choice (i.e., the degree to which people choose different walking routes for their outbound and return journeys). The study utilizes a large volume of traces of individual routes, captured using a smartphone application. The routes are aggregated to a regular grid, and matrix statistics are developed to estimate the aggregate degree of route asymmetry for different types of route (shortest, longest, weekday, weekend, etc.). The results suggest that people change their route approximately 15% of the time. Although this varied little when observing trips made at the weekend or on a weekday, people taking journeys that deviated substantially from the shortest possible path were 6 percentage points less likely to change their routes than those taking journeys that were closest to the shortest path (14 and 20% asymmetry, respectively). The absolute length also impacted on the asymmetry of journeys, but not as substantially. This result is important because, for the first time, it reports a correlation between deviation from shortest route and aggregate pedestrian choice

On approximating shortest paths in weighted triangular tessellations

© 2023 Elsevier. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/We study the quality of weighted shortest paths when a continuous 2-dimensional space is discretized by a weighted triangular tessellation. In order to evaluate how well the tessellation approximates the 2-dimensional space, we study three types of shortest paths: a weighted shortest path , which is a shortest path from s to t in the space; a weighted shortest vertex path , which is an any-angle shortest path; and a weighted shortest grid path , which is a shortest path whose edges are edges of the tessellation. Given any arbitrary weight assignment to the faces of a triangular tessellation, thus extending recent results by Bailey et al. (2021) [6], we prove upper and lower bounds on the ratios , , , which provide estimates on the quality of the approximation. It turns out, surprisingly, that our worst-case bounds are independent of any weight assignment. Our main result is that in the worst case, and this is tight. As a corollary, for the weighted any-angle path we obtain the approximation result .P. B. is partially supported by NSERC. G. E., D. O. and R. I. S. are partially supported by H2020-MSCA-RISE project 734922 - CONNECT and project PID2019-104129GB-I00 funded by MCIN/AEI/10.13039/501100011033. G. E. and D. O. are also supported by PIUAH21/IA-062 and CM/JIN/2021-004. G. E. is also funded by an FPU of the Universidad de Alcalá.Peer ReviewedPostprint (published version