Linear-Time Algorithms for Geometric Graphs with Sublinearly Many Edge Crossings

We provide linear-time algorithms for geometric graphs with sublinearly many crossings. That is, we provide algorithms running in O(n) time on connected geometric graphs having n vertices and k crossings, where k is smaller than n by an iterated logarithmic factor. Specific problems we study include Voronoi diagrams and single-source shortest paths. Our algorithms all run in linear time in the standard comparison-based computational model; hence, we make no assumptions about the distribution or bit complexities of edge weights, nor do we utilize unusual bit-level operations on memory words. Instead, our algorithms are based on a planarization method that "zeroes in" on edge crossings, together with methods for extending planar separator decompositions to geometric graphs with sublinearly many crossings. Incidentally, our planarization algorithm also solves an open computational geometry problem of Chazelle for triangulating a self-intersecting polygonal chain having n segments and k crossings in linear time, for the case when k is sublinear in n by an iterated logarithmic factor.Comment: Expanded version of a paper appearing at the 20th ACM-SIAM Symposium on Discrete Algorithms (SODA09

Crossing Patterns in Nonplanar Road Networks

We define the crossing graph of a given embedded graph (such as a road network) to be a graph with a vertex for each edge of the embedding, with two crossing graph vertices adjacent when the corresponding two edges of the embedding cross each other. In this paper, we study the sparsity properties of crossing graphs of real-world road networks. We show that, in large road networks (the Urban Road Network Dataset), the crossing graphs have connected components that are primarily trees, and that the remaining non-tree components are typically sparse (technically, that they have bounded degeneracy). We prove theoretically that when an embedded graph has a sparse crossing graph, it has other desirable properties that lead to fast algorithms for shortest paths and other algorithms important in geographic information systems. Notably, these graphs have polynomial expansion, meaning that they and all their subgraphs have small separators.Comment: 9 pages, 4 figures. To appear at the 25th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems(ACM SIGSPATIAL 2017

Information systems: a cyborg discipline?

This paper argues for a model of information systems in terms of cyborgs – a boundary-crossing mixture of the technical and the social. The argument for this model is substantiated from the personal experience of the author, presented as examples of being a cyborg researcher within a disciplinary context. Lessons for information systems are drawn

Determining the Effects of Central-Peripheral interactions on the Distribution of Human Activity in Space

Natural advantages determine where agglomerations emerge. Also, efficiency and economies of scale determine how many agglomerations subsist and how they interact, forming complex urban hierarquies. Moreover, physical characteristics influence the way humans divide land into irregular parcels we call administrative regions. If, on one hand, initial location advantages are responsible for defining where the main urban nodes will grow and subsist because of lock-in effects, central-peripheral relations play a decisive role in defining the distribution of activity in space. This paper explores the importance of location in relation to the main centripetal nodes. A central-peripheral model, taking into account spatial heterogeneity patterns, explains how activity is organized in Continental Portugal. A bayesian framework will allow the comparison of posterior densities for distinct parts of the country.

Embalmed|Unembalmed: the problems of the lived event within media studies 2.0

Media Studies 2.0 seeks to rewire the discipline of media studies from prevailing notions of aggregate third-person, top-down or imposed identities (as found within the domain of industrial mass communications media) toward what it sees as the communication of new bottom-up, first-person or singular reflexive identities favored within the post-fordist, post-industrial spaces of the internet, social networking sites, second life-like domains and computer game spaces. This article will point toward many of the hidden, though still important, intersections between these two supposedly separate conceptions through the use of a case study that throws notions of clean “communication” into question. From this it will go on to argue for a recognition of such new media spaces as better conceptualized through Batailleʼs notion of ʻGeneral Economyʼ and Derridaʼs notion of ʻUndecidabilityʼ, as dually taken forward in the work of Arkady Plotnitsky. The conclusion? Far from modern teletechnologies offering a new sense of micro-community or as channels of individual self-expression (a new Rousseauian or McLuhanesque global village of intimate contact), these emergent teletechnologies serve to further displace or undecide the locus of any signature context of communication, which this article takes as a cause for celebration

Transportation Risk ANalysis tool for hazardous Substances (TRANS): a user-friendly, semi-quantitative multi-mode hazmat transport route safety risk estimation methodology for Flanders

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Chaotic and regular motion around generalized Kalnajs discs

The motion of test particles in the gravitational fields generated by the first four members of the infinite family of generalized Kalnajs discs, is studied. In first instance, we analyze the stability of circular orbits under radial and vertical perturbations and describe the behavior of general equatorial orbits and so we find that radial stability and vertical instability dominate such disc models. Then we study bounded axially symmetric orbits by using the Poincare surfaces of section and Lyapunov characteristic numbers and find chaos in the case of disc-crossing orbits and completely regular motion in other cases

An ETH-Tight Exact Algorithm for Euclidean TSP

We study exact algorithms for {\sc Euclidean TSP} in $\mathbb{R}^d$. In the early 1990s algorithms with $n^{O(\sqrt{n})}$ running time were presented for the planar case, and some years later an algorithm with $n^{O(n^{1-1/d})}$ running time was presented for any $d\geq 2$. Despite significant interest in subexponential exact algorithms over the past decade, there has been no progress on {\sc Euclidean TSP}, except for a lower bound stating that the problem admits no $2^{O(n^{1-1/d-\epsilon})}$ algorithm unless ETH fails. Up to constant factors in the exponent, we settle the complexity of {\sc Euclidean TSP} by giving a $2^{O(n^{1-1/d})}$ algorithm and by showing that a $2^{o(n^{1-1/d})}$ algorithm does not exist unless ETH fails.Comment: To appear in FOCS 201

Distribution of the spacing between two adjacent avoided crossings

We consider the frequency at which avoided crossings appear in an energy level structure when an external field is applied to a quantum chaotic system. The distribution of the spacing in the parameter between two adjacent avoided crossings is investigated. Using a random matrix model, we find that the distribution of these spacings is well fitted by a power-law distribution for small spacings. The powers are 2 and 3 for the Gaussian orthogonal ensemble and Gaussian unitary ensemble, respectively. We also find that the distributions decay exponentially for large spacings. The distributions in concrete quantum chaotic systems agree with those of the random matrix model.Comment: 11 page