Spatial information retrieval and geographical ontologies: an overview of the SPIRIT project

A large proportion of the resources available on the world-wide web refer to information that may be regarded as geographically located. Thus most activities and enterprises take place in one or more places on the Earth's surface and there is a wealth of survey data, images, maps and reports that relate to specific places or regions. Despite the prevalence of geographical context, existing web search facilities are poorly adapted to help people find information that relates to a particular location. When the name of a place is typed into a typical search engine, web pages that include that name in their text will be retrieved, but it is likely that many resources that are also associated with the place may not be retrieved. Thus resources relating to places that are inside the specified place may not be found, nor may be places that are nearby or that are equivalent but referred to by another name. Specification of geographical context frequently requires the use of spatial relationships concerning distance or containment for example, yet such terminology cannot be understood by existing search engines. Here we provide a brief survey of existing facilities for geographical information retrieval on the web, before describing a set of tools and techniques that are being developed in the project SPIRIT : Spatially-Aware Information Retrieval on the Internet (funded by European Commission Framework V Project IST-2001-35047)

Higher order Delaunay triangulations

For a set P of points in the plane, we introduce a class of triangulations that is an extension of the Delaunay triangulation. Instead of requiring that for each triangle the circle through its vertices contains no points of P inside, we require that at most k points are inside the circle. Since there are many different higher-order Delaunay triangulations for a point set, other useful criteria for triangulations can be incorporated without sacrificing the well-shapedness too much. Applications include realistic terrain modelling and mesh generation

Finding a minimum stretch of a function

Given a piecewise monotone function f : R ! R and a real value Tmin, we develop an algorithm that finds an interval of length at least Tmin for which the average value of f is minimized. The run-time of the algorithm is linear in the number of monotone pieces of f if certain operations are available in constant time for f. We use this algorithm to solve a basic problem arising in the analysis of trajectories: Finding the most similar subtrajectories of two given trajectories, provided that the duration is at least Tmin. Since the precise solution requires complex operations, we also give a simple (1+")approximation algorithm in which these operations are not needed

Finding long and similar parts of trajectories

A natural time-dependent similarity measure for two trajectories is their average distance at corresponding times. We give algorithms for computing the most similar subtrajectories under this measure, assuming the two trajectories are given as two polygonal, possibly self-intersecting lines. When a minimum duration is specified for the subtrajectories, and they must start at exactly corresponding times in the input trajectories, we give a linear-time algorithm for computing the starting time and duration of the most similar subtrajectories. The algorithm is based on a result of independent interest: We present a linear-time algorithm to find, for a piece-wise monotone function, an interval of at least a given length that has minimum average value. When the two subtrajectories can start at different times in the two input trajectories, it appears difficult to give an exact algorithm for the most similar subtrajectories problem, even if the duration of the desired two subtrajectories is fixed to some length. We show that the problem can be solved approximately, and with a performance guarantee. More precisely, we present (1 + e)-approximation algorithms for computing the most similar subtrajectories of two input trajectories for the case where the duration is specified, and also for the case where only a minimum on the duration is specified

Evaluation of Labeling Strategies for Rotating Maps

We consider the following problem of labeling points in a dynamic map that allows rotation. We are given a set of points in the plane labeled by a set of mutually disjoint labels, where each label is an axis-aligned rectangle attached with one corner to its respective point. We require that each label remains horizontally aligned during the map rotation and our goal is to find a set of mutually non-overlapping active labels for every rotation angle $\alpha \in [0, 2\pi)$ so that the number of active labels over a full map rotation of 2$\pi$ is maximized. We discuss and experimentally evaluate several labeling models that define additional consistency constraints on label activities in order to reduce flickering effects during monotone map rotation. We introduce three heuristic algorithms and compare them experimentally to an existing approximation algorithm and exact solutions obtained from an integer linear program. Our results show that on the one hand low flickering can be achieved at the expense of only a small reduction in the objective value, and that on the other hand the proposed heuristics achieve a high labeling quality significantly faster than the other methods.Comment: 16 pages, extended version of a SEA 2014 pape

Orientation-Constrained Rectangular Layouts

We construct partitions of rectangles into smaller rectangles from an input consisting of a planar dual graph of the layout together with restrictions on the orientations of edges and junctions of the layout. Such an orientation-constrained layout, if it exists, may be constructed in polynomial time, and all orientation-constrained layouts may be listed in polynomial time per layout.Comment: To appear at Algorithms and Data Structures Symposium, Banff, Canada, August 2009. 12 pages, 5 figure

Modeling Checkpoint-Based Movement with the Earth Mover's Distance

Movement data comes in various forms, including trajectory data and checkpoint data. While trajectories give detailed information about the movement of individual entities, checkpoint data in its simplest form does not give identities, just counts at checkpoints. However, checkpoint data is of increasing interest since it is readily available due to privacy reasons and as a by-product of other data collection. In this paper we propose to use the Earth Mover’s Distance as a versatile tool to reconstruct individual movements or flow based on checkpoint counts at different times. We analyze the modeling possibilities and provide experiments that validate model predictions, based on coarse-grained aggregations of data about actual movements of couriers in London, UK. While we cannot expect to reconstruct precise individual movements from highly granular checkpoint data, the evaluation does show that the approach can generate meaningful estimates of object movements. B. Speckmann and K. Verbeek are supported by the Netherlands Organisation for Scientific Research (NWO) under project nos. 639.023.208 and 639.021.541, respectively. This paper arose from work initiated at Dagstuhl seminar 12512 “Representation, analysis and visualization of moving objects”, December 2012. The authors gratefully acknowledge Schloss Dagstuhl for their support

Edges and switches, tunnels and bridges

Abstract. Edge casing is a well-known method to improve the readability of drawings of non-planar graphs. A cased drawing orders the edges of each edge crossing and interrupts the lower edge in an appropriate neighborhood of the crossing. Certain orders will lead to a more readable drawing than others. We formulate several optimization criteria that try to capture the concept of a "good" cased drawing. Further, we address the algorithmic question of how to turn a given drawing into an optimal cased drawing. For many of the resulting optimization problems, we either find polynomial time algorithms or NP-hardness results