Constrained set-up of the tGAP structure for progressive vector data transfer

A promising approach to submit a vector map from a server to a mobile client is to send a coarse representation first, which then is incrementally refined. We consider the problem of defining a sequence of such increments for areas of different land-cover classes in a planar partition. In order to submit well-generalised datasets, we propose a method of two stages: First, we create a generalised representation from a detailed dataset, using an optimisation approach that satisfies certain cartographic constraints. Second, we define a sequence of basic merge and simplification operations that transforms the most detailed dataset gradually into the generalised dataset. The obtained sequence of gradual transformations is stored without geometrical redundancy in a structure that builds up on the previously developed tGAP (topological Generalised Area Partitioning) structure. This structure and the algorithm for intermediate levels of detail (LoD) have been implemented in an object-relational database and tested for land-cover data from the official German topographic dataset ATKIS at scale 1:50 000 to the target scale 1:250 000. Results of these tests allow us to conclude that the data at lowest LoD and at intermediate LoDs is well generalised. Applying specialised heuristics the applied optimisation method copes with large datasets; the tGAP structure allows users to efficiently query and retrieve a dataset at a specified LoD. Data are sent progressively from the server to the client: First a coarse representation is sent, which is refined until the requested LoD is reached

A Network Flow Model for the Analysis of Green Spaces in Urban Areas

Green spaces in urban areas offer great possibilities of recreation, provided that they are easily accessible. Therefore, an ideal city should offer large green spaces close to where its residents live. Although there are several measures for the assessment of urban green spaces, the existing measures usually focus either on the total size of green spaces or on their accessibility. Hence, in this paper, we present a new methodology for assessing green-space provision and accessibility in an integrated way. The core of our methodology is an algorithm based on linear programming that computes an optimal assignment between residential areas and green spaces. In a basic setting, it assigns a green space of a prescribed size exclusively to each resident such that the average distance between residents and assigned green spaces is minimized. We contribute a detailed presentation on how to engineer an assignment-based method such that it yields reasonable results (e.g., by considering distances in the road network) and becomes efficient enough for the analysis of large metropolitan areas (e.g., we were able to process an instance of Berlin with about 130000 polygons representing green spaces, 18000 polygons representing residential areas, and 6 million road segments). Furthermore, we show that the optimal assignments resulting from our method enable a subsequent analysis that reveals both interesting global properties of a city as well as spatial patterns. For example, our method allows us to identify neighborhoods with a shortage of green spaces, which will help spatial planners in their decision making

Bicriteria Aggregation of Polygons via Graph Cuts

We present a new method for the task of detecting groups of polygons in a given geographic data set and computing a representative polygon for each group. This task is relevant in map generalization where the aim is to derive a less detailed map from a given map. Following a classical approach, we define the output polygons by merging the input polygons with a set of triangles that we select from a constrained Delaunay triangulation of the input polygons\u27 exterior. The innovation of our method is to compute the selection of triangles by solving a bicriteria optimization problem. While on the one hand we aim at minimizing the total area of the outputs polygons, we aim on the other hand at minimizing their total perimeter. We combine these two objectives in a weighted sum and study two computational problems that naturally arise. In the first problem, the parameter that balances the two objectives is fixed and the aim is to compute a single optimal solution. In the second problem, the aim is to compute a set containing an optimal solution for every possible value of the parameter. We present efficient algorithms for these problems based on computing a minimum cut in an appropriately defined graph. Moreover, we show how the result set of the second problem can be approximated with few solutions. In an experimental evaluation, we finally show that the method is able to derive settlement areas from building footprints that are similar to reference solutions

Balanced Independent and Dominating Sets on Colored Interval Graphs

We study two new versions of independent and dominating set problems on vertex-colored interval graphs, namely \emph{$f$-Balanced Independent Set} ($f$-BIS) and \emph{$f$-Balanced Dominating Set} ($f$-BDS). Let $G=(V,E)$ be a vertex-colored interval graph with a $k$-coloring $\gamma \colon V \rightarrow \{1,\ldots,k\}$ for some $k \in \mathbb N$. A subset of vertices $S\subseteq V$ is called \emph{$f$-balanced} if $S$ contains $f$ vertices from each color class. In the $f$-BIS and $f$-BDS problems, the objective is to compute an independent set or a dominating set that is $f$-balanced. We show that both problems are \NP-complete even on proper interval graphs. For the BIS problem on interval graphs, we design two \FPT\ algorithms, one parameterized by $(f,k)$ and the other by the vertex cover number of $G$. Moreover, we present a 2-approximation algorithm for a slight variation of BIS on proper interval graphs

Map schematization with circular arcs

We present an algorithm to compute schematic maps with circular arcs. Our algorithm iteratively replaces two consecutive arcs with a single arc to reduce the complexity of the output map and thus to increase its level of abstraction. Our main contribution is a method for replacing arcs that meet at high-degree vertices. This allows us to greatly reduce the output complexity, even for dense networks. We experimentally evaluate the effectiveness of our algorithm in three scenarios: territorial outlines, road networks, and metro maps. For the latter, we combine our approach with an algorithm to more evenly distribute stations. Our experiments show that our algorithm produces high-quality results for territorial outlines and metro maps. However, the lack of caricature (exaggeration of typical features) makes it less useful for road networks

Combinatorial optimization applied to VLBI scheduling

Due to the advent of powerful solvers, today linear programming has seen many applications in production and routing. In this publication, we present mixed-integer linear programming as applied to scheduling geodetic very-long-baseline interferometry (VLBI) observations. The approach uses combinatorial optimization and formulates the scheduling task as a mixed-integer linear program. Within this new method, the schedule is considered as an entity containing all possible observations of an observing session at the same time, leading to a global optimum. In our example, the optimum is found by maximizing the sky coverage score. The sky coverage score is computed by a hierarchical partitioning of the local sky above each telescope into a number of cells. Each cell including at least one observation adds a certain gain to the score. The method is computationally expensive and this publication may be ahead of its time for large networks and large numbers of VLBI observations. However, considering that developments of solvers for combinatorial optimization are progressing rapidly and that computers increase in performance, the usefulness of this approach may come up again in some distant future. Nevertheless, readers may be prompted to look into these optimization methods already today seeing that they are available also in the geodetic literature. The validity of the concept and the applicability of the logic are demonstrated by evaluating test schedules for five 1-h, single-baseline Intensive VLBI sessions. Compared to schedules that were produced with the scheduling software sked, the number of observations per session is increased on average by three observations and the simulated precision of UT1-UTC is improved in four out of five cases (6μs average improvement in quadrature). Moreover, a simplified and thus much faster version of the mixed-integer linear program has been developed for modern VLBI Global Observing System telescopes