On d-regular Schematization of Embedded Paths

In the d-regular path schematization problem we are given an embedded path P (e.g.,a route in a road network) and an integer d. The goal is to find a d-schematized embedding of P in which the orthogonal order of allvertices in the input is preserved and in which every edge has a slope that is an integer multiple of 90/d. We show that deciding whether a path can be d-schematized is NP-hard for any integer d. We further model the problem as a mixed-integer linear program. An experimental evaluation indicates that this approach generates reasonable route sketches for real-world data

Route schematization with landmarks

Predominant navigation applications make use of a turn-by-turn instructions approach and are mostly supported by small screen devices. This combination does little to improve users\u27 orientation or spatial knowledge acquisition. Considering this limitation, we propose a route schematization method aimed for small screen devices to facilitate the readability of route information and survey knowledge acquisition. Current schematization methods focus on the route path and ignore context information, specially polygonal landmarks (such as lakes, parks, and regions), which is crucial for promoting orientation. Our schematization method, in addition to the route path, takes as input: adjacent streets, point-like landmarks, and polygonal landmarks. Moreover, our schematic route map layout highlights spatial relations between route and context information, improves the readability of turns at decision points, and the visibility of survey information on small screen devices. The schematization algorithm combines geometric transformations and integer linear programming to produce the maps. The contribution of this paper is a method that produces schematic route maps with context information to support the user in wayfinding and orientation

Information measures and cognitive limits in multilayer navigation

Cities and their transportation systems become increasingly complex and multimodal as they grow, and it is natural to wonder if it is possible to quantitatively characterize our difficulty to navigate in them and whether such navigation exceeds our cognitive limits. A transition between different searching strategies for navigating in metropolitan maps has been observed for large, complex metropolitan networks. This evidence suggests the existence of another limit associated to the cognitive overload and caused by large amounts of information to process. In this light, we analyzed the world's 15 largest metropolitan networks and estimated the information limit for determining a trip in a transportation system to be on the order of 8 bits. Similar to the "Dunbar number," which represents a limit to the size of an individual's friendship circle, our cognitive limit suggests that maps should not consist of more than about $250$ connections points to be easily readable. We also show that including connections with other transportation modes dramatically increases the information needed to navigate in multilayer transportation networks: in large cities such as New York, Paris, and Tokyo, more than $80\%$ of trips are above the 8-bit limit. Multimodal transportation systems in large cities have thus already exceeded human cognitive limits and consequently the traditional view of navigation in cities has to be revised substantially.Comment: 16 pages+9 pages of supplementary materia

Vertex-Coloring with Star-Defects

Defective coloring is a variant of traditional vertex-coloring, according to which adjacent vertices are allowed to have the same color, as long as the monochromatic components induced by the corresponding edges have a certain structure. Due to its important applications, as for example in the bipartisation of graphs, this type of coloring has been extensively studied, mainly with respect to the size, degree, and acyclicity of the monochromatic components. In this paper we focus on defective colorings in which the monochromatic components are acyclic and have small diameter, namely, they form stars. For outerplanar graphs, we give a linear-time algorithm to decide if such a defective coloring exists with two colors and, in the positive case, to construct one. Also, we prove that an outerpath (i.e., an outerplanar graph whose weak-dual is a path) always admits such a two-coloring. Finally, we present NP-completeness results for non-planar and planar graphs of bounded degree for the cases of two and three colors

MetroSets: Visualizing Sets as Metro Maps

We propose MetroSets, a new, flexible online tool for visualizing set systems using the metro map metaphor. We model a given set system as a hypergraph $\mathcal{H} = (V, \mathcal{S})$, consisting of a set $V$ of vertices and a set $\mathcal{S}$, which contains subsets of $V$ called hyperedges. Our system then computes a metro map representation of $\mathcal{H}$, where each hyperedge $E$ in $\mathcal{S}$ corresponds to a metro line and each vertex corresponds to a metro station. Vertices that appear in two or more hyperedges are drawn as interchanges in the metro map, connecting the different sets. MetroSets is based on a modular 4-step pipeline which constructs and optimizes a path-based hypergraph support, which is then drawn and schematized using metro map layout algorithms. We propose and implement multiple algorithms for each step of the MetroSet pipeline and provide a functional prototype with \new{easy-to-use preset configurations.} % many real-world datasets. Furthermore, \new{using several real-world datasets}, we perform an extensive quantitative evaluation of the impact of different pipeline stages on desirable properties of the generated maps, such as octolinearity, monotonicity, and edge uniformity.Comment: 19 pages; accepted for IEEE INFOVIS 2020; for associated live system, see http://metrosets.ac.tuwien.ac.a

Schematic bus transit maps for the web using genetic algorithms

Dissertation submitted in partial fulfilment of the requirements for the degree of Master of Science in Geospatial TechnologiesThe octilinear schematic map, layout recognized worldwide in metro maps, is an important transit informative tool. This research investigates how algorithms for the visualization of schematic maps can be availed in mobile web devices context in order to empower the efficiency in transmitting information of bus transit maps. A genetic algorithm for path octilinear schematization technique has been used and tested to create the schematic data. Location-based and interactivity functionalities were embedded to the resulting digital maps in order to create personalized maps to meet specific user needs. A prototype of a web application and real transit data of the city of Castellón in Spain was used to test the methodology. The results have shown that real time schematizations open possibilities concerning usability that add extra value to schematic transit maps. Additionally, suggested improvements have been made to the genetic algorithm and performance tests show that genetic algorithms are adequate, in terms of efficiency, to sketch bus transit maps automatically