Recognizing Partial Cubes in Quadratic Time

We show how to test whether a graph with n vertices and m edges is a partial cube, and if so how to find a distance-preserving embedding of the graph into a hypercube, in the near-optimal time bound O(n^2), improving previous O(nm)-time solutions.Comment: 25 pages, five figures. This version significantly expands previous versions, including a new report on an implementation of the algorithm and experiments with i

The State-of-the-Art of Set Visualization

Sets comprise a generic data model that has been used in a variety of data analysis problems. Such problems involve analysing and visualizing set relations between multiple sets defined over the same collection of elements. However, visualizing sets is a non-trivial problem due to the large number of possible relations between them. We provide a systematic overview of state-of-the-art techniques for visualizing different kinds of set relations. We classify these techniques into six main categories according to the visual representations they use and the tasks they support. We compare the categories to provide guidance for choosing an appropriate technique for a given problem. Finally, we identify challenges in this area that need further research and propose possible directions to address these challenges. Further resources on set visualization are available at http://www.setviz.net

Ontology of core concept data types for answering geo-analytical questions

In geographic information systems (GIS), analysts answer questions by designing workflows that transform a certain type of data into a certain type of goal. Semantic data types help constrain the application of computational methods to those that are meaningful for such a goal. This prevents pointless computations and helps analysts design effective workflows. Yet, to date it remains unclear which types would be needed in order to ease geo-analytical tasks. The data types and formats used in GIS still allow for huge amounts of syntactically possible but nonsensical method applications. Core concepts of spatial information and related geo-semantic distinctions have been proposed as abstractions to help analysts formulate analytic questions and to compute appropriate answers over geodata of different formats. In essence, core concepts reflect particular interpretations of data which imply that certain transformations are possible. However, core concepts usually remain implicit when operating on geodata, since a concept can be represented in a variety of forms. A central question therefore is: Which semantic types would be needed to capture this variety and its implications for geospatial analysis? In this article, we propose an ontology design pattern of core concept data types that help answer geo-analytical questions. Based on a scenario to compute a liveability atlas for Amsterdam, we show that diverse kinds of geo-analytical questions can be answered by this pattern in terms of valid, automatically constructible GIS workflows using standard sources

Condorcet Domains, Median Graphs and the Single Crossing Property

Condorcet domains are sets of linear orders with the property that, whenever the preferences of all voters belong to this set, the majority relation has no cycles. We observe that, without loss of generality, such domain can be assumed to be closed in the sense that it contains the majority relation of every profile with an odd number of individuals whose preferences belong to this domain. We show that every closed Condorcet domain is naturally endowed with the structure of a median graph and that, conversely, every median graph is associated with a closed Condorcet domain (which may not be a unique one). The subclass of those Condorcet domains that correspond to linear graphs (chains) are exactly the preference domains with the classical single crossing property. As a corollary, we obtain that the domains with the so-called `representative voter property' (with the exception of a 4-cycle) are the single crossing domains. Maximality of a Condorcet domain imposes additional restrictions on the underlying median graph. We prove that among all trees only the chains can induce maximal Condorcet domains, and we characterize the single crossing domains that in fact do correspond to maximal Condorcet domains. Finally, using Nehring's and Puppe's (2007) characterization of monotone Arrowian aggregation, our analysis yields a rich class of strategy-proof social choice functions on any closed Condorcet domain

Complex concept lattices for simulating human prediction in sport

In order to address the study of complex systems, the detection of patterns in their dynamics could play a key role in understanding their evolution. In particular, global patterns are required to detect emergent concepts and trends, some of them of a qualitative nature. Formal concept analysis (FCA) is a theory whose goal is to discover and extract knowledge from qualitative data (organized in concept lattices). In complex environments, such as sport competitions, the large amount of information currently available turns concept lattices into complex networks. The authors analyze how to apply FCA reasoning in order to increase confidence in sports predictions by means of detecting regularities from data through the management of intuitive and natural attributes extracted from publicly available information. The complexity of concept lattices -considered as networks with complex topological structure- is analyzed. It is applied to building a knowledge based system for confidence-based reasoning, which simulates how humans tend to avoid the complexity of concept networks by means of bounded reasoning skills.Ministerio de Ciencia e Innovación TIN2009-09492Junta de Andalucía TIC-606