Embedding Graphs under Centrality Constraints for Network Visualization

Visual rendering of graphs is a key task in the mapping of complex network data. Although most graph drawing algorithms emphasize aesthetic appeal, certain applications such as travel-time maps place more importance on visualization of structural network properties. The present paper advocates two graph embedding approaches with centrality considerations to comply with node hierarchy. The problem is formulated first as one of constrained multi-dimensional scaling (MDS), and it is solved via block coordinate descent iterations with successive approximations and guaranteed convergence to a KKT point. In addition, a regularization term enforcing graph smoothness is incorporated with the goal of reducing edge crossings. A second approach leverages the locally-linear embedding (LLE) algorithm which assumes that the graph encodes data sampled from a low-dimensional manifold. Closed-form solutions to the resulting centrality-constrained optimization problems are determined yielding meaningful embeddings. Experimental results demonstrate the efficacy of both approaches, especially for visualizing large networks on the order of thousands of nodes.Comment: Submitted to IEEE Transactions on Visualization and Computer Graphic

Efficient and Privacy-Preserving Ride Sharing Organization for Transferable and Non-Transferable Services

Ride-sharing allows multiple persons to share their trips together in one vehicle instead of using multiple vehicles. This can reduce the number of vehicles in the street, which consequently can reduce air pollution, traffic congestion and transportation cost. However, a ride-sharing organization requires passengers to report sensitive location information about their trips to a trip organizing server (TOS) which creates a serious privacy issue. In addition, existing ride-sharing schemes are non-flexible, i.e., they require a driver and a rider to have exactly the same trip to share a ride. Moreover, they are non-scalable, i.e., inefficient if applied to large geographic areas. In this paper, we propose two efficient privacy-preserving ride-sharing organization schemes for Non-transferable Ride-sharing Services (NRS) and Transferable Ride-sharing Services (TRS). In the NRS scheme, a rider can share a ride from its source to destination with only one driver whereas, in TRS scheme, a rider can transfer between multiple drivers while en route until he reaches his destination. In both schemes, the ride-sharing area is divided into a number of small geographic areas, called cells, and each cell has a unique identifier. Each driver/rider should encrypt his trip's data and send an encrypted ride-sharing offer/request to the TOS. In NRS scheme, Bloom filters are used to compactly represent the trip information before encryption. Then, the TOS can measure the similarity between the encrypted trips data to organize shared rides without revealing either the users' identities or the location information. In TRS scheme, drivers report their encrypted routes, an then the TOS builds an encrypted directed graph that is passed to a modified version of Dijkstra's shortest path algorithm to search for an optimal path of rides that can achieve a set of preferences defined by the riders

Route Packing: Geospatially-Accurate Visualization of Route Networks

We present route packing}, a novel (geo)visualization technique for displaying several routes simultaneously on a geographic map while preserving the geospatial layout, identity, directionality, and volume of individual routes. The technique collects variable-width route lines side by side while minimizing crossings, encodes them with categorical colors, and decorates them with glyphs to show their directions. Furthermore, nodes representing sources and sinks use glyphs to indicate whether routes stop at the node or merely pass through it. We conducted a crowd-sourced user study investigating route tracing performance with road networks visualized using our route packing technique. Our findings highlight the visual parameters under which the technique yields optimal performance

Can animation support the visualisation of dynamic graphs?

Animation and small multiples are methods for visualizing dynamically evolving graphs. Animations present an interactive movie of the data where positions of nodes are smoothly interpolated as the graph evolves. Nodes fade in/out as they are added/removed from the data set. Small multiples presents the data like a comic book with the graph at various states in separate windows. The user scans these windows to see how the data evolves. In a recent experiment, drawing stability (known more widely as the “mental map”) was shown to help users follow specific nodes or long paths in dynamically evolving data. However, no significant difference between animation and small multiples presentations was found. In this paper, we look at data where the nodes in the graph have low drawing stability and analyze it with new error metrics: measuring how close the given answer is from the correct answer on a continuous scale. We find evidence that when the stability of the drawing is low and important nodes in the task cannot be highlighted throughout the time series, animation can improve task performance when compared to the use of small multiples

Quantifying synergy and redundancy in multiplex networks

Understanding how different networks relate to each other is key for obtaining a greater insight into complex systems. Here, we introduce an intuitive yet powerful framework to characterise the relationship between two networks, comprising the same nodes. We showcase our framework by decomposing the shortest paths between nodes as being contributed uniquely by one or the other source network, or redundantly by either, or synergistically by the two together. Our approach takes into account the networks' full topology, but it also provides insights at multiple levels of resolution: from global statistics, to individual paths of different length. We show that this approach is widely applicable, from brains to the London transport system. In humans and across $123$ other species, we demonstrate that reliance on unique contributions by long-range white matter fibers is a conserved feature of mammalian structural connectomes. Across species, we also find that efficient communication relies on significantly greater synergy between long-range and short-range fibers than expected by chance, and significantly less redundancy. Our framework may find applications to help decide how to trade-off different desiderata when designing network systems, or to evaluate their relative presence in existing systems, whether biological or artificial

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

General scores for accessibility and inequality measures in urban areas

In the last decades, the acceleration of urban growth has led to an unprecedented level of urban interactions and interdependence. This situation calls for a significant effort among the scientific community to come up with engaging and meaningful visualizations and accessible scenario simulation engines. The present paper gives a contribution in this direction by providing general methods to evaluate accessibility in cities based on public transportation data. Through the notion of isochrones, the accessibility quantities proposed measure the performance of transport systems at connecting places and people in urban systems. Then we introduce scores rank cities according to their overall accessibility. We highlight significant inequalities in the distribution of these measures across the population, which are found to be strikingly similar across various urban environments. Our results are released through the interactive platform: www.citychrone.org, aimed at providing the community at large with a useful tool for awareness and decision-making