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

Dynamic Time-Dependent Route Planning in Road Networks with User Preferences

There has been tremendous progress in algorithmic methods for computing driving directions on road networks. Most of that work focuses on time-independent route planning, where it is assumed that the cost on each arc is constant per query. In practice, the current traffic situation significantly influences the travel time on large parts of the road network, and it changes over the day. One can distinguish between traffic congestion that can be predicted using historical traffic data, and congestion due to unpredictable events, e.g., accidents. In this work, we study the \emph{dynamic and time-dependent} route planning problem, which takes both prediction (based on historical data) and live traffic into account. To this end, we propose a practical algorithm that, while robust to user preferences, is able to integrate global changes of the time-dependent metric~(e.g., due to traffic updates or user restrictions) faster than previous approaches, while allowing subsequent queries that enable interactive applications