Malte Renken

Till Fluschnik, Amela Pucic, Malte Renken

Motivated by evacuation scenarios arising in extreme events such as flooding or forest fires, we study the problem of smoothly scheduling a set of paths in graphs where connections become impassable at some point in time. A schedule is smooth if no two paths meet on an edge and the number of paths simultaneously located at a vertex does not exceed its given capacity. We study the computational complexity of the problem when the underlying graph is a tree, in particular a star or a path. We prove that already in these settings, the problem is NP-hard even with further restrictions on the capacities or on the time when all connections ceased. We provide an integer linear program (ILP) to compute the latest possible time to evacuate. Using the ILP and its relaxation, we solve sets of artificial (where each underlying graph forms either a path or star) and semi-artificial instances (where the graphs are obtained from German cities along rivers), study the runtimes, and compare the results of the ILP with those of its relaxation.

Vincent Froese, Brijnesh Jain, Rolf Niedermeier et al.

Within many real-world networks the links between pairs of nodes change over time. Thus, there has been a recent boom in studying temporal graphs. Recognizing patterns in temporal graphs requires a proximity measure to compare different temporal graphs. To this end, we propose to study dynamic time warping on temporal graphs. We define the dynamic temporal graph warping distance (dtgw) to determine the dissimilarity of two temporal graphs. Our novel measure is flexible and can be applied in various application domains. We show that computing the dtgw-distance is a challenging (in general) NP-hard optimization problem and identify some polynomial-time solvable special cases. Moreover, we develop a quadratic programming formulation and an efficient heuristic. In experiments on real-word data we show that the heuristic performs very well and that our dtgw-distance performs favorably in de-anonymizing networks compared to other approaches.