Petra Mutzel

Footprints of buildings can provide cues about architectural styles and functional types. Learning such latent thematic information from geometry is relevant for various applications, such as urban planning and map generalization. A common task in this context is to cluster a set of building footprints based on their shape characteristics. In this paper, we present a novel method for this task which is based on concepts of graph similarity. We use a graph similarity measure that combines ideas from the Weisfeiler-Lehman-method and optimal transport theory. For the final clustering, we use spectral clustering. To obtain a meaningful graph representation, we propose two algorithms that transform the medial axis of a building footprint into a skeleton graph. We tested our algorithm on a data set from Boston and performed a small user study, where we also compared the results to an existing feature-based clustering method. The study gives a first hint that the results of our algorithm are in line with human similarity perception. Future work is needed to improve the stability of the proposed similarity measure and to confirm our findings with more extensive experiments.

The H-index of a node in a static network is the maximum value h such that at least h of its neighbors have a degree of at least h. Recently, a generalized version, the n-th order H-index, was introduced, allowing to relate degree centrality, H-index, and the k-core of a node. We extend the n-th order H-index to temporal networks and define corresponding temporal centrality measures and temporal core decompositions. Our n-th order temporal H-index respects the reachability in temporal networks leading to node rankings, which reflect the importance of nodes in spreading processes. We derive natural decompositions of temporal networks into subgraphs with strong temporal coherence. We analyze a recursive computation scheme and develop a highly scalable streaming algorithm. Our experimental evaluation demonstrates the efficiency of our algorithms and the conceptional validity of our approach. Specifically, we show that the n-th order temporal H-index is a strong heuristic for identifying possible super-spreaders in evolving social networks and detects temporally well-connected components.

We introduce the \emph{temporal graphlet kernel} for classifying dissemination processes in labeled temporal graphs. Such dissemination processes can be spreading (fake) news, infectious diseases, or computer viruses in dynamic networks. The networks are modeled as labeled temporal graphs, in which the edges exist at specific points in time, and node labels change over time. The classification problem asks to discriminate dissemination processes of different origins or parameters, e.g., infectious diseases with different infection probabilities. Our new kernel represents labeled temporal graphs in the feature space of temporal graphlets, i.e., small subgraphs distinguished by their structure, time-dependent node labels, and chronological order of edges. We introduce variants of our kernel based on classes of graphlets that are efficiently countable. For the case of temporal wedges, we propose a highly efficient approximative kernel with low error in expectation. We show that our kernels are faster to compute and provide better accuracy than state-of-the-art methods.

The vertex coloring problem asks for the minimum number of colors that can be assigned to the vertices of a given graph such that each two adjacent vertices get different colors. For this NP-hard problem, a variety of integer linear programming (ILP) models have been suggested. Among them, the assignment based and the partial-ordering based ILP models are attractive due to their simplicity and easy extendability. Moreover, on sparse graphs, both models turned out to be among the strongest exact approaches for solving the vertex coloring problem. In this work, we suggest additional strengthening constraints for the partial-ordering based ILP model, and show that they lead to improved lower bounds of the corresponding LP relaxation. Our computational experiments confirm that the new constraints are also leading to practical improvements. In particular, we are able to find the optimal solution of a previously open instance from the DIMACS benchmark set for vertex coloring problems

Rational drug design deals with computational methods to accelerate the development of new drugs. Among other tasks, it is necessary to analyze huge databases of small molecules. Since a direct relationship between the structure of these molecules and their effect (e.g., toxicity) can be assumed in many cases, a wide set of methods is based on the modeling of the molecules as graphs with attributes.Here, we discuss our results concerning structural molecular similarity searches and molecular clustering and put them into the wider context of graph similarity search. In particular, we discuss algorithms for computing graph similarity w.r.t. maximum common subgraphs and their extension to domain specific requirements.