Bläsius, Thomas; Fischbeck, Philipp; Friedrich, Tobias; Schirneck, MartinUnderstanding the Effectiveness of Data Reduction in Public Transportation Networks. Workshop on Algorithms and Models for the Web Graph (WAW) 2019
Given a public transportation network of stations and connections, we want to find a minimum subset of stations such that each connection runs through a selected station. Although this problem is NP-hard in general, real-world instances are regularly solved almost completely by a set of simple reduction rules. To explain this behavior, we view transportation networks as hitting set instances and identify two characteristic properties, locality and heterogeneity. We then devise a randomized model to generate hitting set instances with adjustable properties. While the heterogeneity does influence the effectiveness of the reduction rules, the generated instances show that locality is the significant factor. Beyond that, we prove that the effectiveness of the reduction rules is independent of the underlying graph structure. Finally, we show that high locality is also prevalent in instances from other domains, facilitating a fast computation of minimum hitting sets.
Bläsius, Thomas; Friedrich, Tobias; Katzmann, Maximilian; Krohmer, Anton; Striebel, JonathanTowards a Systematic Evaluation of Generative Network Models. Workshop on Algorithms and Models for the Web Graph (WAW) 2018: 99-114
Generative graph models play an important role in network science. Unlike real-world networks, they are accessible for mathematical analysis and the number of available networks is not limited. The explanatory power of results on generative models, however, heavily depends on how realistic they are. We present a framework that allows for a systematic evaluation of generative network models. It is based on the question whether real-world networks can be distinguished from generated graphs with respect to certain graph parameters. As a proof of concept, we apply our framework to four popular random graph models (Erdős-Rényi, Barabási-Albert, Chung-Lu, and hyperbolic random graphs). Our experiments for example show that all four models are bad representations for Facebook's social networks, while Chung-Lu and hyperbolic random graphs are good representations for other networks, with different strengths and weaknesses.
Our research focus is on theoretical computer science and algorithm engineering. We are equally interested in the mathematical foundations of algorithms and developing efficient algorithms in practice. A special focus is on random structures and methods.