Graph-based Analysis of Dynamic Systems

The analysis of dynamic systems provides insights into their time-dependent characteristics. This enables us to monitor, evaluate, and improve systems from various areas. They are often represented as graphs that model the system's components and their relations. The analysis of the resulting dynamic graphs yields great insights into the system's underlying structure, its characteristics, as well as properties of single components. The interpretation of these results can help us understand how a system works and how parameters influence its performance. This knowledge supports the design of new systems and the improvement of existing ones. The main issue in this scenario is the performance of analyzing the dynamic graph to obtain relevant properties. While various approaches have been developed to analyze dynamic graphs, it is not always clear which one performs best for the analysis of a specific graph. The runtime also depends on many other factors, including the size and topology of the graph, the frequency of changes, and the data structures used to represent the graph in memory. While the benefits and drawbacks of many data structures are well-known, their runtime is hard to predict when used for the representation of dynamic graphs. Hence, tools are required to benchmark and compare different algorithms for the computation of graph properties and data structures for the representation of dynamic graphs in memory. Based on deeper insights into their performance, new algorithms can be developed and efficient data structures can be selected. In this thesis, we present four contributions to tackle these problems: A benchmarking framework for dynamic graph analysis, novel algorithms for the efficient analysis of dynamic graphs, an approach for the parallelization of dynamic graph analysis, and a novel paradigm to select and adapt graph data structures. In addition, we present three use cases from the areas of social, computer, and biological networks to illustrate the great insights provided by their graph-based analysis. We present a new benchmarking framework for the analysis of dynamic graphs, the Dynamic Network Analyzer (DNA). It provides tools to benchmark and compare different algorithms for the analysis of dynamic graphs as well as the data structures used to represent them in memory. DNA supports the development of new algorithms and the automatic verification of their results. Its visualization component provides different ways to represent dynamic graphs and the results of their analysis. We introduce three new stream-based algorithms for the analysis of dynamic graphs. We evaluate their performance on synthetic as well as real-world dynamic graphs and compare their runtimes to snapshot-based algorithms. Our results show great performance gains for all three algorithms. The new stream-based algorithm StreaM_k, which counts the frequencies of k-vertex motifs, achieves speedups up to 19,043 x for synthetic and 2882 x for real-world datasets. We present a novel approach for the distributed processing of dynamic graphs, called parallel Dynamic Graph Analysis (pDNA). To analyze a dynamic graph, the work is distributed by a partitioner that creates subgraphs and assigns them to workers. They compute the properties of their respective subgraph using standard algorithms. Their results are used by the collator component to merge them to the properties of the original graph. We evaluate the performance of pDNA for the computation of five graph properties on two real-world dynamic graphs with up to 32 workers. Our approach achieves great speedups, especially for the analysis of complex graph measures. We introduce two novel approaches for the selection of efficient graph data structures. The compile-time approach estimates the workload of an analysis after an initial profiling phase and recommends efficient data structures based on benchmarking results. It achieves speedups of up to 5.4 x over baseline data structure configurations for the analysis of real-word dynamic graphs. The run-time approach monitors the workload during analysis and exchanges the graph representation if it finds a configuration that promises to be more efficient for the current workload. Compared to baseline configurations, it achieves speedups up to 7.3 x for the analysis of a synthetic workload. Our contributions provide novel approaches for the efficient analysis of dynamic graphs and tools to further investigate the trade-offs between different factors that influence the performance.:1 Introduction 2 Notation and Terminology 3 Related Work 4 DNA - Dynamic Network Analyzer 5 Algorithms 6 Parallel Dynamic Network Analysis 7 Selection of Efficient Graph Data Structures 8 Use Cases 9 Conclusion A DNA - Dynamic Network Analyzer B Algorithms C Selection of Efficient Graph Data Structures D Parallel Dynamic Network Analysis E Graph-based Intrusion Detection System F Molecular Dynamic