Parameterized Algorithmics for Network Analysis: Clustering & Querying

Preface This thesis summarizes some of my results on NP-hard graph problems that have applications in the areas of network clustering and querying. The research for obtaining these results was Forschungsgemeinschaft (DFG), as a researcher in the DFG project " Parameterized Algorithmics for Bioinformatics " (PABI, NI 369/7). I want to express my gratitude to Rolf Niedermeier for giving me the opportunity to work in his group and for his advice and support that eventually led to this thesis. Furthermore, I want to thank my colleagues and former colleagues for creating an enjoyable working atmosphere and for many inspiring and instructive discussions. Moreover, I owe sincere thanks to my coauthors for the pleasant and productive cooperation. In particular, I would like to thank René van Bevern for his implementation of the algorithms in Chapter 6. Finally, I want to thank the anonymous referees of several journals and scientific conferences for many pieces of advice that helped improving this work. The results in this thesis are partially contained in journal and conference publications that were created in close collaboration with coauthors. Below, I will describe which publications contributed to which chapters, and I will also specify my contributions to these publications. Further work to which I have contributed but that is not part of this thesis is concerned with parameterized algorithmics for graph modification problems [van Bevern et al. The latter collection of publications deals with extensions of the classical clustering notion, for example with hierarchical clusterings. In this work, the focus is on " classical " clusterings, that is, partitions of a set of objects. iii iv Preface Part II: Clustering. Chapter 2 is based on parts of the publication " Alternative Parameterizations for Cluster Editing " , which appeared in the proceedings of the 37th International Conference on Current Trends in Theory and Practice of Computer Science (SOFSEM '11) [Komusiewicz and Uhlmann 2011]; a full version of this publication is in preparation. I proposed to study the parameter " local modification bound " , participated in the development of the reduction from 3-SAT to CLUSTER EDITING, and observed the connections between CLUSTER DELETION and PARTITION INTO TRIANGLES. Furthermore, I developed the kernelization algorithms. Chapter 3 is based on the two publications " A More Relaxed Model for Graph-Based Data Clustering: s-Plex Cluster Editing " , which appeared in SIAM Journal on Discrete Mathematics [Guo et al. 2010b], and " …

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