Submodularity in Combinatorial Optimization

2007 Preface This a continually updated version of my second PhD thesis, submitted to the Department of Applied Mathematics at Charles University. It serves mainly for myself as a compendium of my research on submodular optimization and related problems, Acknowledgement This thesis would not have seen the light of day without the support and perseverance of Martin Loebl, and significant assistance of several others. I would like to thank first and foremost Uriel Feige for introducing me to this subject and being a wonderful guide. I am also grateful to Chandra Chekuri for enlightening conversations and bringing my attention to one of the topics presented here. Let me not forget Gruia Calinescu, Mohammad Mahdian, Vahab Mirrokni, Benny Sudakov and others who have been very helpful in their discussions. Most of this work has been published together with some of the co-authors mentioned above; the copyright belongs to the respective periodicals.