Efficient Algorithms for Graph Optimization Problems

Abstract

I am very grateful to my supervisor, Zoltán Király, for his deep knowledge, agility, and enthusiasm, which have greatly influenced me. Without his assistance and encouragement, this thesis could not have been written. Additionally, I would like to express my sincere appreciation to him for setting an excellent example of a lecturer and researcher.I am also grateful to Alpár Jüttner for the opportunity to participate in the LEMON project as well as for his reliable guidance with regard to every detail. I have learned a lot from him over the years. Furthermore, I am thankful to Balázs Dezső for his help and many useful suggestions related to the development of the LEMON library.I would like to express my gratitude and appreciation to András Frank for inviting me to the EGRES research group and for his outstanding knowledge and inspiring personality. In addition, I would like to thank all members of the EGRES group for working together.I am also thankful to the professors and lecturers of the Faculty of Informatics and the Institute of Mathematics at ELTE. I am especially grateful to István Fekete for his valuable assistance and friendship.The financial support of the Communication Networks Laboratory (CNL) is highly appreciated, as well as the opportunity to participate in its regular workshops.Furthermore, I would like to express my thanks to Péter Englert for the effective and inspiring joint work at ChemAxon, which remains a memorable experience for me.My special thanks are due to Miklós Vargyas for being a great mentor during my first years at ChemAxon. I was impressed and influenced by his generosity and exceptional ability to pay attention and listen to others. I also thank Ferenc Csizmadia and my co-workers at ChemAxon for the motivating and supporting atmosphere.On a personal note, I would like to express my gratitude to my family. I cannot be thankful enough to my parents for their love, devoted support, and so many things I have learned from them. Finally, I am deeply grateful to my wife, Dia, and our children, Viktor, Dávid, and Ádám, for their unconditional love, understanding, and making my life complete. I dedicate this work to them. Publications of the author BibliographyChapter 1 * O(n 3 / log n) Cheriyan, Hagerupm and Mehlhorn (1990) [57, 58] O(nm log m/(n log n) n) King, Rao, and Tarjan (1994) [155] * O(m min{n 2/3 , m 1/2 } log(n 2 /m) log U ) Goldberg and Rao (1997) [121, 122] * O(nm) Orlin (2013) [191] (together with the algorithm of King, Rao, and Tarjan)