First of all, I would like to thank Anne Kaldewaij for his continuous support and guidance over the past four years. We both enjoyed working on the subject of amortization and learned a lot of interesting new things. Also, I very much appreciate his advice to write and explain things in a relaxed pace (and which he demonstrated to me every so often). Lex Bijlsma, Victor Dielissen, and Wim Nuij are gratefully acknowledged for discussing and reading together with Anne and me drafts of this thesis and related work. In particular, Wim Nuij is acknowledged for providing me with the basis for Lemma 11.6. Ronald Heutinck is acknowledged for his initial study of Fibonacci heaps which led to the notion of "diagonal bags " . The late Peter van den Hurk is acknowledged for his study (see [18, Chapter 3]) of the path/insert problem , which triggered the research reported in Section 3.2. I thank Wim Kloosterhuis for his assistance with some of the mathematics in the analyses of bottom-up melding and splaying.