3-partition problem

Abstract: Preface In order to obtain a master's degree, all I have to do is answer the last question at my final presentation. Before I will be allowed to answer it, however, a number of tasks have to be performed. One of them is writing this thesis. In order to be able to write this thesis, I needed something to write about. I have been in the fortunate position to be able to do research on a quite wide variety of subjects. Most of this research was carried out at the computer science department of the Radboud University Nijmegen. I was situated in the formal methods group, a very inspiring environment. Aliated with this group-and a reason I chose this group-is Hans Zantema. Hans Zantema is a professor at Eindhoven University of Technology, and part time so at Radboud University Nijmegen. As such, Hans Zantema was my supervisor during the course of my master's research. Hans Zantema proved to be a great supervisor for me. Hans was able to inspire me into investigating a great variety of problems. While discussing my progress, Hans would find new angles, new questions or solutions. By gently steering me in the right direction, Hans was a tremendous help to keep me focused. My supervisor at my own university, the University of Twente, was Walter Kern. Walter has also been a great help in the research I did. Like Hans, Walter was able to come up with creative angles to look at problems. An important contribution of Walter was to introduce me to bin packing games. This turned out to be a very fruitful research direction, which ultimately led to the main part of this thesis. For writing this thesis, I decided to make a selection of results obtained during my research. In making this decision, I selected a central topic that could serve as a backbone for related results. This central topic is the 3-partition problem. In particular, the nearly-feasible instances, a type of infeasible 3-partition problem for which a certain half-integral relaxation has a solution. Before I started writing this thesis, I have written an article on this very topic [9]. I wrote this together with my supervisor Hans Zantema, and it is currently in submission. For me, writing this article has been a great practice. In addition, it allowed me to obtain some focus while doing this research. There are, however, some major …