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Online Bin Stretching: Algorithms and Computer Lower Bounds
 Böhm, Martin ; Sgall, Jiří (advisor) ; Durr, Christoph (referee) ; Kellerer, Hans (referee)
Online Bin Stretching: Algorithms and Computer Lower Bounds Author: Martin Böhm Abstract: We investigate a problem in semi-online algorithm design, called Online Bin Stretching. The problem can be understood as an online repacking problem: the goal of the algorithm is to repack items of various sizes into m containers of identical size R > 1. The input items arrive one by one and the algorithm must assign an item to a container before the next item arrives. A specialty of this problem is that there is a specific guarantee made to the algorithm: the algorithm learns at the start of the input that there exists a packing of all input items into m containers of capacity 1. Our goal is to design algorithms for this problem which successfully pack the entire incoming sequence one by one while requiring the lowest container capacity R possible. In this thesis, we show several new results about Online Bin Stretching: First, we design an algorithm that is able to pack the entire input into m containers of capacity 1.5 regardless of what the vale of m will be. Second, we show a specialized algorithm for the setting of just 3 containers; this algorithm is able to pack into 3 bins of capacity 1.375. Finally, we design and implement an involved search algorithm which is able to find lower bounds for Online Bin...
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