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New Results In Partition Theory., Luat. Bui
New Results In Partition Theory., Luat. Bui
Electronic Theses and Dissertations
This thesis includes a brief review of the literature of methods of how partition identities may be derived. In the third and fourth chapters we introduce a totally new and different approach in partition theory. With the use of computers we will apply the method of sampling and simulation to estimate the number of partitions of an integer. We give an algorithm for generating partitions so that every partition is equally likely to be generated. We use Capture-Recapture method and an estimation technique of Boneh, Boneh, and Caron. In chapter five we give some new results in partition theory, using …
Two-Dimensional Bin Packing: Innovations And Statistical Analysis., Todd Arthur. Braithwaite
Two-Dimensional Bin Packing: Innovations And Statistical Analysis., Todd Arthur. Braithwaite
Electronic Theses and Dissertations
In this thesis, we introduce and analyze a new two dimensional bin packing algorithm. We focus on the problem of packing rectangles with known dimensions into a fixed width, infinite height bin so as to minimize the total height of the packing. To analyze the algorithm we use statistical methods to compare the known optimal pack heights with the pack heights obtained by the algorithm on a set of randomly generated test problems. This gives us a general technique to not only analyze a single algorithm, but also one which may be used to compare existing algorithms. The method to …