Topological Lower Bounds in Complexity Theory; Topologiska undre gränser i komplexitetsteori
Institution: | KTH Royal Institute of Technology |
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Department: | |
Year: | 2015 |
Keywords: | Natural Sciences; Mathematics; Naturvetenskap; Matematik; Master of Science - Mathematics; Teknologie masterexamen - Matematik; Mathematics; Matematik |
Record ID: | 1356584 |
Full text PDF: | http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-161067 |
The first goal of this thesis is to present two different methods, originally developed by Björner, Lovász and Yao [4], for proving lower bounds on the worst-case complexity in the linear decision tree model, by applying them to the k -EQUAL PROBLEM. Both methods are based on the computation of topological properties of the intersection lattice of a subspace arrangement. The second goal is to use one of these methods (based on estimates of Betti numbers) to improve upon a lower bound, due to Linusson [12], on the linear decision tree complexity c ′( n,k ) of the k -of-EACH PROBLEM on n elements. We show that c ′( n,k ) ≥ n log₃( n /6 k ).