Excerpt from Robotics Research Technical Report, Vol. 255: The Complexity of Many Faces in Arrangements of Lines and of Segments
In our present application, the desired upper bound on K(m,n) is obtained by analyz ing the space complexity of the resulting algorithm. The time complexity of the algo rithm is roughly a polylogarithmic factor times the upper bound on K(m,n) men tioned above (see Section 3 for a more precise bound). The algorithm is based on a random sampling technique akin to the e - net method of Haussler and Welzl [hw] and to the random sampling method of Clarkson [cl]. We obtain a randomized algorithm which always terminates and produces the desired output and which, with high pro bability, does so within the stated time bound.
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Paperback. Condizione: New. Print on Demand. This book offers a highly analytical exploration of line arrangements in the plane, an important topic in computational geometry. The author delves into determining the maximum number of edges that bound a collection of faces within a given arrangement of lines or line segments. This investigation sheds light on the inherent combinatorial complexity of such arrangements, a subject that has captivated mathematicians for centuries. Through rigorous analysis and intricate algorithms, the author uncovers captivating insights into the intricate relationships between lines and their intersections, providing a deeper understanding of the fundamental structures that govern geometric configurations. Forgotten Books publishes hundreds of thousands of rare and classic books. This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works. The digital edition of all books may be viewed on our website before purchase. print-on-demand item. Codice articolo 9781332115396_0
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