Robotics Research Technical Report: Nonlinearity of Davenport-Schinzel, Sequences and of Generalized, Path Compression Schemes (Classic Reprint) - Softcover

Hart, Sergiu

9781332092116: Robotics Research Technical Report: Nonlinearity of Davenport-Schinzel, Sequences and of Generalized, Path Compression Schemes (Classic Reprint)

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ISBN 10: 133209211X ISBN 13: 9781332092116

Verlag: Forgotten Books, 2018

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Excerpt from Robotics Research Technical Report: Nonlinearity of Davenport-Schinzel, Sequences and of Generalized, Path Compression Schemes

Davenport-schinzel sequences are sequences that do not contain forbidden subsequences of alternating symbols. They arise in the computation of the envelope of a set of functions. We show that the maximal length of a davenport-schinzel sequence composed of n symbols is where o(u) is the functional inverse of Ackermann's function, and is thus very slowly increasing to infinity. This is achieved by establishing an equivalence between such sequences and generalized path compression schemes on rooted trees, and then by analyzing these schemes.

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Excerpt from Robotics Research Technical Report: Nonlinearity of Davenport-Schinzel, Sequences and of Generalized, Path Compression Schemes

This problem has originally been posed by Davenport and Schinzel Ds. Their interest in it arose from its connection to the analysis of solutions of linear differential equations. Recently, Atallah At has raised it again independently, because of its significance for problems in dynamic computational geometry. These two applications are quite similar, and can be briefly described a follows.

Thus, in this setting, Davenport-Schinzel sequences are strongly related to the problem of computing the (lower) envelope of a set of functions which intersect each other in pairs in at most some fixed number of points. This problem has many applications in computational geometry and related areas, many of which are given in [At]; some additional applications will be noted in Section 7.

About the Publisher

Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com

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.

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