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Partitioning Arrangements of Lines: I. An Efficient Deterministic Algorithm
Excerpt from Partitioning Arrangements of I. An Efficient Deterministic Algorithm
Implicit point location Given a collection of m points and a collection Of (possibly intersecting) n triangles in the plane, find which points lie in the union of the triangles. This turns out to be a special case of a general problem of implicit point location of planar maps formed by overlapping figures. We present a deterministic algorithm with O(m2/3n2/3 log3 n (m n) log n) time complexity.
Approximate half-plane range Given a set S of n points in the plane and a parameter (not necessarily constant) e 0, preprocess them so that, for any query line 2, we can approximately count the number of points lying above 8 with an error of at most We give an algorithm that preprocesses S, in time O(% log n log f), into a data structure of size O(f), so that a query can be answered in C(log n) time.
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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.
Implicit point location Given a collection of m points and a collection Of (possibly intersecting) n triangles in the plane, find which points lie in the union of the triangles. This turns out to be a special case of a general problem of implicit point location of planar maps formed by overlapping figures. We present a deterministic algorithm with O(m2/3n2/3 log3 n (m n) log n) time complexity.
Approximate half-plane range Given a set S of n points in the plane and a parameter (not necessarily constant) e 0, preprocess them so that, for any query line 2, we can approximately count the number of points lying above 8 with an error of at most We give an algorithm that preprocesses S, in time O(% log n log f), into a data structure of size O(f), so that a query can be answered in C(log n) time.
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.
54 pages, Hardcover
Published February 5, 2018
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