Very Fast Algorithms for the Area of the Union of Many Circles (Classic Reprint) - Softcover

Spirakis, Paul G.

Softcover

ISBN 10: 1333725426 ISBN 13: 9781333725426

Verlag: Forgotten Books, 2018

Inhaltsangabe

This book presents two novel algorithms for calculating the combined area of a group of circles on a two-dimensional plane. The first algorithm, deterministic in nature, has an algorithmic complexity of 0(n2), where n denotes the number of circles. The second algorithm is probabilistic, with a complexity of o(n), making it more efficient for larger sets of circles. The author employs recent developments in the field of reliability estimation to establish the fast convergence of the probabilistic method and extends the algorithm to calculate the volume of n-dimensional spheres with complexity 0(nk). The author situates this work within the broader discourse on estimating the area of unions of geometric shapes, providing a valuable resource for researchers and practitioners in computer science and related fields.

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Excerpt from Very Fast Algorithms for the Area of the Union of Many Circles

The problem of estimating the area of the union of many circles in the plane was first posed by [shamos, We present here an 0(n2) deterministic and an o(u) probabilistic algorithm for solving the problem. The recent work of [karp, Luby, 83] on estimating the failure probability of an n-component system helped us a lot in stating the algorithm and formulating the proof of fast convergence. The probabilistic algorithm can be modified to compute the area of the union of other planar objects (of fixed description) e.g. Triangles or boxes. The time is again o(u). The algorithm can also be extended to compute the volume of the union of n spheres in k dimensions, in time 0(nk). The algorithm has similar time complexity for k-dimensional objects other than spheres, provided that each object has a fixed description (not dependent on n).

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Details zur Ausgabe

• Verlag: Forgotten Books
• Erscheinungsdatum: 2018
• Sprache: Englisch
• ISBN 10: 1333725426
• ISBN 13: 9781333725426
• Einband: Tapa blanda
• Anzahl der Seiten: 47
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