Bouncing Bubble: A fast algorithm for Minimal Enclosing Ball problem

Nonfiction, Computers, Advanced Computing, Theory
Cover of the book Bouncing Bubble: A fast algorithm for Minimal Enclosing Ball problem by Bo Tian, GRIN Publishing
View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart
Author: Bo Tian ISBN: 9783656326663
Publisher: GRIN Publishing Publication: November 29, 2012
Imprint: GRIN Publishing Language: English
Author: Bo Tian
ISBN: 9783656326663
Publisher: GRIN Publishing
Publication: November 29, 2012
Imprint: GRIN Publishing
Language: English

Scientific Essay from the year 2012 in the subject Computer Science - Theory, , language: English, abstract: In this paper, a new algorithm for solving MEB problem is proposed based on new understandings on the geometry property of minimal enclosing ball problem. A substitution of Ritter's algorithm is proposed to get approximate results with higher precision, and a 1+? approximation algorithm is presented to get the approximation with specified precision within much less time comparing with present algorithms. Like Ritter's algorithm, this algorithm iterates over all points and increase the radius gradually. However, the algorithm does not try to cover all seen points in each step, instead, it will create a new ball (or circle in 2D case) to just touch the new point and cover half of the existing ball. This approach makes sure that the new ball is always increasing in its size and still be smaller than the optimal ball. And finally, a Ritter's algorithm is applied to ensure every point is covered. The result is an approximate solution to the MEB problem. The radius is usually just slightly bigger than the optimal solution (around 1%) instead (5-20% with Ritter's algorithm). This paper also explained how to compute 1+? approximation solution, where ? is specified to a given precision.

View on Amazon View on AbeBooks View on Kobo View on B.Depository View on eBay View on Walmart

Scientific Essay from the year 2012 in the subject Computer Science - Theory, , language: English, abstract: In this paper, a new algorithm for solving MEB problem is proposed based on new understandings on the geometry property of minimal enclosing ball problem. A substitution of Ritter's algorithm is proposed to get approximate results with higher precision, and a 1+? approximation algorithm is presented to get the approximation with specified precision within much less time comparing with present algorithms. Like Ritter's algorithm, this algorithm iterates over all points and increase the radius gradually. However, the algorithm does not try to cover all seen points in each step, instead, it will create a new ball (or circle in 2D case) to just touch the new point and cover half of the existing ball. This approach makes sure that the new ball is always increasing in its size and still be smaller than the optimal ball. And finally, a Ritter's algorithm is applied to ensure every point is covered. The result is an approximate solution to the MEB problem. The radius is usually just slightly bigger than the optimal solution (around 1%) instead (5-20% with Ritter's algorithm). This paper also explained how to compute 1+? approximation solution, where ? is specified to a given precision.

More books from GRIN Publishing

Cover of the book Entry strategies in the Chinese market by Bo Tian
Cover of the book Assimilation or replacement - a study about Neanderthals and modern humans by Bo Tian
Cover of the book Canadian foreign policy after the Westminster Statute of 1931 -The shift from British hegemon to an American one by Bo Tian
Cover of the book Corporate governance based on business reporting in accordance with IAS/IFRS accounting by Bo Tian
Cover of the book De- and Reconstructing Leadership by Bo Tian
Cover of the book Difficulties in expressing voters` true preferences by Bo Tian
Cover of the book Staffing in Educational Institutions: Experiences from Tanzania by Bo Tian
Cover of the book The Just Cause: How the American Public supports War by Bo Tian
Cover of the book Teaching Intercultural Communicative Competence with a Textbook by Bo Tian
Cover of the book Analysis of Strategic move by Chipotle by Bo Tian
Cover of the book Frauen auf Kreuzzügen by Bo Tian
Cover of the book Überblick über die gesellschaftliche Stellung der muslimischen Frau by Bo Tian
Cover of the book The Anatomy of the Saint: Tarrou in Camus' The Plague by Bo Tian
Cover of the book The Male and the Female in Tennessee Williams's Plays by Bo Tian
Cover of the book AOL-Time Warner - The end of democracy? by Bo Tian
We use our own "cookies" and third party cookies to improve services and to see statistical information. By using this website, you agree to our Privacy Policy