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  Inserting Points Uniformly at Every Instance

Teramoto, S., Asano, T., Katoh, N., & Doerr, B. (2006). Inserting Points Uniformly at Every Instance. IEICE - Transactions on Information and Systems, E89-D, 2348-2356.

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Item Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2338-5 Version Permalink: https://hdl.handle.net/11858/00-001M-0000-000F-2339-3
Genre: Journal Article

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 Creators:
Teramoto, Sachio, Author
Asano, Tetsuo1, Author           
Katoh, Naoki, Author
Doerr, Benjamin1, Author           
Affiliations:
1Algorithms and Complexity, MPI for Informatics, Max Planck Society, ou_24019              

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 Abstract: Arranging n points as uniformly as possible is a frequently occurring problem. It is equivalent to packing n equal and non-overlapping circles in a unit square. In this paper we generalize this problem in such a way that points are inserted one by one with uniformity preserved at every instance. Our criterion for uniformity is to minimize the gap ratio (which is the maximum gap over the minimum gap) at every point insertion. We present a linear time algorithm for finding an optimal n-point sequence with the maximum gap ratio bounded by 2n/2 /(n/2+1) in the 1-dimensional case. We describe how hard the same problem is for a point set in the plane and propose a local search heuristics for finding a good solution.

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Language(s): eng - English
 Dates: 2007-02-102006
 Publication Status: Issued
 Pages: -
 Publishing info: -
 Table of Contents: -
 Rev. Type: Peer
 Identifiers: eDoc: 314534
Other: Local-ID: C1256428004B93B8-AA6C18ED7CFD2C64C125725700568662-inserpoints2006
 Degree: -

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Title: IEICE - Transactions on Information and Systems
Source Genre: Journal
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Pages: - Volume / Issue: E89-D Sequence Number: - Start / End Page: 2348 - 2356 Identifier: ISSN: 0916-8532