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Journal Article

Inserting Points Uniformly at Every Instance

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Asano,  Tetsuo
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Doerr,  Benjamin
Algorithms and Complexity, MPI for Informatics, Max Planck Society;

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Citation

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.


Cite as: https://hdl.handle.net/11858/00-001M-0000-000F-2338-5
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.