Inserting Points Uniformly at Every Instance

A problem of arranging n points as uniformly as possible, which is equivalent to that of packing n equal and non-overlapping circles in a unit square, is frequently asked. In this paper we generalize this problem in such a way that points be inserted one by one with uniformity preserved at every instance. Our criteria on 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 2 n/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.

• Type: Journal
• Year: 2006
• Where: IEICET
• Authors: Sachio Teramoto, Tetsuo Asano, Naoki Katoh, Benjamin Doerr
• Keywords: Gap Ratio, IEICET 2006, Maximum Gap, Non-overlapping Circles