Spreading grid cells
Minghui Jiang, Pedro J. Tejada

TL;DR
This paper investigates how to arrange symbols in two grids to maximize the minimum combined distance between any two symbols, providing asymptotically optimal bounds and a linear-time approximation algorithm.
Contribution
It establishes asymptotically optimal bounds for the maximum minimum combined distance in two grids and offers a simple linear-time approximation algorithm.
Findings
Bounds are (\u221a n) for all p=1,2,..., infinity.
Results extend to d-dimensional grids for any constant d .
Provides a linear-time constant-factor approximation algorithm.
Abstract
Let be a set of symbols. Let be an square grid with each cell labeled by a distinct symbol in . Let be another square grid, also with each cell labeled by a distinct symbol in . Then each symbol in labels two cells, one in and one in . Define the \emph{combined distance} between two symbols in as the distance between the two cells in plus the distance between the two cells in that are labeled by the two symbols. Bel\'en Palop asked the following question at the open problems session of CCCG 2009: How to arrange the symbols in the two grids such that the minimum combined distance between any two symbols is maximized? In this paper, we give a partial answer to Bel\'en Palop's question. Define , where and range over all pairs of $n\times…
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Taxonomy
TopicsDigital Image Processing Techniques · Computational Geometry and Mesh Generation · Mathematical Approximation and Integration
