Algorithms for Coloring Quadtrees

Details Algorithms for Coloring Quadtrees Algorithms for Coloring Quadtrees

1999-07-19

arxiv.org/abs/cs/9907030v1

Algorithmica 32(1):87-94, 2002

Computer Science

Computational Geometry

7 pages, 9 figures

Scientific paper

10.1007/s00453-001-0054-2

We describe simple linear time algorithms for coloring the squares of balanced and unbalanced quadtrees so that no two adjacent squares are given the same color. If squares sharing sides are defined as adjacent, we color balanced quadtrees with three colors, and unbalanced quadtrees with four colors; these results are both tight, as some quadtrees require this many colors. If squares sharing corners are defined as adjacent, we color balanced or unbalanced quadtrees with six colors; for some quadtrees, at least five colors are required.

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