Exploring Simple Triangular and Hexagonal Grid Polygons Online

We examine online grid covering with hexagonal and triangular grids. For arbitrary environments without obstacles we provide a strategy that produces tours of length S C + 1 4 E - 5 2 for hexagonal grids, and S C + E - 4 for triangular grids. C is the number of cells--the area--, E is the number of boundary edges--the perimeter--of the environment. We show that our strategy is 4 3 -competitive, and give lower bounds of 14 13 (7 6 ) for hexagonal (triangular) grids.

• Type: Journal
• Year: 2010
• Where: CORR
• Authors: Daniel Herrmann, Tom Kamphans, Elmar Langetepe
• Keywords: CORR 2010, Education, Grids, Hexagonal, Triangular Grids