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A Covering Problem for Tori
Patric R.J. Östergård and Taneli Riihonen
Department of Electrical and Communications Engineering, Helsinki University of Technology P.O. Box 3000, 02015 HUT, Finland
{patric.ostergard, taneli.riihonen}@hut.fi
Annals of Combinatorics 7 (3) p.357-363 September, 2003
AMS Subject Classification: 05C70, 94B25
Abstract:
The problem of covering an n-dimensional torus with n-dimensional grid graphs is studied. This is the dual problem of a packing problem concerning the capacity of a graph, which has been studied in information theory. It is related to several other problems as well, including weighted coverings, Keller's cube-tiling problem, and the recreational problem of how to obtain zero correct predictions in the football pools. Motivated by the last problem, bounds on the minimum size of such coverings are tabulated for q = 3, p = 2, and small n.
Keywords: covering, grid graph, tabu search, ternary code, torus

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