Sphere-packings, lattices, and groups
Sphere-packings, lattices, and groups
Labelling graphs with a condition at distance 2
SIAM Journal on Discrete Mathematics
A characterization of root lattices
Discrete Mathematics
Assigning codes in wireless networks: bounds and scaling properties
Wireless Networks
Efficient use of radio spectrum in wireless networks with channel separation between close stations
DIALM '00 Proceedings of the 4th international workshop on Discrete algorithms and methods for mobile computing and communications
Channel Assignment with Separation for Special Classes of Wireless Networks: Grids and Rings
IPDPS '02 Proceedings of the 16th International Parallel and Distributed Processing Symposium
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
IWDC'04 Proceedings of the 6th international conference on Distributed Computing
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In this paper, we study the problem of channel assignment for wireless networks modelled as d-dimensional grids. In particular, for d-dimensional square grids, we present optimal assignments that achieve a channel separation of 2 for adjacent stations where the reuse distance is 3 or 4. We also introduce the notion of a colouring schema for d- dimensional square grids, and present an algorithm that assigns colours to the vertices of the grid satisfying the schema constraints.