We address various channel assignment problems on the Cayley graphs of certain groups, computing the frequency spans by applying group theoretic techniques. In particular, we show that if G is the Cayley graph of an n-generated group with a certain kind of presentation, then (G; k, 1) โค 2(k +n-1). F
Graph labeling and radio channel assignment
โ Scribed by van den Heuvel, J.; Leese, R. A.; Shepherd, M. A.
- Publisher
- John Wiley and Sons
- Year
- 1998
- Tongue
- English
- Weight
- 438 KB
- Volume
- 29
- Category
- Article
- ISSN
- 0364-9024
No coin nor oath required. For personal study only.
โฆ Synopsis
The vertex-labeling of graphs with nonnegative integers provides a natural setting in which to study problems of radio channel assignment. Vertices correspond to transmitter locations and their labels to radio channels. As a model for the way in which interference is avoided in real radio systems, each pair of vertices has, depending on their separation, a constraint on the difference between the labels that can be assigned. We consider the question of finding labelings of minimum span, given a graph and a set of constraints. The focus is on the infinite triangular lattice, infinite square lattice, and infinite line lattice, and optimal labelings for up to three levels of constraint are obtained. We highlight how accepted practice can lead to suboptimal channel assignments.
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