Paper Info
Title
On the span in channel assignment problems: bounds, computing and counting
Abstract
The channel assignment problem involves assigning radio channels to transmitters, using a small span of channels but without causing excessive interference. We consider a standard model for channel assignment, the constraint matrix model, which extends ideas of graph colouring. Given a graph G = (V,E) and a length l(uv) for each edge uv of G, we call an assignment φ : V → {1,...,t} feasible if |φ(u)-φ(v)| ≥ l(uv) for each edge uv. The least t for which there is a feasible assignment is the span of the problem. We first derive two bounds on the span, an upper bound (from a sequential assignment method) and a lower bound. We then see that an extension of the Gallai-Roy theorem on chromatic number and orientations shows that the span can be calculated in O(n!) steps for a graph with n nodes, neglecting a polynomial factor. We prove that, if the edge-lengths are bounded, then we may calculate the span in exponential time, that is, in time O(cn) for a constant c. Finally we consider counting feasible assignments and related quantities.
Year
DOI
Venue
2003
10.1016/S0012-365X(02)00821-X
Discrete Mathematics
Keywords
Field
DocType
lower bound,standard model,polynomial factorization,upper bound
Graph theory,Discrete mathematics,Standard Model,Combinatorics,Exponential function,Polynomial,Upper and lower bounds,Communication channel,Interference (wave propagation),Mathematics,Bounded function
Journal
Volume
Issue
ISSN
266
1-3
0012-365X
Citations 
PageRank 
References 
26
1.64
6
Authors
1
Name
Order
Citations
PageRank
Colin McDiarmid11071167.05