On wireless spectrum estimation and generalized graph coloring
Khanna, S.; Kumaran, K.
INFOCOM apos;98. Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies. Proceedings. IEEE
Volume 3, Issue , 29 Mar-2 Apr 1998 Page(s):1273 - 1283 vol.3
Digital Object Identifier 10.1109/INFCOM.1998.662942
Summary:We address the problem of estimating the spectrum required in a
wireless network for a given demand and interference pattern. This
problem can be abstracted as a generalization of the graph coloring
problem, which typically presents additional degree of hardness compared
to the standard coloring problem. It is worthwhile to note that the
question of estimating the spectrum requirement differs markedly from
that of allocating channels. The main focus of this work is to obtain
strong upper and lower bounds on the spectrum requirement, as opposed to
the study of spectrum allocation/management. While the relation to graph
coloring establishes the intractability of the spectrum estimation
problem for arbitrary network topologies, useful bounds and algorithms
are obtainable for specific topologies. We establish some new results
regarding generalized coloring, which we use to derive tight bounds for
specific families of graphs. We also examine the hexagonal grid
topology, a commonly used topology for wireless networks. We design
efficient algorithms that exploit the geometric structure of the
hexagonal grid topology to determine upper bounds on the spectrum
requirement for arbitrary demand patterns. The slack in our upper bounds
is estimated by analyzing subgraphs with specific properties. While we
consider the worst-case demand patterns to evaluate the performance of
our algorithms, we expect them to perform much better in practice
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