Worst-case performance of cellular channel assignment policies
Wireless Networks - Special issue on performance evaluation methods for wireless networks
Journal of Combinatorial Theory Series B - Special issue: dedicated to Professor W. T. Tutte on the occasion of his eightieth birthday
Online channel allocation in FDMA networks with reuse constraints
Information Processing Letters
Distributed online frequency assignment in cellular networks
Journal of Algorithms
Frequency Channel Assignment on Planar Networks
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Worst-case analysis of a dynamic channel assignment strategy
Discrete Applied Mathematics
Algorithms and experiments on colouring squares of planar graphs
WEA'03 Proceedings of the 2nd international conference on Experimental and efficient algorithms
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The static frequency assignment problem on cellular networks can be abstracted as a multicoloring problem on a weighted graph, where each vertex of the graph is a base station in the network, and the weight associated with each vertex represents the number of calls to be served at the vertex. The edges of the graph model interference constraints for frequencies assigned to neighboring stations. In this paper, we first propose an algorithm to multicolor any weighted planar graph with at most $\frac{11}{4}W$ colors, where W denotes the weighted clique number. Next, we present a polynomial time approximation algorithm which garantees at most 2W colors for multicoloring a power square mesh. Further, we prove that the power triangular mesh is a subgraph of the power square mesh. This means that it is possible to multicolor the power triangular mesh with at most 2W colors, improving on the known upper bound of 4W. Finally, we show that any power toroidal mesh can be multicolored with strictly less than 4W colors using a distributed algorithm.