Distributed online frequency assignment in cellular networks
Journal of Algorithms
Channel assignment and graph multicoloring
Handbook of wireless networks and mobile computing
Finding a five bicolouring of a triangle-free subgraph of the triangular lattice
Discrete Mathematics - Algebraic and topological methods in graph theory
2-Local 5/4-competitive algorithm for multicoloring triangle-free hexagonal graphs
Information Processing Letters
2-local 4/3-competitive algorithm for multicoloring hexagonal graphs
Journal of Algorithms
1-local 17/12-competitive algorithm for multicoloring hexagonal graphs
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
A 1-local 4/3-competitive algorithm for multicoloring a subclass of hexagonal graphs
Discrete Applied Mathematics
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In the frequency allocation problem, we are given a cellular telephone network whose geographical coverage area is divided into cells, where phone calls are serviced by assigned frequencies, so that none of the pairs of calls emanating from the same or neighboring cells is assigned the same frequency. The problem is to use the frequencies efficiently, i.e. minimize the span of frequencies used. The frequency allocation problem can be regarded as a multicoloring problem on a weighted hexagonal graph, where each vertex knows its position in the graph. We present a 1-local 33/24-competitive distributed algorithm for multicoloring a hexagonal graph, thereby improving the previous 1-local 7/5-competitive algorithm.