Online frequency allocation in cellular networks
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Three results on frequency assignment in linear cellular networks
Theoretical Computer Science
Frequency allocation problems for linear cellular networks
ISAAC'06 Proceedings of the 17th international conference on Algorithms and Computation
A 1-local 13/9-competitive algorithm for multicoloring hexagonal graphs
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
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We study frequency allocation in wireless networks. A wireless network is modeled by an undirected graph, with vertices corresponding to cells. In each vertex we have a certain number of requests, and each of those requests must be assigned a different frequency. Edges represent conflicts between cells, meaning that frequencies in adjacent vertices must be different as well. The objective is to minimize the total number of used frequencies. The offline version of the problem is known to be NP-hard. In the incremental version, requests for frequencies arrive over time and the algorithm is required to assign a frequency to a request as soon as it arrives. Competitive incremental algorithms have been studied for several classes of graphs. For paths, the optimal (asymptotic) ratio is known to be 4/3, while for hexagonal-cell graphs it is between 1.5 and 1.9126. For ξ-colorable graphs, the ratio of (ξ + 1)/2 can be achieved. In this paper, we prove nearly tight bounds on the asymptotic competitive ratio for bipartite graphs, showing that it is between 1.428 and 1.433. This improves the previous lower bound of 4/3 and upper bound of 1.5. Our proofs are based on reducing the incremental problem to a purely combinatorial (equivalent) problem of constructing set families with certain intersection properties.