Distributed online frequency assignment in cellular networks
Journal of Algorithms
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
Online frequency allocation in cellular networks
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
SIGACT news online algorithms column 14
ACM SIGACT News
1-local 17/12-competitive algorithm for multicoloring hexagonal graphs
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Analysing local algorithms in location-aware quasi-unit-disk graphs
Discrete Applied Mathematics
1-local 33/24-competitive algorithm for multicoloring hexagonal graphs
WAW'11 Proceedings of the 8th international conference on Algorithms and models for the web graph
A linear time algorithm for 7-[3]coloring triangle-free hexagonal graphs
Information Processing Letters
A 1-local 13/9-competitive algorithm for multicoloring hexagonal graphs
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
ACM Computing Surveys (CSUR)
A 1-local 4/3-competitive algorithm for multicoloring a subclass of hexagonal graphs
Discrete Applied Mathematics
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An important optimization problem in the design of cellular networks is to assign sets of frequencies to transmitters to avoid unacceptable interference. A cellular network is generally modeled as a subgraph of the infinite triangular lattice. Frequency assignment problem can be abstracted as a multicoloring problem on a weighted hexagonal graph, where the weights represent the number of calls to be assigned at vertices. In this paper we present a distributed algorithm for multicoloring hexagonal graphs using only the local clique numbers ω1(v) and ω2(v) at each vertex v of the given hexagonal graph, which can be computed from local information available at the vertex. We prove the algorithm uses no more than ⌈4ω(G)/3⌉ colors for any hexagonal graph G, without explicitly computing the global clique number ω(G). We also prove that our algorithm is 2-local, i.e., the computation at a vertex v ∈ G uses only information about the demands of vertices whose graph distance from v is less than or equal to 2.