2-local 3/4-competitive algorithm for multicoloring hexagonal graphs
Šparl, Petra, 1975-2016 ; Žerovnik, Janez, 1958-
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 asa 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 ▫$\omega_1(v)$▫ and ▫$\omega_2(v)$▫ at each vertex v of the given hexagonal graph, which can be computed from local information available at thevertex. We prove the algorithm uses no more than ▫$4\omega(G)/3$▫ colors for any hexagonal graph G, without explicitly computing the global clique number ▫$\omega(G)$▫. We also prove that our algorithm is 2-local, i.e., the computation at a vertex v ▫$\in$▫ G uses only information about the demands of vertices whose graph distance from v is less than or equal to 2.
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