2-local 5/4-competitive algorithm for multicoloring triangle-free hexagonal graphs. ## AbstractAn important optimization problem in the design of cellular networks is to assign sets of frequencies to transmitters to avoid unacceptable interference. A cellular networks is generally modeled as a subgraph of the infinite triangular lattice. The distributed frequency assignment problem can be abstracted as a multicoloring problem on a weighted hexagonal graph, where the weight vector represents the number of calls to be assigned at vertices. In this paper we present a 2-local distributed algorithm for multicoloring triangle-free hexagonal graphs using only the local clique number $\omega_1(v)$ and $\omega_2(v)$ at each vertex $v$ of the given hexagonal graph, which can be computed from the local information available at the vertex. We prove the algorithm uses no more than $\lceil \frac{5\omega(G)}{4} \rceil + 3$ colors for any triangle-free hexagonal graph $G$, without explicitly computing the global clique number $\omega(G)$. Hence the competetive ratio of the algorithm is 5/4.
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