Tight lower bound for the channel assignment problem

Arkadiusz Socala

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arXiv · 1407.7162

Tight lower bound for the channel assignment problem

Arkadiusz Socala

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Abstract

We study the complexity of the Channel Assignment problem. A major open problem asks whether Channel Assignment admits an $O(c^n)$-time algorithm, for a constant $c$ independent of the weights on the edges. We answer this question in the negative i.e. we show that there is no $2^{o(n\log n)}$-time algorithm solving Channel Assignment unless the Exponential Time Hypothesis fails. Note that the currently best known algorithm works in time $O^*(n!) = 2^{O(n\log n)}$ so our lower bound is tight.

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Arkadiusz Socala. 2014-07-26. Tight lower bound for the channel assignment problem. https://arxiv.org/abs/1407.7162

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