An integer program and new lower bounds for computing the strong rainbow connection numbers of graphs

06/04/2020

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by   Logan A. Smith, et al.

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We present an integer programming model to compute the strong rainbow connection number src(G) of any simple graph G. We introduce several enhancements to the proposed model, including a fast heuristic, a novel class of valid inequalities, and a variable elimination scheme. Moreover, we present a novel lower bound for src(G) which may be of independent research interest. We evaluate our model with a traditional branch and cut approach as well as an alternative scheme based on iterative lower bound improvement, which we show to be highly effective in practice. To our knowledge, these are the first computational methods for the strong rainbow connection problem. We demonstrate the efficacy of our methods by computing the strong rainbow connection numbers of graphs with up to 167 vertices.