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, and a variable elimination scheme. Moreover, we present a novel lower bound for src(G) which may be of independent research interest. We solve the integer program both directly and using an alternative method based on iterative lower bound improvement, the latter of 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 containing up to 379 vertices.

中文翻译：

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计算图的强彩虹连接数的整数程序和新下界

我们提出了一个整数规划模型来计算任何简单图G的强彩虹连接数src ( G ) 。我们对所提出的模型进行了一些改进，包括快速启发式和变量消除方案。此外，我们提出了一个新的src下界（G) 可能具有独立的研究兴趣。我们直接和使用基于迭代下界改进的替代方法求解整数规划，我们证明后者在实践中非常有效。据我们所知，这些是强彩虹连接问题的第一个计算方法。我们通过计算包含多达 379 个顶点的图的强彩虹连接数来证明我们方法的有效性。