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

Autor:	Smith, Logan A., Mildebrath, David T., Hicks, Illya V.
Rok vydání:	2020
Předmět:	Mathematics - Combinatorics Computer Science - Discrete Mathematics Mathematics - Optimization and Control 05C15 G.2.1 G.2.2 F.2.2
Druh dokumentu:	Working Paper
Popis:	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. Comment: 27 pages, 7 figures
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2006.02988 Zobrazit plný text záznamu View this record from Arxiv