An integer program and new lower bounds for computing the strong rainbow connection numbers of graphs. Issue 1 (28th February 2021)

• Record Type: Journal Article
• Authors: Smith, Logan A.; Mildebrath, David; Hicks, Illya V.
• Is Part Of: Networks. Volume 79:Issue 1(2022)
• Page Start: 3
• Page End: 19
• Publication Date: 2021-02-28
• Subjects: combinatorial optimization -- graph -- graph coloring -- heuristic -- integer programming -- strong rainbow connection; Network analysis (Planning) -- Periodicals; 658.4032
• DOI: 10.1002/net.22031
• Languages: English
• ISSNs: 0028-3045

Abstract

Abstract: 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.