An integer program and new lower bounds for computing the strong rainbow connection numbers of graphs
| Autor: | Logan A. Smith, David T. Mildebrath, Illya V. Hicks |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
FOS: Computer and information sciences
Discrete Mathematics (cs.DM) Computer Networks and Communications 0211 other engineering and technologies G.2.1 G.2.2 02 engineering and technology Upper and lower bounds Integer 0502 economics and business FOS: Mathematics Mathematics - Combinatorics Graph coloring Variable elimination Mathematics - Optimization and Control Integer programming Mathematics Discrete mathematics 050210 logistics & transportation 021103 operations research Heuristic 05 social sciences F.2.2 05C15 Optimization and Control (math.OC) Hardware and Architecture Combinatorial optimization Combinatorics (math.CO) Branch and cut Software Computer Science - Discrete Mathematics Information Systems |
| Zdroj: | Networks. 79:3-19 |
| ISSN: | 1097-0037 0028-3045 |
| 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: | OpenAIRE |
| Externí odkaz: |
|
Plný text