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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| Materias: | |
| Acceso en línea: | https://arxiv.org/abs/2402.07771 |
| Etiquetas: |
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- A graph is called a $(k,ρ)$-graph iff every node can reach $ρ$ of its nearest neighbors in at most k hops. This property proved useful in the analysis and design of parallel shortest-path algorithms. Any graph can be transformed into a $(k,ρ)$-graph by adding shortcuts. Formally, the $(k,ρ)$-Minimum-Shortcut problem asks to find an appropriate shortcut set of minimal cardinality. We show that the $(k,ρ)$-Minimum-Shortcut problem is NP-complete in the practical regime of $k \ge 3$ and $ρ= Θ(n^ε)$ for $ε> 0$. With a related construction, we bound the approximation factor of known $(k,ρ)$-Minimum-Shortcut problem heuristics from below and propose algorithmic countermeasures improving the approximation quality. Further, we describe an integer linear problem (ILP) solving the $(k,ρ)$-Minimum-Shortcut problem optimally. Finally, we compare the practical performance and quality of all algorithms in an empirical campaign.