Scalable Algorithms for 2-Packing Sets on Arbitrary Graphs
A 2-packing set for an undirected graph $G=(V,E)$ is defined as a subset $\mathcal{S}\subseteq V$ such that for each pair of vertices $v_1 \neq v_2 \in \mathcal{S}$, the shortest path between $v_1$ and $v_2$ has at least length three. Finding a 2-packing set of maximum cardinality is an NP-hard prob...
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| Veröffentlicht in: | Journal of graph algorithms and applications Jg. 29; H. 1; S. 159 - 186 |
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| Hauptverfasser: | , , , |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
02.07.2025
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| ISSN: | 1526-1719, 1526-1719 |
| Online-Zugang: | Volltext |
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| Zusammenfassung: | A 2-packing set for an undirected graph $G=(V,E)$ is defined as a subset $\mathcal{S}\subseteq V$ such that for each pair of vertices $v_1 \neq v_2 \in \mathcal{S}$, the shortest path between $v_1$ and $v_2$ has at least length three. Finding a 2-packing set of maximum cardinality is an NP-hard problem. We develop a new approach to solve this problem on arbitrary graphs using its close relation to the independent set problem. Our approach uses new data reduction rules as well as a graph transformation. Experiments show that this technique outperforms the state-of-the-art for arbitrary graphs with respect to solution quality. Furthermore, we can compute solutions multiple orders of magnitude faster than previously possible. Our approach solves 63% of the graphs in the tested data set to optimality in under a second. In contrast, the competitor for arbitrary graphs can only solve 5% of these graphs to optimality even with a 10-hour time limit. Moreover, our approach can solve a wide range of large instances that have previously been unsolved. |
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| ISSN: | 1526-1719 1526-1719 |
| DOI: | 10.7155/jgaa.v29i1.3064 |