Abstract
We consider the Directed Steiner Path Cover problem on directed co-graphs. Given a directed graph \(G=(V(G),E(G))\) and a set \(T \subseteq V(G)\) of so-called terminal vertices, the problem is to find a minimum number of directed vertex-disjoint paths, which contain all terminal vertices and a minimum number of non-terminal vertices (Steiner vertices). The primary minimization criteria is the number of paths. We show how to compute a minimum Steiner path cover for directed co-graphs in linear time. For \(T = V(G)\), the algorithm computes a directed Hamiltonian path if such a path exists.
This work was funded in part by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) – 388221852.
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Abu-Affash, A.K., Carmi, P., Katz, M.J., Segal, M.: The euclidean bottleneck steiner path problem and other applications of (\(\alpha \),\(\beta \))-pair decomposition. Discret. Comput. Geom. 51(1), 1–23 (2014)
Bang-Jensen, J., Maddaloni, A.: Arc-disjoint paths in decomposable digraphs. J. Graph Theory 77, 89–110 (2014)
Bechet, D., de Groote, P., Retoré, C.: A complete axiomatisation for the inclusion of series-parallel partial orders. In: Comon, H. (ed.) RTA 1997. LNCS, vol. 1232, pp. 230–240. Springer, Heidelberg (1997). https://doi.org/10.1007/3-540-62950-5_74
Borndörfer, R., Karbstein, M., Pfetsch, M.: The steiner connectivity problem. Math. Program. 142(1), 133–167 (2013)
Corneil, D., Lerchs, H., Stewart-Burlingham, L.: Complement reducible graphs. Discrete Appl. Math. 3, 163–174 (1981)
Crespelle, C., Paul, C.: Fully dynamic recognition algorithm and certificate for directed cographs. Discrete Appl. Math. 154(12), 1722–1741 (2006)
Gurski, F., Komander, D., Rehs, C.: Computing digraph width measures on directed co-graphs. In: Gąsieniec, L.A., Jansson, J., Levcopoulos, C. (eds.) FCT 2019. LNCS, vol. 11651, pp. 292–305. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-25027-0_20
Gurski, F., Rehs, C.: Directed path-width and directed tree-width of directed co-graphs. In: Wang, L., Zhu, D. (eds.) COCOON 2018. LNCS, vol. 10976, pp. 255–267. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94776-1_22
Gurski, F., Wanke, E., Yilmaz, E.: Directed NLC-width. Theor. Comput. Sci. 616, 1–17 (2016)
Lin, R., Olariu, S., Pruesse, G.: An optimal path cover algorithm for cographs. Comput. Math. Appl. 30, 75–83 (1995)
Moharana, S.S., Joshi, A., Vijay, S.: Steiner path for trees. Int. J. Comput. Appl. 76(5), 11–14 (2013)
Nøjgaard, N., El-Mabrouk, N., Merkle, D., Wieseke, N., Hellmuth, M.: Partial homology relations - satisfiability in terms of di-cographs. In: Wang, L., Zhu, D. (eds.) COCOON 2018. LNCS, vol. 10976, pp. 403–415. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-94776-1_34
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Gurski, F., Hoffmann, S., Komander, D., Rehs, C., Rethmann, J., Wanke, E. (2020). Computing Directed Steiner Path Covers for Directed Co-graphs (Extended Abstract). In: Chatzigeorgiou, A., et al. SOFSEM 2020: Theory and Practice of Computer Science. SOFSEM 2020. Lecture Notes in Computer Science(), vol 12011. Springer, Cham. https://doi.org/10.1007/978-3-030-38919-2_45
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DOI: https://doi.org/10.1007/978-3-030-38919-2_45
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