Abstract
Weighted independent domination is an NP-hard graph problem, which remains computationally intractable in many restricted graph classes. Only few examples of classes are available, where the problem admits polynomial-time solutions. In the present paper, we extend the short list of such classes with two new examples.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Balas, E., Yu, C.S.: On graphs with polynomially solvable maximum-weight clique problem. Networks 19, 247–253 (1989)
Bodlaender, H.L., Brandstädt, A., Kratsch, D., Rao, M., Spinrad, J.: On algorithms for \((P_5, gem)\)-free graphs. Theoret. Comput. Sci. 349, 2–21 (2005)
Boliac, R., Lozin, V.: Independent domination in finitely defined classes of graphs. Theoret. Comput. Sci. 301, 271–284 (2003)
Chang, G.J.: The weighted independent domination problem is NP-complete for chordal graphs. Discret. Appl. Math. 143, 351–352 (2004)
Damaschke, P., Muller, H., Kratsch, D.: Domination in convex and chordal bipartite graphs. Inf. Process. Lett. 36, 231–236 (1990)
Farber, M.: Independent domination in chordal graphs. Oper. Res. Lett. 1, 134–138 (1982)
Giakoumakis, V., Rusu, I.: Weighted parameters in \((P_5,\overline{P}_5)\)-free graphs. Discret. Appl. Math. 80, 255–261 (1997)
Karthick, T.: On atomic structure of \(P_5\)-free subclasses and maximum weight independent set problem. Theoret. Comput. Sci. 516, 78–85 (2014)
Lokshantov, D., Vatshelle, M., Villanger, Y.: Independent set in \(P_5\)-free graphs in polynomial time. In: Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms, pp. 570–581 (2014)
Lozin, V., Mosca, R., Purcell, C.: Independent domination in finitely defined classes of graphs: polynomial algorithms. Discret. Appl. Math. 182, 2–14 (2015)
McConnell, R.M., Spinrad, J.: Modular decomposition and transitive orientation. Discret. Math. 201, 189–241 (1999)
Möhring, R.H., Radermacher, F.J.: Substitution decomposition for discrete structures and connections with combinatorial optimization. Ann. Discret. Math. 19, 257–356 (1984)
Whitesides, S.H.: An algorithm for finding clique cut-sets. Inf. Process. Lett. 12, 31–32 (1981)
Yannakakis, M., Gavril, F.: Edge dominating sets in graphs. SIAM J. Appl. Math. 38, 364–372 (1980)
Zverovich, I.E.: Satgraphs and independent domination. Part 1. Theoret. Comput. Sci. 352, 47–56 (2006)
Acknowledgements
The results of Sect. 3 were obtained under financial support of the Russian Science Foundation grant No. 17-11-01336. The results of Sect. 4 were obtained under financial support of the Russian Foundation for Basic Research, grant No. 16-31-60008-mol-a-dk, RF President grant MK-4819.2016.1 and LATNA laboratory, National Research University Higher School of Economics.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Lozin, V., Malyshev, D., Mosca, R., Zamaraev, V. (2017). New Results on Weighted Independent Domination. In: Bodlaender, H., Woeginger, G. (eds) Graph-Theoretic Concepts in Computer Science. WG 2017. Lecture Notes in Computer Science(), vol 10520. Springer, Cham. https://doi.org/10.1007/978-3-319-68705-6_30
Download citation
DOI: https://doi.org/10.1007/978-3-319-68705-6_30
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-68704-9
Online ISBN: 978-3-319-68705-6
eBook Packages: Computer ScienceComputer Science (R0)