Abstract
We present an O *(1.3160n)-time algorithm for the edge dominating set problem in an n-vertex graph, which improves previous exact algorithms for this problem. The algorithm is analyzed by using the “Measure and Conquer method.” We design new branching rules based on conceptually simple local structures, called “clique-producing vertices/cycles,” which significantly simplify the algorithm and its running time analysis, attaining an improved time bound at the same time.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Binkele-Raible, D., Fernau, H.: Enumerate and Measure: Improving Parameter Budget Management. In: Raman, V., Saurabh, S. (eds.) IPEC 2010. LNCS, vol. 6478, pp. 38–49. Springer, Heidelberg (2010)
Eppstein, D.: Quasiconvex analysis of backtracking algorithms. In: SODA, pp. 781–790. ACM Press (2004)
Fernau, H.: edge dominating set: Efficient Enumeration-Based Exact Algorithms. In: Bodlaender, H.L., Langston, M.A. (eds.) IWPEC 2006. LNCS, vol. 4169, pp. 142–153. Springer, Heidelberg (2006)
Fomin, F., Gaspers, S., Saurabh, S., Stepanov, A.: On two techniques of combining branching and treewidth. Algorithmica 54(2), 181–207 (2009)
Fomin, F.V., Grandoni, F., Kratsch, D.: Measure and Conquer: Domination – A Case Study. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 191–203. Springer, Heidelberg (2005)
Johnson, D., Yannakakis, M., Papadimitriou, C.: On generating all maximal independent sets. Information Processing Letters 27(3), 119–123 (1988)
Plesnik, J.: Constrained weighted matchings and edge coverings in graphs. Disc. Appl. Math. 92, 229–241 (1999)
Moon, J.W., Moser, L.: On cliques in graphs. Israel J. Math. 3, 23–28 (1965)
Raman, V., Saurabh, S., Sikdar, S.: Efficient exact algorithms through enumerating maximal independent sets and other techniques. Theory of Computing Systems 42(3), 563–587 (2007)
Randerath, B., Schiermeyer, I.: Exact algorithms for minimum dominating set. Technical Report zaik 2005-501, Universität zu Köln, Germany (2005)
van Rooij, J.M.M., Bodlaender, H.L.: Exact Algorithms for Edge Domination. In: Grohe, M., Niedermeier, R. (eds.) IWPEC 2008. LNCS, vol. 5018, pp. 214–225. Springer, Heidelberg (2008)
Xiao, M.: A Simple and Fast Algorithm for Maximum Independent Set in 3-Degree Graphs. In: Rahman, M. S., Fujita, S. (eds.) WALCOM 2010. LNCS, vol. 5942, pp. 281–292. Springer, Heidelberg (2010)
Xiao, M.: Exact and Parameterized Algorithms for Edge Dominating Set in 3-Degree Graphs. In: Wu, W., Daescu, O. (eds.) COCOA 2010, Part II. LNCS, vol. 6509, pp. 387–400. Springer, Heidelberg (2010)
Xiao, M., Kloks, T., Poon, S.-H.: New Parameterized Algorithms for the Edge Dominating Set Problem. In: Murlak, F., Sankowski, P. (eds.) MFCS 2011. LNCS, vol. 6907, pp. 604–615. Springer, Heidelberg (2011)
Xiao, M., Nagamochi, H.: Parameterized Edge Dominating Set in Cubic Graphs. In: Atallah, M., Li, X.-Y., Zhu, B. (eds.) FAW-AAIM 2011. LNCS, vol. 6681, pp. 100–112. Springer, Heidelberg (2011)
Xiao, M., Nagamochi, H.: A Refined Exact Algorithm for Edge Dominating Set. TR 2011-014. Kyoto University (2011)
Yannakakis, M., Gavril, F.: Edge dominating sets in graphs. SIAM J. Appl. Math. 38(3), 364–372 (1980)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Xiao, M., Nagamochi, H. (2012). A Refined Exact Algorithm for Edge Dominating Set. In: Agrawal, M., Cooper, S.B., Li, A. (eds) Theory and Applications of Models of Computation. TAMC 2012. Lecture Notes in Computer Science, vol 7287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29952-0_36
Download citation
DOI: https://doi.org/10.1007/978-3-642-29952-0_36
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-29951-3
Online ISBN: 978-3-642-29952-0
eBook Packages: Computer ScienceComputer Science (R0)