Abstract
Lexicographic depth first search (LexDFS) is a graph search protocol which has already proved to be a powerful tool on cocomparability graphs. Cocomparability graphs have been well studied by investigating their complements (comparability graphs) and their corresponding posets. Recently however LexDFS has led to a number of elegant polynomial and near linear time algorithms on cocomparability graphs when used as a preprocessing step [2,3,11]. The nonlinear runtime of some of these results is a consequence of complexity of this preprocessing step. We present the first linear time algorithm to compute a LexDFS cocomparability ordering, therefore answering a problem raised in [2] and helping achieve the first linear time algorithms for the minimum path cover problem, and thus the Hamilton path problem, the maximum independent set problem and the minimum clique cover for this graph family.
This is an extended abstract. The full version is available in [13]
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Brandstädt, A., Dragan, F.F., Nicolai, F.: LexBFS-orderings and powers of chordal graphs. Discrete Mathematics 171(1), 27–42 (1997)
Corneil, D.G., Dalton, B., Habib, M.: LDFS-based certifying algorithm for the minimum path cover problem on cocomparability graphs. SIAM Journal on Computing 42(3), 792–807 (2013)
Corneil, D.G., Dusart, J., Habib, M., Köhler, E.: On the power of graph searching for cocomparability graphs (in preparation)
Corneil, D.G., Krueger, R.M.: A unified view of graph searching. SIAM Journal on Discrete Mathematics 22(4), 1259–1276 (2008)
Corneil, D.G., Olariu, S., Stewart, L.: The LBFS structure and recognition of interval graphs. SIAM Journal on Discrete Mathematics 23(4), 1905–1953 (2009)
Golumbic, M.C.: Algorithmic graph theory and perfect graphs, vol. 57. Elsevier (2004)
Habib, M., McConnell, R.M., Paul, C., Viennot, L.: LexBFS and partition refinement, with applications to transitive orientation and consecutive ones testing. Theoretical Computer Science 234 (2000)
Habib, M., Paul, C., Viennot, L.: Partition refinement techniques: An interesting algorithmic tool kit. International Journal of Foundations of Computer Science 10(02), 147–170 (1999)
Kratsch, D., Stewart, L.: Domination on cocomparability graphs. SIAM Journal on Discrete Mathematics 6(3), 400–417 (1993)
McConnell, R.M., Spinrad, J.P.: Modular decomposition and transitive orientation. Discrete Mathematics 201(1), 189–241 (1999)
Mertzios, G.B., Corneil, D.G.: A simple polynomial algorithm for the longest path problem on cocomparability graphs. SIAM Journal on Discrete Mathematics 26(3), 940–963 (2012)
Spinrad, J.P.: Efficient implementation of lexicographic depth first search (submitted)
Köhler, E., Mouatadid, L.: Linear time lexdfs on cocomparability graphs. available on arXiv at http://arxiv.org/pdf/1404.5996v1.pdf
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2014 Springer International Publishing Switzerland
About this paper
Cite this paper
Köhler, E., Mouatadid, L. (2014). Linear Time LexDFS on Cocomparability Graphs.. In: Ravi, R., Gørtz, I.L. (eds) Algorithm Theory – SWAT 2014. SWAT 2014. Lecture Notes in Computer Science, vol 8503. Springer, Cham. https://doi.org/10.1007/978-3-319-08404-6_28
Download citation
DOI: https://doi.org/10.1007/978-3-319-08404-6_28
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-08403-9
Online ISBN: 978-3-319-08404-6
eBook Packages: Computer ScienceComputer Science (R0)