Abstract
This paper presents an optimal fully-dynamic recognition algorithm for directed cographs. Given the modular decomposition tree of a directed cograph G, the algorithm supports arc and vertex modification (insertion or deletion) in \(\mathcal{O}(d)\) time where d is the number of arcs involved in the operation. Moreover, if the modified graph remains a directed cograph, the modular tree decomposition is updated; otherwise, a certificate is returned within the same complexity.
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
Preview
Unable to display preview. Download preview PDF.
References
Bretscher, A., Corneil, D.G., Habib, M., Paul, C.: A simple linear time lexBFS cograph recognition algorithm. In: Bodlaender, H.L. (ed.) WG 2003. LNCS, vol. 2880, pp. 119–130. Springer, Heidelberg (2003)
Capelle, C., Habib, M.: Graph decompositions and factorizing permutations. In: Fifth Israel Symposium on the Theory of Computing Systems (ISTCS 1997), pp. 132–143. IEEE Computer Society Press, Los Alamitos (1997)
Corneil, D.G., Lerchs, H., Stewart Burlingham, L.: Complement reducible graphs. Discrete Applied Mathematics 3(1), 163–174 (1981)
Corneil, D.G., Perl, Y., Stewart, L.K.: A linear time recognition algorithm for cographs. SIAM Journal on Computing 14(4), 926–934 (1985)
Ehrenfeucht, A., Rozenberg, G.: Primitivity is hereditary for 2-structures. Theoretical Computer Science 70(3), 343–359 (1990)
Fouquet, J.-L., Giakoumakis, V., Vanherpe, J.-M.: Bipartite graphs totally decomposable by canonical decomposition. International Journal of Foundation of Computer Science 10(4), 513–533 (1999)
Giakoumakis, V., Vanherpe, J.-M.: Linear time recognition and optimizations for weak-bisplit graphs, bi-cographs and bipartite p6-free graphs. International Journal of Foundation of Computer Science 14(1), 107–136 (2003)
Hell, P., Shamir, R., Sharan, R.: A fully dynamic algorithm for recognizing and representing proper interval graphs. SIAM Journal on Computing 31(1), 289–305 (2002)
Ibarra, L.: Fully dynamic algorithms for chordal graphs. In: 10th ACM-SIAM Annual Symposium on Discrete Algorithm (SODA 2003), pp. 923–924 (1999)
Kratsch, D., McConnell, R.M., Mehlhorn, K., Spinrad, J.P.: Certifying algorithm for recognition of interval graphs and permutation graphs. In: 14th ACM-SIAM Annual Symposium on Discrete Algorithm (SODA 2003), pp. 153–167 (2003)
Lawler, E.L.: Graphical algorithm and their complexity. Mathematical center tracts 81, 3–32 (1976)
Möhring, R.H., Radermacher, F.J.: Substitution decomposition for discrete structures and connections with combinatorial optimization. Annals of Discrete Mathematics 19, 257–356 (1984)
Shamir, R., Sharan, R.: A fully dynamic algorithm for modular decomposition and representation of cographs. Discrete Applied Mathematics 136(2-3), 329–340 (2004)
Valdes, J., Tarjan, R.E., Lawler, E.L.: The recognition of series parallel digraphs. SIAM Journal on Computing 11, 298–313 (1982)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Crespelle, C., Paul, C. (2004). Fully-Dynamic Recognition Algorithm and Certificate for Directed Cographs. In: Hromkovič, J., Nagl, M., Westfechtel, B. (eds) Graph-Theoretic Concepts in Computer Science. WG 2004. Lecture Notes in Computer Science, vol 3353. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30559-0_8
Download citation
DOI: https://doi.org/10.1007/978-3-540-30559-0_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24132-4
Online ISBN: 978-3-540-30559-0
eBook Packages: Computer ScienceComputer Science (R0)