Abstract
In the early 1980’s, Cunningham described a unique decomposition of a strongly-connected graph. A linear time bound for finding it in the special case of an undirected graph has been given previously, but up until now, the best bound known for the general case has been O(n 3). We give an O(m logn) bound.
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References
Aho, A.V., Hopcroft, J.E., Ullman, J.D.: The Design and Analysis of Computer Algorithms. Addison-Wesley, Reading (1974)
Bouchet, A.: Digraph decompositions and eulerian systems. SIAM Journal on Algebraic and Discrete Methods 8 (1987)
Cunningham, W.H.: Decomposition of directed graphs. SIAM J. Algebraic Discrete Methods 3, 214–228 (1982)
Dahlhaus, E.: Parallel algorithms for hierarchical clustering, and applications to split decomposition and parity graph recognition. Journal of Algorithms 36, 205–240 (2000)
Gabor, C.P., Supowit, K.J., Hsu, W.-L.: Recognizing circle graphs in polynomial time. Journal of the ACM 36, 435–473 (1989)
Ma, T.H., Spinrad, J.: An O(n 2) algorithm for undirected split decomposition. Journal of Algorithms 16, 145–160 (1994)
Möhring, R.H.: Algorithmic aspects of the substitution decomposition in optimization over relations, set systems and boolean functions. Annals of Operations Research 4, 195–225 (1985)
Möhring, R.H., Radermacher, F.J.: Substitution decomposition for discrete structures and connections with combinatorial optimization. Annals of Discrete Mathematics 19, 257–356 (1984)
Rao, M.: Solving some NP-complete problems using split decomposition. Discrete Applied Mathematics (2007)
Spinrad, J.: Prime testing for the split decomposition of a graph. SIAM Journal on Discrete Mathematics 2, 590–599 (1989)
Spinrad, J.P.: Two Dimensional Partial Orders. Ph.D thesis, Princeton University (1982)
Spinrad, J.P.: Graph partitioning (1985) (unpublished manuscript)
Spinrad, J.P.: On comparability and permutation graphs. Siam J. Comput. 14, 658–670 (1985)
Spinrad, J.P., Valdes, J.: Recognition and isomorphism of two-dimensional partial orders. In: Proceedings of the 10th Colloquium on Automata, Languages and Programming. LNCS, pp. 676–686. Springer, Berlin (1983)
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Joeris, B.L., Lundberg, S., McConnell, R.M. (2009). O(m logn) Split Decomposition of Strongly Connected Graphs. In: Lipshteyn, M., Levit, V.E., McConnell, R.M. (eds) Graph Theory, Computational Intelligence and Thought. Lecture Notes in Computer Science, vol 5420. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02029-2_16
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DOI: https://doi.org/10.1007/978-3-642-02029-2_16
Publisher Name: Springer, Berlin, Heidelberg
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