Computing the 2-blocks of directed graphs
RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 49 (2015) no. 2, pp. 93-119.

Let G be a directed graph. A 2-directed block in G is a maximal vertex set C 2d V with |C 2d |2 such that for each pair of distinct vertices x, yC 2d , there exist two vertex-disjoint paths from x to y and two vertex-disjoint paths from y to x in G. In this paper we present two algorithms for computing the 2-directed blocks of G in O(min{m,(t sap +t sb )n}n) time, where t sap is the number of the strong articulation points of G and t sb is the number of the strong bridges of G. Furthermore, we study two related concepts: the 2-strong blocks and the 2-edge blocks of G. We give two algorithms for computing the 2-strong blocks of G in O(min{m,t sap n}n) time and we show that the 2-edge blocks of G can be computed in O(min{m,t sb n}n) time. In this paper we also study some optimization problems related to the strong articulation points and the 2-blocks of a directed graph. Given a strongly connected graph G=(V,E), we want to find a minimum strongly connected spanning subgraph G * =(V,E * ) of G such that the strong articulation points of G coincide with the strong articulation points of G * . We show that there is a linear time 17/3 approximation algorithm for this NP-hard problem. We also consider the problem of finding a minimum strongly connected spanning subgraph with the same 2-blocks in a strongly connected graph G. We present approximation algorithms for three versions of this problem, depending on the type of 2-blocks.

Reçu le :
Accepté le :
DOI : 10.1051/ita/2015001
Classification : 05C85, 05C20, 68W25
Mots clés : Directed graphs, strong articulation points, strong bridges, 2-blocks, graph algorithms, approximation algorithms
Jaberi, Raed 1

1 Faculty of Computer Science and Automation, Teschnische Universität Ilmenau, 98693 Ilmenau, Germany
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Jaberi, Raed. Computing the $2$-blocks of directed graphs. RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications, Tome 49 (2015) no. 2, pp. 93-119. doi : 10.1051/ita/2015001. http://archive.numdam.org/articles/10.1051/ita/2015001/

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