Minimum-cost augmentation to 3-edge-connect all specified vertices in a graph

Watanabe, Takahiro; Taoka, Satoshi; Mashima, Toshiya

doi:10.1109/iscas.1993.394225

Cited by 7 publications

(3 citation statements)

References 17 publications

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“…Proof: Recall that, by Lemmata 3 and 4, we can assume that G is 3-edgeconnected. If not, we iteratively decompose G into 3-edge-connected components using the linear-time algorithm of [22]. A tree-cut decomposition of G can easily built from the tree-cut decomposition of its 3-edge-connected components using Lemma 3.…”

Section: Piecing Everything Togethermentioning

confidence: 99%

An FPT 2-Approximation for Tree-Cut Decomposition

Kim¹,

Oum

Paul

et al. 2016

Algorithmica

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Abstract. The tree-cut width of a graph is a graph parameter defined by Wollan [J. Comb. Theory, Ser. B, 110:47-66, 2015] with the help of tree-cut decompositions. In certain cases, tree-cut width appears to be more adequate than treewidth as an invariant that, when bounded, can accelerate the resolution of intractable problems. While designing algorithms for problems with bounded tree-cut width, it is important to have a parametrically tractable way to compute the exact value of this parameter or, at least, some constant approximation of it. In this paper we give a parameterized 2-approximation algorithm for the computation of tree-cut width; for an input n-vertex graph G and an integer w, our algorithm either confirms that the tree-cut width of G is more than w or returns a tree-cut decomposition of G certifying that its tree-cut width is at most 2w, in time 2 O(w 2 log w) · n 2 . Prior to this work, no constructive parameterized algorithms, even approximated ones, existed for computing the tree-cut width of a graph. As a consequence of the Graph Minors series by Robertson and Seymour, only the existence of a decision algorithm was known.

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Section: Piecing Everything Togethermentioning

confidence: 99%

An FPT 2-Approximation for Tree-Cut Decomposition

Kim¹,

Oum

Paul

et al. 2016

Algorithmica

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“…There is a long history of applications for the problem of adding edges to a graph in order to satisfy connectivity specifications (see [7,11,17] for recent examples). Correspondingly, the problem has been extensively studied for making general graphs k-edge connected or k-vertex connected for various values of k [5,10,12,16,25,29] as well as for making vertex subsets suitably connected [6,13,[26][27][28]30].…”

Section: Introductionmentioning

confidence: 99%

Optimal Augmentation for Bipartite Componentwise Biconnectivity in Linear Time

Hsu¹,

Kao²

2005

SIAM J. Discrete Math.

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“…Some known results on W-k-ECA are summarized in the following. See [1,3,5.15,19,21,25] for UW-k-ECA(M), [24,26] for UW-3-ECA(S) and UW-3-ECA(M). For W-2-ECA(S), [4] showed that it remains NP-complete even if G' is restricted to a tree with edge costs from (1,2).…”

Section: Introductionmentioning

confidence: 99%