Linear‐time algorithms for the 2‐connected steiner subgraph problem on special classes of graphs

Coullard, Collette R.; Rais, Abdur; Rardin, Ronald L.; Wagner, Donald K.

doi:10.1002/net.3230230307

Cited by 19 publications

(20 citation statements)

References 13 publications

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“…This generalizes results given by Monma et al [34] for the case when k = 2. In [9,10], Coullard et al study the Steiner two-node connected subgraph problem. They devise in [9] a linear time algorithm for this problem on some special classes of graphs.…”

Section: Kecsp(g) = Conv{xmentioning

confidence: 99%

A branch‐and‐cut algorithm for the k‐edge connected subgraph problem

Bendali¹,

Diarrassouba²,

Mahjoub³

et al. 2009

Networks

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International audienceIn this article, we consider the k-edge connected subgraph problem from a polyhedral point of view. We introduce further classes of valid inequalities for the associated polytope and describe sufficient conditions for these inequalities to be facet defining. We also devise separation routines for these inequalities and discuss some reduction operations that can be used in a preprocessing phase for the separation. Using these results, we develop a Branch-and-Cut algorithm and present some computational results

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Section: Kecsp(g) = Conv{xmentioning

confidence: 99%

A branch‐and‐cut algorithm for the k‐edge connected subgraph problem

Bendali¹,

Diarrassouba²,

Mahjoub³

et al. 2009

Networks

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“…In [14], Barahona and Mahjoub gave a complete description of the polytope NSNDP(G, r) on Halin graphs when r(u) = 2 for all u ∈ V . Coullard et al [32,33] studied the Steiner 2-node connected subgraph problem, that is, the NSDNP where r ∈ {0, 2} V . In [32], they gave a linear time algorithm for the Steiner 2-node connected subgraph problem on Halin graphs and on graphs noncontractible to W 4 , the latter being the graphs that do not reduce to W 4 (i.e., the wheel on five nodes) by means of deletions and contractions of edges.…”

Section: Theorem 4 [22] If G = (V E) Is Outerplanar R(u) = K For mentioning

confidence: 99%

“…Coullard et al [32,33] studied the Steiner 2-node connected subgraph problem, that is, the NSDNP where r ∈ {0, 2} V . In [32], they gave a linear time algorithm for the Steiner 2-node connected subgraph problem on Halin graphs and on graphs noncontractible to W 4 , the latter being the graphs that do not reduce to W 4 (i.e., the wheel on five nodes) by means of deletions and contractions of edges. They also described, in [33], the dominant of the polytope LNSDP (G, r) where G is a graph noncontractible to W 4 and r ∈ {0, 2} V .…”

Section: Theorem 4 [22] If G = (V E) Is Outerplanar R(u) = K For mentioning

confidence: 99%

“…On Halin graphs, Winter [122] also gave polynomial-time algorithms to solve the survivable network design problem for both survivability conditions and r ∈ {0, 3} V . If the graph G does not have W 4 (the wheel on five nodes) as a minor or if G is a Halin graph, Coullard et al [32] devised a linear time algorithm for the SNDP with the node-survivability conditions and r ∈ {0, 2} V . (A graph H is a minor of a graph G if H arises from G by a series of deletions and contractions of edges and deletions of nodes.)…”

Section: Polynomially Solvable Casesmentioning

confidence: 99%

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Design of Survivable Networks: A survey

2005

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For the past few decades, combinatorial optimization techniques have been shown to be powerful tools for formulating and solving optimization problems arising from practical situations. In particular, many network design problems have been formulated as combinatorial optimization problems. With the advances of optical technologies and the explosive growth of the Internet, telecommunication networks have seen an important evolution and therefore designing survivable networks has become a major objective for telecommunication operators. Over the past years, much research has been carried out to devise efficient methods for survivable network models, and particularly cutting plane based algorithms. In this paper, we attempt to survey some of these models and the optimization methods used for solving them.

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“…STESNP). In (Coullard et al, 1991) the authors developed a linear algorithm to solve the STNCSP in the case of graphs without W 4 (a wheel graph with four nodes) and Halin graphs. The authors of this chapter have previously developed a parallel method (of worst case exponential complexity) for the general case (Cancela et al, 2005).…”

mentioning

confidence: 99%