Strong lower bounds for the prize collecting Steiner problem in graphs

Lucena, Abílio; Resende, Maurício G. C.

doi:10.1016/s0166-218x(03)00380-9

Cited by 56 publications

(57 citation statements)

References 10 publications

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“…The PCSTLib benchmark [13], was used in several studies, e.g., [18,19], and contains graphs divided into two groups K and P, where 15%-27% and 34%-50% of the nodes are customers, respectively. The former are similar to street map layouts.…”

Section: Benchmark Instancesmentioning

confidence: 99%

Orientation-based models for {0,1,2}-survivable network design: theory and practice

et al. 2010

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We consider {0,1,2}-Survivable Network Design problems with node-connectivity constraints. In the most prominent variant, we are given an edge-weighted graph and two customer sets R 1 and R 2 ; we ask for a minimum cost subgraph that connects all customers, and guarantees two-node-connectivity for the R 2 customers.We also consider an alternative of this problem, in which 2-node-connectivity is only required w.r.t. a certain root node, and its prize-collecting variant.The central result of this paper is a novel graph-theoretical characterization of 2-node-connected graphs via orientation properties. This allows us to derive two classes of ILP formulations based on directed graphs, one using multi-commodity flow and one using cut-inequalities. We prove the theoretical advantages of these directed models compared to the previously known ILP approaches. We show that our two concepts are equivalent from the polyhedral point of view. On the other hand, our experimental study shows that the cut formulation is much more powerful in practice. Moreover, we propose a collection of benchmark instances that can be used for further research on this topic.

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Section: Benchmark Instancesmentioning

confidence: 99%

Orientation-based models for {0,1,2}-survivable network design: theory and practice

et al. 2010

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“…Heuristic procedures are implemented in [Canuto et al, 2001, Klau et al, 2004 and [Salles da Cunha et al, 2009]. The first published work on polyhedral studies for the PCStT is [Lucena and Resende, 2004], where a cutting plane algorithm is proposed. The cuts are efficiently generated when a violation of a generalized subtour elimination constraint (GSEC) is verified.…”

Section: The Prize Collecting Steiner Tree Problemmentioning

confidence: 99%

Networks, uncertainty, applications and a crusade for optimality

Álvarez-Miranda

2015

4OR-Q J Oper Res

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“…Constraints (2) and (3) force the network to be a tree. This model with T = ∅ was used by Lucena and Resende [35]. Margot et al [36] have proved that the x i j variables need not be declared as integer.…”

Section: Network Location Modelsmentioning

confidence: 99%

Planning rapid transit networks

Laporte

Mesa

Ortega

et al. 2011

Socio-Economic Planning Sciences

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Rapid transit construction projects are major endeavours that require long-term planning by several players, including politicians, urban planners, engineers, management consultants, and citizen groups. Traditionally, operations research methods have not played a major role at the planning level but several tools developed in recent years can assist the decision process and help produce tentative network designs that can be submitted to the planners for further evaluation. This article reviews some indices for the quality of a rapid transit network, as well as mathematical models and heuristics that can be used to design networks.

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Strong lower bounds for the prize collecting Steiner problem in graphs

Cited by 56 publications

References 10 publications

Orientation-based models for {0,1,2}-survivable network design: theory and practice

Orientation-based models for {0,1,2}-survivable network design: theory and practice

Networks, uncertainty, applications and a crusade for optimality

Planning rapid transit networks

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