Primal-dual approximation algorithms for the Prize-Collecting Steiner Tree Problem

Feofiloff, Paulo; Fernandes, Cristina G.; Ferreira, Carlos Eduardo; Pina, José Coelho de

doi:10.1016/j.ipl.2007.03.012

Cited by 23 publications

(15 citation statements)

References 6 publications

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“…The new algorithm of Feofiloff et al (2003) achieves a ratio of 2 − 2/n within the same time complexity. A multistart heuristic that makes use of a randomized Goemans and Williamson algorithm and local search with perturbations is presented in Canuto et al (2001).…”

Section: Applications and Survey Of The Literaturementioning

confidence: 94%

An exact algorithm for the node weighted Steiner tree problem

Cordone

Trubian

2006

4OR

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The Node Weighted Steiner Tree Problem (NW-STP) is a generalization of the Steiner Tree Problem. A lagrangean heuristic presented in Engevall et al. (1998), and based on the work in Lucena (1992), solves the problem by relaxing an exponential family of generalized subtour elimination constraints and taking into account only the violated ones as the computation proceeds. In Engevall et al. (1998) the computational results refer to complete graphs up to one hundred vertices. In this paper, we present a branch-and-bound algorithm based on this formulation. Its performance on the instances from the literature confirms the effectiveness of the approach. The experimentation on a newly generated set of benchmark problems, more similar to the real-world applications, shows that the approach is still valid, provided that suitable refinements on the bounding procedures and a preprocessing phase are introduced. The algorithm solves to optimality all of the considered instances up to one thousand vertices, with the exception of 11 hard instances, derived from the literature of a similar problem, the Prize Collecting Steiner Tree Problem.

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Section: Applications and Survey Of The Literaturementioning

confidence: 94%

An exact algorithm for the node weighted Steiner tree problem

Cordone

Trubian

2006

4OR

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“…A 2-approximation with O(n 3 logn) running time is proposed in [3] by using the primal-dual method, improved by [4] to O(n 2 logn) execution time. That runtime was maintained in [5], which improved the approximation factor to 2 − 2 n . Exact methods were devised in [6,7] using mixed integer linear programming, and a branch-and-cut algorithm based on directed edges was proposed to solve the model.…”

Section: Related Workmentioning

confidence: 99%

A Fast Prize-Collecting Steiner Forest Algorithm for Functional Analyses in Biological Networks

Akhmedov

LeNail

Bertoni

et al. 2017

Lecture Notes in Computer Science

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The Prize-collecting Steiner Forest (PCSF) problem is NPhard, requiring extreme computational effort to find exact solutions for large inputs. We introduce a new heuristic algorithm for PCSF which preserves the quality of solutions obtained by previous heuristic approaches while reducing the runtime by a factor of 10 for larger graphs. By decreasing the draw on computational resources, this algorithm affords systems biologists the opportunity to analyze larger biological networks faster and narrow their analyses to individual patients.

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“…Due to the large applicability of the PCSTP, a number of approximation algorithms were proposed for it [Bienstock et al 1993, Goemans and Williamson 1996, Johnson et al 2000, Feofllofl et al 2007. A multi-start algorithm with Variable Neighborhood Search and Path-relinking [Canuto et al 2001] was applied to the instances of classes K, P, C and D. The initial solutions of the multi-start algorithm were built with a primal-dual method [Goemans and Williamson 1996] …”

Section: The Prize Collecting Steiner Tree Problemmentioning

confidence: 99%

A Hybrid Transgenetic Algorithm for the Prize Collecting Steiner Tree Problem

Schmidt

Goldbarg

2007

Seventh International Conference on Intelligent Systems Design and Applications (ISDA 2007)

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Evolutionary algorithms are effective search tools for tackling difficult optimization problems. In this paper an algorithm based on living processes where cooperation is the main evolutionary strategy is applied to the Prize Collecting Steiner Tree Problem, an NP-hard combinatorial optimization problem. The Transgenetic Algorithm presented here is hybridized with path-relinking. Computational results of an experiment performed with benchmark instances are reported. The results obtained for the Prize Collecting Steiner Tree Problem with the application of the hybrid Transgenetic Algorithm are compared with the results of three effective approaches presented previously. The computational experiment shows that the proposed approach is very competitive concerning both quality of solution and processing time.

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Primal-dual approximation algorithms for the Prize-Collecting Steiner Tree Problem

Cited by 23 publications

References 6 publications

An exact algorithm for the node weighted Steiner tree problem

An exact algorithm for the node weighted Steiner tree problem

A Fast Prize-Collecting Steiner Forest Algorithm for Functional Analyses in Biological Networks

A Hybrid Transgenetic Algorithm for the Prize Collecting Steiner Tree Problem

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