SteinLib: An Updated Library on Steiner Tree Problems in Graphs

Koch, Thorsten; Martín, Alexander; Voß, Stefan

doi:10.1007/978-1-4613-0255-1_9

Cited by 125 publications

(104 citation statements)

References 40 publications

Supporting

Mentioning

102

Contrasting

Order By: Relevance

“…For Min Steiner Tree, we consider five data sets taken from the SteinLib [KMV01], namely B, C, D, I640, and PUC. Cut coordination is achieved by considering the cut diversity w.r.t.…”

Section: Pure Cutting Plane Settingmentioning

confidence: 99%

Coordinated cutting plane generation via multi-objective separation

2012

View full text Add to dashboard Cite

In cutting plane methods, the question of how to generate the "best possible" set of cuts is both central and crucial. We propose a lexicographic multi-objective cutting plane generation scheme that generates, among all the maximally violated valid inequalities of a given family, an inequality that is undominated and maximally diverse w.r.t. the cuts that were previously found. By optimizing a diversity measure, we introduce a form of coordination between successive cuts. Our focus is on valid inequalities with 0-1 coefficients in the left-hand side and a constant right-hand side, which encompasses several families of valid inequalities. As cut diversity measure, we consider an aggregate of the 1-norm distances w.r.t. the normal vectors of the previous cuts. In this case, our lexicographic multi-objective separation problem reduces to the standard separation problem with different values for the objective function coefficients. The impact of our coordinated cutting plane generation scheme is assessed in a pure cutting plane setting when separating Stable Set and Cut Set inequalities for, respectively, the Max Clique and Min Steiner Tree problems. Compared to the standard separation of undominated maximally violated cuts, we close the same fraction of the duality gap in a considerably smaller number of rounds and cuts. The potential of our scheme is also indicated by the results obtained in a cut-and-branch setting for Max Clique, where cut coordination allows for a substantial reduction, on average, of the number of branch-and-bound nodes.

show abstract

“…For Min Steiner Tree, we consider five data sets taken from the SteinLib [KMV01], namely B, C, D, I640, and PUC. Cut coordination is achieved by considering the cut diversity w.r.t.…”

Section: Pure Cutting Plane Settingmentioning

confidence: 99%

Coordinated cutting plane generation via multi-objective separation

2012

View full text Add to dashboard Cite

show abstract

“…There are two major benchmark libraries for the Steiner problem in networks: the collection in the ORLibrary [2] and SteinLib [15]. We have chosen the group with the largest instances (2500 vertices) from the OR-Library and a group of VLSI-instances (up to 6836 vertices) from SteinLib for the comparisons in this paper.…”

Section: Appendix 1: Empirical Results On Benchmark Instancesmentioning

confidence: 99%

Primal-Dual Approaches to the Steiner Problem

Polzin

Daneshmand

2000

Approximation Algorithms for Combinatorial Optimization

View full text Add to dashboard Cite

Abstract. We study several old and new algerithms for computing lower and upper bounds for the Steiner problem in networks using dual-ascent and primal-dual strategies. These strategies have been proven to be very useful. for the algorithmic treatment of the Steiner problem. We show that none of the known algorithms can both generate tight lower bounds empirically and guarantee their quality theoretically; and we present a new algorithm which combines both features. The new algorithm has running time O(relogn) and guarantees a ratio of at most two between the generated upper and lower bounds, whereas the fastest previous algorithm with comparably tight empiricalbounds has running time O( e 2 ) without a constant approximation ratio. We show that the approximation ratio two between the bounds can even be achieved in time O(e + nlog n), improving the.previous time bound of O(n 2 log n).The presented insights can also behelpful for the development of further relaxation based approximation algorithms for the Steiner problem.

show abstract

“…We evaluated the performance of our proposed method using the test sets provided in SteinLib [13]. The results of the numerical simulations indicate that the proposed method achieves a stable performance compared with the conventional KMB algorithm.…”

Section: Discussionmentioning

confidence: 99%

“…From this perspective, we set α to 30% of the maximum edge cost for each network in these simulations. Tables 1, 2, and 3 present the error rates obtained by the conventional KMB algorithm and the proposed method for the test sets B, C, and D in SteinLib [13]. It is seen from these tables that the proposed method achieved a better performance than the conventional KMB algorithm in the maximum and median values.…”

Section: Numerical Experimentsmentioning

confidence: 98%

See 1 more Smart Citation

An Effective Construction Algorithm for the Steiner Tree Problem Based on Edge Betweenness

Kimura

Jin’no

2016

Journal of Signal Processing

View full text Add to dashboard Cite

Given an undirected weighted graph G = (V, E, c) and a set T , where V is the set of nodes, E is the set of edges, c is a cost function, and T is a subset of nodes called terminals, the Steiner tree problem in graphs is that of finding the subgraph of the minimum weight that connects all of terminals.The Steiner tree problem is an example of an NP-complete combinatorial optimization problem [1]. Thus, approximate methods are usually employed for constructing the Steiner tree. In this study, the KMB algorithm [2], which is an efficient construction method for Steiner tree problems, is enhanced by considering edge betweenness [3]. The results of numerical simulations indicate that our improved KMB algorithm shows good performances for various types of benchmark Steiner tree problems.

show abstract

SteinLib: An Updated Library on Steiner Tree Problems in Graphs

Cited by 125 publications

References 40 publications

Coordinated cutting plane generation via multi-objective separation

Coordinated cutting plane generation via multi-objective separation

Primal-Dual Approaches to the Steiner Problem

An Effective Construction Algorithm for the Steiner Tree Problem Based on Edge Betweenness

Contact Info

Product

Resources

About