Improved Steiner tree algorithms for bounded treewidth

Chimani, Markus; Mutzel, Petra; Zey, Bernd

doi:10.1016/j.jda.2012.04.016

Cited by 32 publications

(24 citation statements)

References 20 publications

(30 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Chimani et al [10] give an efficient algorithm for Steiner tree for graphs given with a tree decomposition, that runs in time O(B 2 k+2 kn) time, with k the width of the tree decomposition. We have chosen not to use the coloring scheme from Chimani et al [10], but instead use hash tables (as discussed above) to store the tables. Of course, our choice has the disadvantage that we lose a guarantee on the worst case running time (as we cannot rule out scenarios where many elements are hashed to the same position in the hash table), but gives a simple mechanism which works in practice very well.…”

Section: Methodsmentioning

confidence: 99%

“…Our description of the classic algorithm departs somewhat from the description in Korach and Solel [21], but the underlying technique is essentially the same. We have chosen not to use the coloring schemes from Chimani et al [10], but instead use hash tables to store information. Wei-Kleiner [30] gives a tree decomposition based algorithm for Steiner tree, that particularly aims at instances with a small set of Steiner vertices.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Speeding Up Dynamic Programming with Representative Sets: An Experimental Evaluation of Algorithms for Steiner Tree on Tree Decompositions

2014

View full text Add to dashboard Cite

Abstract. Dynamic programming on tree decompositions is a frequently used approach to solve otherwise intractable problems on instances of small treewidth. In recent work by Bodlaender et al. [7], it was shown that for many connectivity problems, there exist algorithms that use time, linear in the number of vertices, and single exponential in the width of the tree decomposition that is used. The central idea is that it suffices to compute representative sets, and these can be computed efficiently with help of Gaussian elimination. In this paper, we give an experimental evaluation of this technique for the Steiner Tree problem. A comparison of the classic dynamic programming algorithm and the improved dynamic programming algorithm that employs the table reduction shows that the new approach gives significant improvements on the running time of the algorithm and the size of the tables computed by the dynamic programming algorithm, and thus that the rank based approach from Bodlaender et al. [7] does not only give significant theoretical improvements but also is a viable approach in a practical setting, and showcases the potential of exploiting the idea of representative sets for speeding up dynamic programming algorithms.

show abstract

Section: Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Speeding Up Dynamic Programming with Representative Sets: An Experimental Evaluation of Algorithms for Steiner Tree on Tree Decompositions

2014

View full text Add to dashboard Cite

show abstract

“…Note that computing the values of subsolution κ i are linear in the treewidth. Thus our time complexity is of the same as order as that of [6]. In particular, it is linear for graphs with fixed treewidth, in this case the tree decomposition can also be computed in linear time and hence the total complexity is linear.…”

Section: Discussionmentioning

confidence: 90%

Secluded Connectivity Problems

et al. 2016

View full text Add to dashboard Cite

Consider a setting where possibly sensitive information sent over a path in a network is visible to every neighbor of the path, i.e., every neighbor of some node on the path, thus including the nodes on the path itself. The exposure of a path P can be measured as the number of nodes adjacent to it, denoted by N [P ]. A path is said to be secluded if its exposure is small. A similar measure can be applied to other connected subgraphs, such as Steiner trees connecting a given set of terminals. Such subgraphs may be relevant due to considerations of privacy, security or revenue maximization. This paper considers problems related to minimum exposure connectivity structures such as paths and Steiner trees. It is shown that on unweighted undirected n-node graphs, the problem of finding the minimum exposure path connecting a given pair of vertices is strongly inapproximable, i.e., hard to approximate within a factor of O(2 log 1− n ) for any > 0 (under an appropriate complexity assumption), but is approximable with ratio √ ∆ + 3, where ∆ is the maximum degree in the graph. One of our main results concerns the class of bounded-degree graphs, which is shown to exhibit the following interesting dichotomy. On the one hand, the minimum exposure path problem is NP-hard on node-weighted or directed boundeddegree graphs (even when the maximum degree is 4). On the other hand, we present *

show abstract

“…Similarly, DP algorithms applied to tree decompositions to solve the STP use time polynomial in | V | and exponential in the treewidth, resulting in polynomial‐time algorithms on graphs with a bounded treewidth [31, 48, 129]. Roughly speaking, the treewidth of a graph G measures how “similar” is G to a tree.…”

Section: Exact Methodsmentioning

confidence: 99%

Solving Steiner trees: Recent advances, challenges, and perspectives

Ljubić

2020

Networks

View full text Add to dashboard Cite

The Steiner tree problem (STP) in graphs is one of the most studied problems in combinatorial optimization. Since its inception in 1970, numerous articles published in the journal Networks have stimulated new theoretical and computational studies on Steiner trees: from approximation algorithms, heuristics, metaheuristics, all the way to exact algorithms based on (mixed) integer linear programming, fixed parameter tractability, or combinatorial branch‐and‐bounds. The pervasive applicability and relevance of Steiner trees have been reinforced by the recent 11th DIMACS Implementation Challenge in 2014 and the PACE 2018 Challenge. This article provides an overview of the rich developments from the last three decades for the STP in graphs and highlights the most recent computational studies for some of its closely related variants.

show abstract

Improved Steiner tree algorithms for bounded treewidth

Cited by 32 publications

References 20 publications

Speeding Up Dynamic Programming with Representative Sets: An Experimental Evaluation of Algorithms for Steiner Tree on Tree Decompositions

Speeding Up Dynamic Programming with Representative Sets: An Experimental Evaluation of Algorithms for Steiner Tree on Tree Decompositions

Secluded Connectivity Problems

Solving Steiner trees: Recent advances, challenges, and perspectives

Contact Info

Product

Resources

About