Treewidth: Characterizations, Applications, and Computations

Bodlaender, Hans L.

doi:10.1007/11917496_1

Cited by 78 publications

(63 citation statements)

References 53 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We extend his work and obtain a linear-time algorithm on graphs of bounded treewidth [7]. Note that compared to Zito's work our dynamic programming approach uses a different encoding to store the partial solutions in the updating process.…”

Section: Induced Matching On Graphs With Bounded Treewidthmentioning

confidence: 93%

“…Here we describe only the basic definitions and those parts of the algorithm which are important in showing the improved running time. We also refer the reader to the standard literature about tree decompositions [5][6][7]30]. The definitions of tree decomposition and nice tree decomposition can be found in the appendix.…”

Section: Induced Matching On Graphs With Bounded Treewidthmentioning

confidence: 99%

See 1 more Smart Citation

The Parameterized Complexity of the Induced Matching Problem in Planar Graphs

Moser

Sikdar

Frontiers in Algorithmics

View full text Add to dashboard Cite

Given a graph G and an integer k ≥ 0, the NP-complete Induced Matching problem asks whether there exists an edge subset M of size at least k such that M is a matching and no two edges of M are joined by an edge of G. The complexity of this problem on general graphs as well as on many restricted graph classes has been studied intensively. However, other than the fact that the problem is W[1]-hard on general graphs little is known about the parameterized complexity of the problem in restricted graph classes. In this work, we provide first-time fixed-parameter tractability results for planar graphs, bounded-degree graphs, graphs with girth at least six, bipartite graphs, line graphs, and graphs of bounded treewidth. In particular, we give a linear-size problem kernel for planar graphs.

show abstract

Section: Induced Matching On Graphs With Bounded Treewidthmentioning

confidence: 93%

Section: Induced Matching On Graphs With Bounded Treewidthmentioning

confidence: 99%

The Parameterized Complexity of the Induced Matching Problem in Planar Graphs

Moser

Sikdar

Frontiers in Algorithmics

View full text Add to dashboard Cite

show abstract

“…Fortunately, most of the real-life pipe networks are outerplanar or, taking this more generally, the corresponding graphs have bounded treewidth; see e.g. [5,6,10]. For this type of networks we have the following results.…”

Section: Algorithms For Graphs Of Bounded Treewidthmentioning

confidence: 99%

“…Also, there are fast algorithms that construct tree decompositions of optimal width for graphs of treewidth at most three (including outerplanar graphs), see e.g. [6] for a discussion.…”

Section: Theorem 16mentioning

confidence: 99%

The Valve Location Problem in Simple Network Topologies

Bodlaender

Hendriks

Grigoriev

et al. 2010

INFORMS Journal on Computing

Self Cite

View full text Add to dashboard Cite

To control possible spills in liquid or gas transporting pipe systems, the systems are usually equipped with shutoff valves. In case of an accidental leak these valves separate the system into a number of pieces limiting the spill effect. In this paper, we consider the problem, for a given edge-weighted network representing a pipe system and for a given number of valves, to place the valves in the network in such a way that the maximum possible spill, i.e. the maximum total weight of a piece, is minimized. We show that the problem is NP-hard even if restricted to any of the following settings: (i) for series-parallel graphs and hence for graphs of treewidth two; (ii) if all edge weights equal one. If the network is a simple path, a cycle, or a tree, the problem can be solved in polynomial time. We also give a pseudo-polynomial time algorithm and a fully polynomial approximation scheme for networks of bounded treewidth.

show abstract

“…The result of the branchwidth implies a 1.5-approximation algorithm for the treewidth of planar graphs. Readers may refer to the recent papers by Bodlaender [8] and Hicks et al [15] for extensive literature in the theory and application of branch/tree-decompositions.…”

Section: Introductionmentioning

confidence: 99%

Computing Branch Decomposition of Large Planar Graphs

Bian

Experimental Algorithms

View full text Add to dashboard Cite

A graph of small branchwidth admits efficient dynamic programming algorithms for many NP-hard problems on the graph. A key step in these algorithms is to find a branch decomposition of small width for the graph. Given a planar graph G of n vertices, an optimal branch decomposition of G can be computed in polynomial time, e.g., by the edge-contraction method in O(n 3 ) time. All known algorithms for the planar branch decomposition use Seymour and Thomas procedure which, given an integer β, decides whether G has the branchwidth at least β or not in O(n 2 ) time. Recent studies report efficient implementations of Seymour and Thomas procedure that compute the branchwidth of planar graphs of size up to one hundred thousand edges in a practical time and memory space. Using the efficient implementations as a subroutine, it is reported that the edge-contraction method computes an optimal branch decomposition for planar graphs of size up to several thousands edges in a practical time but it is still time consuming for graphs with larger size. In this paper, we propose divide-and-conquer based algorithms of using Seymour and Thomas procedure to compute optimal branch decompositions of planar graphs. Our algorithms have time complexity O(n 3 ). Computational studies show that our algorithms are much faster than the edge-contraction algorithms and can compute an optimal branch decomposition of some planar graphs of size up to 50,000 edges in a practical time.

show abstract

Treewidth: Characterizations, Applications, and Computations

Cited by 78 publications

References 53 publications

The Parameterized Complexity of the Induced Matching Problem in Planar Graphs

The Parameterized Complexity of the Induced Matching Problem in Planar Graphs

The Valve Location Problem in Simple Network Topologies

Computing Branch Decomposition of Large Planar Graphs

Contact Info

Product

Resources

About