Treewidth: Algorithmic techniques and results

Bodlaender, Hans L.

doi:10.1007/bfb0029946

Cited by 168 publications

(123 citation statements)

References 95 publications

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“…Such results usually generalize similar polynomial time solvability results for trees; see for instance Bodlaender (1997). In this section, we show how to extend the results of the previous two sections to graphs of bounded treewidth.…”

Section: Operator Graphs That Have Bounded Treewidthsupporting

confidence: 75%

Scheduling of pipelined operator graphs

Bodlaender

Schuurman

Woeginger

2011

J Sched

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We investigate a class of scheduling problems that arise in the optimization of SQL queries for parallel machines (Chekuri et al. in PODS'95, pp. 255-265, 1995). In these problems, an undirected graph is used to represent communication and inter-operator parallelism. The goal is to minimize the global response time of the system.We provide a polynomial time approximation scheme for the special cases where the operator graph is a tree, thereby improving on a polynomial time 2.87-approximation algorithm by Chekuri et al. The approximation scheme is generalized to the case where the operator graph has treewidth bounded by a constant. We analyze instances with small response times for general operator graphs: Deciding whether a response time of four time units can be reached is easy, but deciding whether a response time of six time units can be reached is NP-hard. Finally, we prove that for general operator graphs the existence of a polynomial time approx- imation algorithm with worst case performance guarantee better than 4/3 would imply P = NP.

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Section: Operator Graphs That Have Bounded Treewidthsupporting

confidence: 75%

Scheduling of pipelined operator graphs

Bodlaender

Schuurman

Woeginger

2011

J Sched

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“…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%

The Parameterized Complexity of the Induced Matching Problem in Planar Graphs

Moser

Sikdar

Frontiers in Algorithmics

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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.

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“…Furthermore, many graphs arising from natural applications have bounded treewidth. A good survey on the topic is given by Bodlaender [Bodlaender 1997]. Here is one of the many equivalent definitions of treewidth:…”

Section: Defining Treewidthmentioning

confidence: 99%

“…We observe that it is possible to produce such a tree decomposition for a graph of treewidth k in time linear in the number of edges and vertices (but exponential in k) [Bodlaender 1997]. Assuming k is constant, we are therefore able to produce a tree decomposition in polynomial time.…”

Section: Defining Treewidthmentioning

confidence: 99%

Simultaneous Source Location

Andreev¹,

Garrod²,

Maggs³

et al. 2004

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques

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We consider the problem of Simultaneous Source Location -selecting locations for sources in a capacitated graph such that a given set of demands can be satisfied simultaneously, with the goal of minimizing the number of locations chosen. For general directed and undirected graphs we give an O(log D) approximation algorithm, where D is the sum of demands, and prove matching Ω(log D) hardness results assuming P = NP. For undirected trees, we give an exact algorithm and show how this can be combined with a result of Räcke to give a solution that exceeds edge capacities by at most O(log 2 n log log n), where n is the number of nodes. For undirected graphs of bounded treewidth we show that the problem is still NP-Hard, but we are able to give a PTAS with at most (1 + ) violation of the capacities for arbitrarily small , or a (k + 1)-approximation with exact capacities, where k is the treewidth.

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Treewidth: Algorithmic techniques and results

Cited by 168 publications

References 95 publications

Scheduling of pipelined operator graphs

Scheduling of pipelined operator graphs

The Parameterized Complexity of the Induced Matching Problem in Planar Graphs

Simultaneous Source Location

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