Open AccessBook Chapter10.1007/978-3-642-10217-2_37

Simpler Parameterized Algorithm for OCT

- 10 Nov 2009

- Vol. 5874, pp 380-384

TL;DR: This work gives a simple and intuitive fixed parameter tractable algorithm for the Odd Cycle Transversal problem, running in time O(3 k ·k ·|E| ·|V|).

Abstract: We give a simple and intuitive fixed parameter tractable algorithm for the Odd Cycle Transversal problem, running in time O(3 k ·k ·|E| ·|V|). Our algorithm is best viewed as a reinterpretation of the classical Iterative Compression algorithm for Odd Cycle Transversal by Reed, Smith and Vetta [8].

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In this paper, a simple and intuitive fixed parameter tractable algorithm for the odd cycle transversal problem was given, running in time O ( 3 · k · |E| · |V | ).

Citations

•Journal Article•10.1145/2566616

Faster Parameterized Algorithms Using Linear Programming

Daniel Lokshtanov, +4 more

- 30 Oct 2014

- ACM Transactions on Algorithms

TL;DR: It is argued that combining previously known preprocessing rules with the most straightforward branching algorithm yields an O*(2.618k) algorithm for the problem, and a kernel is obtained for the standard parameterization of Vertex Cover with at most 2k − clog k vertices, simpler than previously known kernels achieving the same size bound.

...read moreread less

221

•Proceedings Article•10.5555/2133036.2133097

Known algorithms on graphs of bounded treewidth are probably optimal

Daniel Lokshtanov, +2 more

- 23 Jan 2011

TL;DR: In this paper, the authors obtained lower bounds on the running time of algorithms for solving problems on graphs of bounded treewidth, and proved the results under the Strong Exponential Time Hypothesis of Impagliazzo and Paturi, assuming that SAT cannot be solved in (2 - ∈)nmO(1) time.

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187

•Journal Article•10.1145/2500119

Finding small separators in linear time via treewidth reduction

Dániel Marx, +2 more

- 03 Oct 2013

- ACM Transactions on Algorithms

TL;DR: A method for reducing the treewidth of a graph while preserving all of its minimal separators up to a certain fixed size is presented, and this technique turns out to be relevant for H-coloring problems as well as cardinality constrained variants of the classical H- Coloring problem.

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163

•Journal Article•10.1145/2797140

Linear Kernels and Single-Exponential Algorithms Via Protrusion Decompositions

Eun Jung Kim, +6 more

- 08 Dec 2015

- ACM Transactions on Algorithms

TL;DR: It is shown that any parameterized graph problem (with parameter k) that has a finite integer index and such that Yes-instances have a treewidth-modulator of size O(k) admits a linear kernel on the class of H-topological-minor-free graphs, for any fixed graph H.

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146

•Posted Content

Faster Parameterized Algorithms using Linear Programming

Daniel Lokshtanov, +4 more

- 05 Mar 2012

- arXiv: Data Structures and Algorithms

TL;DR: In this article, the authors investigated the parameterized complexity of vertex cover parameterized by the difference between the size of the optimal solution and the value of the LP relaxation of the problem.

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References

•Book

Invitation to fixed-parameter algorithms

Rolf Niedermeier

- 01 Jan 2006

TL;DR: This paper discusses Fixed-Parameter Algorithms, Parameterized Complexity Theory, and Selected Case Studies, and some of the techniques used in this work.

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1.9K

Journal Article•10.1016/J.ORL.2003.10.009

Finding odd cycle transversals

Bruce Reed, +2 more

- 01 Jul 2004

- Operations Research Letters

TL;DR: An O(mn) algorithm is presented to determine whether a graph G with m edges and n vertices has an odd cycle transversal of order at most k, for any fixed k, and an algorithm is obtained that determines a graph has a half integral packing of odd cycles of weight k.

...read moreread less

523

Journal Article•10.1145/1411509.1411511

A fixed-parameter algorithm for the directed feedback vertex set problem

Jianer Chen, +4 more

- 05 Nov 2008

- Journal of the ACM

TL;DR: New algorithmic techniques are developed that result in an algorithm with running time 4^k!

...read moreread less

394

Journal Article•10.1007/S00453-008-9233-8

Chordal Deletion is Fixed-Parameter Tractable

Dániel Marx

- 01 Aug 2010

- Algorithmica

TL;DR: In this article, a uniformly polynomial-time algorithm for chordal deletion is presented, where the running time is f(k)⋅n α for some constant α not depending on k and some f depending only on k. For large values of n, this algorithm is much better than trying all the O(n k ) possibilities.

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168

Journal Article•10.1007/S00224-007-1345-Z

An O(2O(k)n3) FPT Algorithm for the Undirected Feedback Vertex Set Problem

Frank Dehne, +4 more

- 01 Oct 2007

- Theory of Computing Systems \/ Mathemati...

TL;DR: It is proved that no FPT algorithm with a parameter function of the form O(2o(k)) is possible, unless there is an unlikely collapse of parameterized complexity classes, namely FPT = M[1].

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137

Simpler Parameterized Algorithm for OCT

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Citations

Faster Parameterized Algorithms Using Linear Programming

Known algorithms on graphs of bounded treewidth are probably optimal

Finding small separators in linear time via treewidth reduction

Linear Kernels and Single-Exponential Algorithms Via Protrusion Decompositions

Faster Parameterized Algorithms using Linear Programming

References

Invitation to fixed-parameter algorithms

Finding odd cycle transversals

A fixed-parameter algorithm for the directed feedback vertex set problem

Chordal Deletion is Fixed-Parameter Tractable

An O(2O(k)n3) FPT Algorithm for the Undirected Feedback Vertex Set Problem

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Invitation to fixed-parameter algorithms

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