Improved algorithms for feedback vertex set problems
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Improved parameterized algorithms for the feedback vertex set problem on both unweighted and weighted graphs are presented, both of which run in time O(5^kkn^2).About:
This article is published in Journal of Computer and System Sciences.The article was published on 2008-11-01 and is currently open access. It has received 155 citations till now. The article focuses on the topics: Feedback vertex set & Neighbourhood (graph theory).read more
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Journal ArticleDOI
A fixed-parameter algorithm for the directed feedback vertex set problem
TL;DR: New algorithmic techniques are developed that result in an algorithm with running time 4k!
Posted Content
Solving connectivity problems parameterized by treewidth in single exponential time
Marek Cygan,Jesper Nederlof,Marcin Pilipczuk,Michał Pilipczuk,Joham M.M. van Rooij,Jakub Onufry Wojtaszczyk +5 more
TL;DR: It is shown that the aforementioned gap cannot be breached for some problems that aim to maximize the number of connected components like Cycle Packing, and in several cases it is able to show that improving those constants would cause the Strong Exponential Time Hypothesis to fail.
Book ChapterDOI
Deterministic single exponential time algorithms for connectivity problems parameterized by treewidth
TL;DR: Two new approaches rooted in linear algebra, based on matrix rank and determinants, which provide deterministic c tw | V | O ( 1 ) time algorithms, also for weighted and counting versions of connectivity problems are presented.
Proceedings ArticleDOI
Planar F-Deletion: Approximation, Kernelization and Optimal FPT Algorithms
TL;DR: In this paper, a constant factor approximation algorithm for the optimization version of planar F-deletion was proposed, which runs in time O(exp(2, O(k))n).
Journal ArticleDOI
Linear Kernels and Single-Exponential Algorithms Via Protrusion Decompositions
Eun Jung Kim,Alexander Langer,Christophe Paul,Felix Reidl,Peter Rossmanith,Ignasi Sau,Somnath Sikdar +6 more
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.
References
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Book
Introduction to Algorithms
TL;DR: The updated new edition of the classic Introduction to Algorithms is intended primarily for use in undergraduate or graduate courses in algorithms or data structures and presents a rich variety of algorithms and covers them in considerable depth while making their design and analysis accessible to all levels of readers.
Book ChapterDOI
Reducibility Among Combinatorial Problems
TL;DR: The work of Dantzig, Fulkerson, Hoffman, Edmonds, Lawler and other pioneers on network flows, matching and matroids acquainted me with the elegant and efficient algorithms that were sometimes possible.
Book
Parameterized Complexity
TL;DR: An approach to complexity theory which offers a means of analysing algorithms in terms of their tractability, and introduces readers to new classes of algorithms which may be analysed more precisely than was the case until now.