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Cutwidth: Obstructions and Algorithmic Aspects

Archontia C. Giannopoulou, Michał Pilipczuk, Jean-Florent Raymond, Dimitrios M. Thilikos, Marcin Wrochna
2018 Algorithmica  
As graphs of cutwidth at most k are closed under taking immersions, the results of Robertson and Seymour imply that there is a finite list of minimal immersion obstructions for admitting a cut layout of  ...  We prove that every minimal immersion obstruction for cutwidth at most k has size at most 2 O(k 3 log k) .  ...  Acknowledgements The second author thanks Mikołaj Bojańczyk for the common work on understanding and reinterpreting the Bodlaender-Kloks dynamic programming algorithm [3] , which influenced the bucketing  ... 
doi:10.1007/s00453-018-0424-7 fatcat:gla2zavswrdqzmglnloo5kmovq

Cutwidth: obstructions and algorithmic aspects [article]

Archontia C. Giannopoulou, Michał Pilipczuk, Jean-Florent Raymond, Dimitrios M. Thilikos, Marcin Wrochna
2017 arXiv   pre-print
Algorithms, 56(1):1--24, 2005] and [Cutwidth II: Algorithms for partial w-trees of bounded degree, J.  ...  We prove that every minimal immersion obstruction for cutwidth at most k has size at most 2^O(k^3 k).  ...  As finding a layout of optimum width is NP-hard [9] , the algorithmic and combinatorial aspects of cutwidth were intensively studied.  ... 
arXiv:1606.05975v2 fatcat:ppdh4ejxsnf4hbxoc5jd6e256u

Lean Tree-Cut Decompositions: Obstructions and Algorithms

Archontia C. Giannopoulou, O-Joung Kwon, Jean-Florent Raymond, Dimitrios M. Thilikos, Michael Wagner
2019 Symposium on Theoretical Aspects of Computer Science  
ACM Subject Classification Mathematics of computing → Graph algorithms; Theory of computation → Fixed parameter tractability Keywords and phrases tree-cut width, lean decompositions, immersions, obstructions  ...  In that sense, tree-cut decompositions can be seen as an edge-version of tree-decompositions and have algorithmic applications on problems that remain intractable on graphs of bounded treewidth.  ...  Acknowledgements We are grateful to Michał Pilipczuk and Marcin Wrochna for extensive discussions about the proof of Theorem 1.  ... 
doi:10.4230/lipics.stacs.2019.32 dblp:conf/stacs/GiannopoulouKRT19 fatcat:h6nfs2hbfbhrxav3fxzesqb2bi

Exploring the complexity of layout parameters in tournaments and semi-complete digraphs [article]

Florian Barbero, Christophe Paul, Michał Pilipczuk
2017 arXiv   pre-print
Our techniques can be also used to analyze the sizes of minimal obstructions for having small cutwidth under the induced subdigraph relation.  ...  We prove that: (1) Both parameters are NP-hard to compute and the known exact and parameterized algorithms for them have essentially optimal running times, assuming the Exponential Time Hypothesis; (2)  ...  and ω min D = min u,v∈V (D) u =v (ω(u, v) + ω(v, u)). 4 Kernelization aspects of Cutwidth and Ola On polynomial kernels As announced in the introduction, the Cutwidth and Ola problems, when respectively  ... 
arXiv:1706.00617v1 fatcat:7aoy6ah4znbbzc6u77xckl2hwe

Page 8632 of Mathematical Reviews Vol. , Issue 2001M [page]

2001 Mathematical Reviews  
The difference in the number of obstructions is at least exponential in the cutwidth and in the square-root of the multiway cutsize.  ...  Examples include graphs of bounded cutwidth and graphs of bounded multiway cutsize.  ... 

Computing the Chromatic Number Using Graph Decompositions via Matrix Rank [article]

Bart M.P. Jansen, Jesper Nederlof
2018 arXiv   pre-print
We present two algorithms for q-Coloring parameterized by cutwidth cutw: a deterministic one that runs in time O^*(2^ω· cutw), where ω is the matrix multiplication constant, and a randomized one with runtime  ...  We fill this gap by studying q-Coloring parameterized by cutwidth, and parameterized by pathwidth in bounded-degree graphs.  ...  Thi- likos, and Marcin Wrochna. Cutwidth: Obstructions and algorithmic aspects. In Proc. 11th IPEC, volume 63 of LIPIcs, pages 15:1-15:13, 2016. doi:10.4230/LIPIcs.IPEC.2016.15. 24 Petr A.  ... 
arXiv:1806.10501v1 fatcat:g74qmq5gmvh4zchs66p5wtcowe

Faster exact algorithms for hard problems: A parameterized point of view

Jochen Alber, Jens Gramm, Rolf Niedermeier
2001 Discrete Mathematics  
In this incomplete, personally biased survey, we re ect on some recent developments and prospects in the ÿeld of ÿxed parameter algorithms.  ...  Parts of this work are an updated and revised version of the invited paper 'Some prospects for e cient ÿxed parameter algorithms' of the third author in the proceedings of the 25th Conference on  ...  Bodlaender, Mike Fellows, Henning Fernau, Mike Hallett, Ton Kloks, Klaus-J orn Lange, Peter Rossmanith, and Ulrike Stege for contributing to our knowledge on parameterized complexity.  ... 
doi:10.1016/s0012-365x(00)00199-0 fatcat:ou2kxgxb5rebpdtkxz5qjnanme

3-Manifold Triangulations with Small Treewidth

Kristóf Huszár, Jonathan Spreer, Michael Wagner
2019 International Symposium on Computational Geometry  
FPT-algorithms in the field.  ...  Our results further validate the parameter of treewidth (and other related parameters such as cutwidth or congestion) to be useful for topological computing, and also shed more light on the scope of existing  ...  Acknowledgements We thank the developers of the free software Regina [11, 12] for creating a fantastic tool, and the anonymous reviewers for useful comments and suggestions regarding the exposition.  ... 
doi:10.4230/lipics.socg.2019.44 dblp:conf/compgeom/HuszarS19 fatcat:zzeippcnvbfwvk5yk533oqbvfm

Jungles, bundles, and fixed parameter tractability [article]

Fedor V. Fomin, Michał Pilipczuk
2012 arXiv   pre-print
We give a fixed-parameter tractable (FPT) approximation algorithm computing the path-width of a tournament, and more generally, of a semi-complete digraph.  ...  Based on this result, we prove that topological containment and rooted immersion problems are FPT on semi-complete digraphs.  ...  The main algorithmic advantage of cutwidth is that there is an FPT-approximation algorithm that in FPT time either finds a vertex ordering of width at most f (k), or constructs an obstruction for cutwidth  ... 
arXiv:1112.1538v2 fatcat:5nnestbt2vbsxh5mwjjmioor5u

On the treewidth of triangulated 3-manifolds [article]

Kristóf Huszár, Jonathan Spreer, Uli Wagner
2018 arXiv   pre-print
We derive these results from work of Agol, of Scharlemann and Thompson, and of Scharlemann, Schultens and Saito by exhibiting explicit connections between the topology of a 3-manifold M on the one hand  ...  In view of these algorithmic results, it is natural to ask whether every 3-manifold admits a triangulation of bounded treewidth.  ...  We would like to thank Arnaud de Mesmay and Stephan Tillmann for helpful discussions and remarks, and the anonymous reviewers for useful comments and suggestions regarding the exposition.  ... 
arXiv:1712.00434v3 fatcat:lkhjnoaicjfsbiqfmpzrfjuyvm

On the treewidth of triangulated 3-manifolds

Kristóf Huszár, Jonathan Spreer, Uli Wagner
2019 Journal of Computational Geometry  
We derive these results from work of Agol, of Scharlemann and Thompson, and of Scharlemann, Schultens and Saito by exhibiting explicit connections between the topology of a 3-manifold M on the one hand  ...  In view of these algorithmic results, it is natural to ask whether every 3-manifold admits a triangulation of bounded treewidth.  ...  Moreover, we would like to thank Jessica Purcell, Jennifer Schultens and Stephan Tillmann for helpful discussions, and the anonymous reviewers for useful comments and suggestions regarding the exposition  ... 
doi:10.20382/jogc.v10i2a5 dblp:journals/jocg/HuszarSW19 fatcat:fxkmg2nkkbewvepedijgdr3rwi

3-Manifold triangulations with small treewidth [article]

Kristóf Huszár, Jonathan Spreer
2018 arXiv   pre-print
FPT algorithms in the field.  ...  Our results further validate the parameter of treewidth (and other related parameters such as cutwidth, or congestion) to be useful for topological computing, and also shed more light on the scope of existing  ...  An algorithmic aspect of layered triangulations Layered triangulations are intimately related to the rich theory of surface homeomorphisms, and in particular the notion of the mapping class group.  ... 
arXiv:1812.05528v1 fatcat:6fj5j5nilnadtdwsvisnxm54um

A partial k-arboretum of graphs with bounded treewidth

Hans L. Bodlaender
1998 Theoretical Computer Science  
The notion of treewidth has seen to be a powerful vehicle for many graph algorithmic studies.  ...  ed cutwidth of G. For the relation between the topological bandwidth and cutwidth of a graph, see [29] . We also have the following relation between cutwidth and pathwidth.  ...  The obstruction sets of graphs with pathwidths 1 and 2 are also known [52] .  ... 
doi:10.1016/s0304-3975(97)00228-4 fatcat:pyfovznhxjebhlvhu5h3u5ffju

Confronting intractability via parameters

Rodney G. Downey, Dimitrios M. Thilikos
2011 Computer Science Review  
This theory has a large number of successes in terms of a rich collection of algorithmic techniques both practical and theoretical, and a fine-grained intractability theory.  ...  One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks.  ...  Kolliopoulos, Moritz Müller, Saket Saurabh, and Geoff Whittle for corrections and helpful comments.  ... 
doi:10.1016/j.cosrev.2011.09.002 fatcat:4efih5lobfbjdgyuu2ccbqlbbq

Confronting Intractability via Parameters [article]

Rodney G. Downey, Dimitrios M. Thilikos
2011 arXiv   pre-print
This theory has a large number of successes in terms of a rich collection of algorithmic techniques both practical and theoretical, and a fine-grained intractability theory.  ...  One approach to confronting computational hardness is to try to understand the contribution of various parameters to the running time of algorithms and the complexity of computational tasks.  ...  Kolliopoulos, Moritz Müller, Saket Saurabh, and Geoff Whittle for corrections and helpful comments.  ... 
arXiv:1106.3161v6 fatcat:6eqwtzfmunffzokn47lqyb6xwq
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