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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

A Menger-like property of tree-cut width [article]

Archontia C. Giannopoulou and O-joung Kwon and Jean-Florent Raymond and Dimitrios M. Thilikos
2020 arXiv   pre-print
We show that every graph admits a tree-cut decomposition of minimum width that additionally satisfies an edge-connectivity condition analogous to Thomas' leanness.  ...  In this paper, we consider tree-cut decompositions, that have been introduced by Wollan as a possible edge-version of tree decompositions [The structure of graphs not admitting a fixed immersion.  ...  Acknowledgments The authors wish to thank Michał Pilipczuk and Marcin Wrochna for valuable discussions about lean tree-cut decompositions.  ... 
arXiv:1808.00863v3 fatcat:ubflmpooljdj7feproa7bjvht4

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  ...  (J Algorithms 56(1):1-24, 2005; Algorithmica (2019) 81:557-588 J Algorithms 56 (1) : 2005), our algorithm has the advantage of being simpler and self-contained; arguably, it explains better the combinatorics  ...  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.  ...  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  ...  In future work, we aim to explore and use linkedness for tree-cut decompositions and carving decompositions in a similar manner as presented here. Acknowledgements.  ... 
arXiv:1606.05975v2 fatcat:ppdh4ejxsnf4hbxoc5jd6e256u

On objects dual to tree-cut decompositions [article]

Łukasz Bożyk, Oscar Defrain, Karolina Okrasa, Michał Pilipczuk
2022 arXiv   pre-print
In this work we propose a variant of the definition of tree-cut width that is functionally equivalent to the original one, but for which we can state and prove a tight duality theorem relating it to naturally  ...  Tree-cut width is a graph parameter introduced by Wollan that is an analogue of treewidth for the immersion order on graphs in the following sense: the tree-cut width of a graph is functionally equivalent  ...  [GKRT19, GKRT21] proved a result about the existence of lean tree-cut decompositions of optimum width, which is an analogue of a classic result of Thomas for tree decompositions [Tho90] .  ... 
arXiv:2103.14667v2 fatcat:lkil7zlcjza5fpvct6jjfnbijy

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

Florian Barbero, Christophe Paul, Michał Pilipczuk
2017 arXiv   pre-print
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)  ...  Our techniques can be also used to analyze the sizes of minimal obstructions for having small cutwidth under the induced subdigraph relation.  ...  Lean orderings and decompositions are commonly used in the analysis of obstructions for various width notions, as well as for proving well quasi-order results.  ... 
arXiv:1706.00617v1 fatcat:7aoy6ah4znbbzc6u77xckl2hwe

High-performance routing at the nanometer scale

Jarrod A. Roy, Igor L. Markov
2007 Computer-Aided Design (ICCAD), IEEE International Conference on  
In this work we describe significant improvements to core routing technologies and outperform the best results from the ISPD '07 Global Routing Contest and ICCAD 2007 in terms of route completion and total  ...  This work was partially supported by the National Science Foundation (NSF) and the Horace H. Rackham School of Graduate Studies at the University of Michigan.  ...  This decomposition has been traditionally done using Minimal Spanning Tree (MST) algorithms, but using fast and extremely accurate Rectilinear Steiner Minimal Tree (RSMT) construction algorithms has become  ... 
doi:10.1109/iccad.2007.4397313 dblp:conf/iccad/RoyM07 fatcat:rrg6hnvy2bfmlnkbxgr5jmuw5y

High-Performance Routing at the Nanometer Scale

Jarrod A. Roy, Igor L. Markov
2008 IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems  
In this work we describe significant improvements to core routing technologies and outperform the best results from the ISPD '07 Global Routing Contest and ICCAD 2007 in terms of route completion and total  ...  This work was partially supported by the National Science Foundation (NSF) and the Horace H. Rackham School of Graduate Studies at the University of Michigan.  ...  This decomposition has been traditionally done using Minimal Spanning Tree (MST) algorithms, but using fast and extremely accurate Rectilinear Steiner Minimal Tree (RSMT) construction algorithms has become  ... 
doi:10.1109/tcad.2008.923255 fatcat:mbg52oigbja3fftyuydz44aoqe

Resource-constrained project scheduling: Notation, classification, models, and methods

Peter Brucker, Andreas Drexl, Rolf Möhring, Klaus Neumann, Erwin Pesch
1999 European Journal of Operational Research  
Also, project scheduling is increasingly important for make-to-order companies where the capacities have been cut down in order to meet lean management concepts.  ...  More speci®cally, we review exact and heuristic algorithms for the single-mode and the multi-mode case, for the time±cost tradeo problem, for problems with minimum and maximum time lags, for problems with  ...  Project scheduling is important for make-toorder companies where the capacities have been cut down in order to cope with lean management concepts.  ... 
doi:10.1016/s0377-2217(98)00204-5 fatcat:7x43eykiwbdrdhmmdnkojld4rq

Linear-Time Safe-Alternating DFS and SCCs [article]

Carlo Comin, Romeo Rizzi
2022 arXiv   pre-print
Both the underlying graph structures and the algorithm generalize the classical decomposition of a directed graph into strongly-connected components.  ...  Our main result is a linear time algorithm for computing this alternating graph decomposition.  ...  The resulting algorithms lean on safe-alternating reachability, the running time is linear on RAMs [14] and at least Ackermann-linear 1 on pointer machines [22] .  ... 
arXiv:1610.09679v9 fatcat:4jfl7z6zqrctler3e74jcjpswy

Killing a Vortex [article]

Dimitrios M. Thilikos, Sebastian Wiederrecht
2022 arXiv   pre-print
The Structural Theorem of the Graph Minors series of Robertson and Seymour asserts that, for every t∈ℕ, there exists some constant c_t such that every K_t-minor-free graph admits a tree decomposition whose  ...  This algorithm yields, on H_t-minor-free graphs, polynomial algorithms for computational problems such as the dimer problem, the exact matching problem, and the computation of the permanent.  ...  The width of a tree decomposition is defined as max t∈V (T ) |β(t)| − 1 and the treewidth of G, denoted by tw(G), is the minimum width over all tree decompositions for G.  ... 
arXiv:2207.04923v2 fatcat:cinm4jsecbhhfphclpwcerq5ly

Man and machine thinking about the smooth 4-dimensional Poincaré conjecture

Michael Freedman, Robert Gompf, Scott Morrison, Kevin Walker
2010 Quantum Topology  
Rasmussen's s-invariant, a slice obstruction within the general framework of Khovanov homology, changes this state of affairs.  ...  We hope that this observation, and the rich relations between Property R and ideas such as taut foliations, contact geometry, and Heegaard Floer homology, will encourage 3-manifold topologists to look  ...  disjoint collection of trees) of bands implies the failure of both SPC4 and AC.  ... 
doi:10.4171/qt/5 fatcat:svtaa43g6fbanhxgfxzyeu3sge

Rubber Tree Crown Segmentation and Property Retrieval using Ground-Based Mobile LiDAR after Natural Disturbances

Yun, Jiang, Hou, An, Chen, Jiang, Li, Xue
2019 Remote Sensing  
A watershed algorithm based on the extracted crown centres was then adopted for tree crown segmentation, and a variety of tree properties were successfully extracted to evaluate the susceptibility of different  ...  and reduces the gaps among tree crowns, inducing strong wind loading on the tree body.  ...  Aerodynamic drag is known to counter wind-induced tree displacement and causes leaning tree bodies and unevenly distributed defoliation phenomena among rubber forests.  ... 
doi:10.3390/rs11080903 fatcat:5uyhoehuyzcobfcmlzgovtnqbi

Fat 4-polytopes and fatter 3-spheres [article]

David Eppstein, Günter M. Ziegler
2002 arXiv   pre-print
We describe and analyze a hyperbolic geometry construction that produces 4-polytopes with fatness \phi(P)>5.048, as well as the first infinite family of 2-simple, 2-simplicial 4-polytopes.  ...  Moreover, using a construction via finite covering spaces of surfaces, we show that fatness is not bounded for the more general class of strongly regular CW decompositions of the 3-sphere.  ...  The same cutting and gluing process may be repeated to form a sequence or tree of 600-cells, connected along cuts that do not share a ridge.  ... 
arXiv:math/0204007v3 fatcat:7ladkqkb2rhcfdzv5py2kwb2me

PRA: A PERSPECTIVE ON STRENGTHS, CURRENT LIMITATIONS, AND POSSIBLE IMPROVEMENTS

ALI MOSLEH
2014 Nuclear Engineering and Technology  
We note that the technology currently exits (PRA codes using BDD-based algorithms [8] for cut set identification and quantification) removing the need for such approximations.  ...  The accident response and evacuation were made extremely difficult due to road damage and obstructions.  ... 
doi:10.5516/net.03.2014.700 fatcat:4jnridbsvrfghkyrabii6bgb5e
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