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Recognizing digraphs of Kelly-width 2

Daniel Meister, Jan Arne Telle, Martin Vatshelle
2010 Discrete Applied Mathematics  
We give an alternative characterization of digraphs of bounded Kelly-width in support of this analogy, and the first polynomial-time algorithm recognizing digraphs of Kelly-width 2.  ...  For an input digraph G = (V , A) the algorithm outputs a vertex ordering and a digraph H = (V , B) with A ⊆ B witnessing either that G has Kelly-width at most 2 or that G has Kelly-width at least 3, in  ...  Acknowledgement We thank anonymous referees for suggesting simplified proofs and giving valuable hints for improving the presentation of the results.  ... 
doi:10.1016/j.dam.2009.09.018 fatcat:7g3agx6tljhelnxfu2uqfja2wy

Classes of Digraphs [chapter]

Jørgen Bang-Jensen, Gregory Z. Gutin
2009 Springer Monographs in Mathematics  
Classes of Digraphs of these three classes. Planar digraphs are discussed in Section 2.12. Digraphs of restricted tree-width are considered in Section 2.13.  ...  Gutin, Digraphs: Theory, Algorithms and Applications, Springer Monographs in Mathematics, DOI 10.1007/978-1-84800-998-1 2, © Springer-Verlag London Limited 2010 31 32 2.  ...  While the authors of [154, 544, 573, 731] managed to obtain some 'positive' algorithmic results on digraphs of bounded directed tree-width, DAG-width and Kelly-width similar to those on undirected graphs  ... 
doi:10.1007/978-1-84800-998-1_2 fatcat:7p2twq5kanaovbwcwmylqwihmi

Upward Planar Drawing of Single-Source Acyclic Digraphs

Michael D. Hutton, Anna Lubiw
1996 SIAM journal on computing (Print)  
The entire testing algorithm (for general single-source directed acyclic graphs) operates in O(n 2 ) t i m e a n d O(n) space (n being the numberof vertices in the input digraph) and represents the rst  ...  An upward plane drawing of a directed acyclic graph is a plane drawing of the digraph in which each directed edge is represented as a curve monotone increasing in the vertical direction.  ...  The general problem of recognizing upward planar digraphs has recently been shown to be NP- complete 12] .  ... 
doi:10.1137/s0097539792235906 fatcat:hlfn74mpz5eszfbiot6lockk5e

Upward planar drawing of single source acyclic digraphs [chapter]

Michael Hutton, Anna Lubiw
1993 Planar Graphs  
The entire testing algorithm (for general single-source directed acyclic graphs) operates in O(n 2 ) t i m e a n d O(n) space (n being the numberof vertices in the input digraph) and represents the rst  ...  An upward plane drawing of a directed acyclic graph is a plane drawing of the digraph in which each directed edge is represented as a curve monotone increasing in the vertical direction.  ...  The general problem of recognizing upward planar digraphs has recently been shown to be NP- complete 12] .  ... 
doi:10.1090/dimacs/009/06 dblp:conf/dimacs/HuttonL91 fatcat:m7uiuria5bhorjs3rgmimq2lvm

Width Parameterizations for Knot-free Vertex Deletion on Digraphs [article]

Stéphane Bessy, Marin Bougeret, Alan D.A. Carneiro, Fábio Protti, Uéverton S. Souza
2019 arXiv   pre-print
by constants, and we remark that KFVD is para-NP-hard even considering many directed width measures as parameters, but in FPT when parameterized by clique-width; (ii) KFVD can be solved in time 2^O(tw)  ...  × n, but assuming ETH it cannot be solved in 2^o(tw)× n^O(1), where tw is the treewidth of the underlying undirected graph.  ...  Thus, for each of these n choices we will obtain a shrinked input of size O(|F|k) that we can solve using an oracle, and we will answer yes iff one of these n reduced instances is a yes-instance.  ... 
arXiv:1910.01783v1 fatcat:uomopm5kove25ib3vgt52vvhke

Problem collection from the IML programme: Graphs, Hypergraphs, and Computing [article]

Klas Markström
2015 arXiv   pre-print
This collection of problems and conjectures is based on a subset of the open problems from the seminar series and the problem sessions of the Institut Mitag-Leffler programme Graphs, Hypergraphs, and Computing  ...  Each problem contributor has provided a write up of their proposed problem and the collection has been edited by Klas Markstr\"om.  ...  It was shown in [1] that one can recognize path-mergeable digraphs in polynomial time.  ... 
arXiv:1511.00270v1 fatcat:nrzxh7as3bbhtdkzu62pueas7u

Characterization and Recognition of Digraphs of Bounded Kelly-width [chapter]

Daniel Meister, Jan Arne Telle, Martin Vatshelle
Graph-Theoretic Concepts in Computer Science  
We apply these results to give the first polynomial-time algorithm recognizing directed graphs of Kelly-width 2.  ...  We give several alternative characterizations of directed graphs of bounded Kelly-width in support of this analogy.  ...  Using the given characterizations we are able to present a fast algorithm recognizing digraphs of Kelly-width 2 in Section 4.  ... 
doi:10.1007/978-3-540-74839-7_26 dblp:conf/wg/MeisterTV07 fatcat:nyzouec66nho5n27wiap245aba

Network Decontamination [chapter]

Nicolas Nisse
2019 Lecture Notes in Computer Science  
This chapter consists of an overview of algorithmic results on graph decontamination and graph searching.  ...  Many different objectives have been studied: the main one being the minimization of the number of mobile agents necessary to clean a contaminated network.  ...  A polynomial-time algorithm to recognize digraphs with Kellywidth at most 2 is given in [MTV10] .  ... 
doi:10.1007/978-3-030-11072-7_19 fatcat:nqoh6llkhjchlk6aeh7iexfbta

Parameterized Algorithms for Parity Games [chapter]

Jakub Gajarský, Michael Lampis, Kazuhisa Makino, Valia Mitsou, Sebastian Ordyniak
2015 Lecture Notes in Computer Science  
We consider a number of natural parameterizations, such as by Directed Feedback Vertex Set, Distance to Tournament, and Modular Width.  ...  In a parameterized complexity setting, the problem has often been considered with parameters such as (directed versions of) treewidth or clique-width, by applying dynamic programming techniques.  ...  For several directed variations of the notion of treewidth, such as entanglement, DAG-width and kelly-width, algorithms running in n O(k) time are known [2, 1, 19] .  ... 
doi:10.1007/978-3-662-48054-0_28 fatcat:nh6whrx2jvdxti4x37wv4ks4ye

Libri

1992 Phonetica: International Journal of Phonetic Science  
Ziel des Buches ist es, 'to provide for imitation an acceptable mode of reading aloud a written Arabic text' (p. 1).  ...  Irritierend wirkt die Verwendung von Zeichen, die weder im IPA noch in der Arabistik allgemein ge-bräuchlich sind, und zwar bereits in den arabischen Beispielen zu Kapitel 2 («Phonetic Essentials»), ob-wohl  ...  of pharynx width (now more commonly referred to as tongue root advancement) as a relevant feature in vowel production.  ... 
doi:10.1159/000261919 fatcat:h4kgvtcwxvc7rl3jtjxwtk7qki

A Trichotomy for Regular Simple Path Queries on Graphs [article]

Guillaume Bagan and Angela Bonifati and Benoit Groz
2012 arXiv   pre-print
We investigate the evaluation of RPQs with an additional constraint that prevents multiple traversals of the same nodes.  ...  In this paper, we establish a comprehensive classification of regular languages with respect to the complexity of the corresponding regular simple path query problem.  ...  It generalizes many other measures such as treewidth, dagwidth or Kelly-width [7, 19] . Directed treewidth measures in some sense how close a digraph is to a DAG. Johnson et al.  ... 
arXiv:1212.6857v1 fatcat:jrbeti57njbmfcsih5uxozaohi

Upward planarization and layout

Hoi-Ming Wong, Technische Universität Dortmund, Technische Universität Dortmund
2011
Observe: Theorem 1 (Di Battista and Tamassia [BT88]; Kelly [Kel87]). A digraph is upward planar if and only if it is a subgraph of a planar st-graph.  ...  Let u be the left neighbor of v on L i andd = X(v) − X(u) − Width(v)/2Width(u)/2their inner distance.  ... 
doi:10.17877/de290r-15700 fatcat:2myuaofdundkzeuql6gzsnaajy

Reference list of indexed articles

1995 Theoretical Computer Science  
On the constructton of regular mmimal broadcast digraphs 124 (2) I 1994) 329-342 381. J.-J.  ...  123 (2) . R. Tamassia and I.G. Tollis, Dynamic reachability m planar digraphs with one source and one sink (Note) 119 (2) (1993) 331-343 292. B. Litow and Ph. Dumas.  ... 
doi:10.1016/0304-3975(95)80003-4 fatcat:5nnk76aalje5potfoeg7hksbce

Preference Restrictions in Computational Social Choice: A Survey [article]

Edith Elkind, Martin Lackner, Dominik Peters
2022 arXiv   pre-print
Particular focus areas of our survey include algorithms for recognizing whether preferences belong to a particular preference domain, and algorithms for winner determination of voting rules that are hard  ...  We do this from the viewpoint of computational social choice, letting computational problems drive our interest, but we include a comprehensive discussion of the economics and social choice literatures  ...  , single-crossing) width, i.e., Γ-width is a very useful concept from an algorithmic point of view.  ... 
arXiv:2205.09092v1 fatcat:a4vbknzskvhotmedlaneakg2am

Parity games, separations, and the modal μ-calculus [article]

Christoph Dittmann, Technische Universität Berlin, Technische Universität Berlin
2017
We present the first FPT algorithms (fixed-parameter tractable) for the model-checking problem of the modal μ-calculus on restricted classes of graphs, specifically on classes of bounded Kelly-width or  ...  bounded DAG-width.  ...  k is the Kelly-width and d is the number of distinct priorities of P , provided a Kelly decomposition of width at most k is given as part of the input.  ... 
doi:10.14279/depositonce-5700 fatcat:ajhnjvhg5zghbdgc3sq4ppkptu
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