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Planar L-Drawings of Directed Graphs [chapter]

Steven Chaplick, Markus Chimani, Sabine Cornelsen, Giordano Da Lozzo, Martin Nöllenburg, Maurizio Patrignani, Ioannis G. Tollis, Alexander Wolff
2018 Lecture Notes in Computer Science  
We show that directed st-graphs admitting an upward-(resp. upward-rightward-) planar L-drawing are exactly those admitting a bitonic (resp. monotonically increasing) st-ordering.  ...  We give a lineartime algorithm that computes a bitonic (resp. monotonically increasing) st-ordering of a planar st-graph or reports that there exists none.  ...  u 1 r v i s max v −2 v −1 G i−1 G i−1 (a) v −2 v −1 u 1 u k v i G i−1 G i−1 (b) Bitonic st-Orderings in the Variable Embedding Setting By Theorem 3, testing for the existence of an upward-(upward-rightward  ... 
doi:10.1007/978-3-319-73915-1_36 fatcat:zbvtqm4uu5cixgvlompcer63rm

Planar L-Drawings of Directed Graphs [article]

Steven Chaplick, Markus Chimani, Sabine Cornelsen, Giordano Da Lozzo, Martin Nöllenburg, Maurizio Patrignani, Ioannis G. Tollis, Alexander Wolff
2017 arXiv   pre-print
We show that directed st-graphs admitting an upward- (resp. upward-rightward-) planar L-drawing are exactly those admitting a bitonic (resp. monotonically increasing) st-ordering.  ...  We give a linear-time algorithm that computes a bitonic (resp. monotonically increasing) st-ordering of a planar st-graph or reports that there exists none.  ...  u 1 r v i s max v −2 v −1 G i−1 G i−1 (a) v −2 v −1 u 1 u k v i G i−1 G i−1 (b) Bitonic st-Orderings in the Variable Embedding Setting By Theorem 3, testing for the existence of an upward-(upward-rightward  ... 
arXiv:1708.09107v2 fatcat:ey73t3deifba5lrmson3ocqn2y

On Upward-Planar L-Drawings of Graphs [article]

Patrizio Angelini, Steven Chaplick, Sabine Cornelsen, Giordano Da Lozzo
2022 arXiv   pre-print
It is known that a plane st-graph, i.e., an embedded st-graph in which the edge (s,t) is incident to the outer face, admits an upward-planar L-drawing if and only if it admits a bitonic st-ordering, which  ...  On the combinatorial side, we show that a plane DAG admits an upward-planar L-drawing if and only if it is a subgraph of a plane st-graph admitting a bitonic st-ordering.  ...  It can be tested in linear time whether a plane st-graph admits a bitonic stordering [17] , and whether a planar st-graph admits a planar embedding that allows for a bitonic st-ordering [1, 9] .  ... 
arXiv:2205.05627v1 fatcat:hydz2epu6zhrpp47b7lynu2d6e

T -shape visibility representations of 1-planar graphs

Franz J. Brandenburg
2018 Computational geometry  
The representations use quadratic area and can be computed in linear time from a given embedding.  ...  A graph is 1-planar if there is a drawing in the plane such that each edge is crossed at most once and is IC-planar if in addition no two crossing edges share a vertex.  ...  We operate in the variable embedding setting and admit changing the embedding.  ... 
doi:10.1016/j.comgeo.2017.10.007 fatcat:6ahx735tkvaq7kck6h5wdlshhu

Universal Slope Sets for Upward Planar Drawings [article]

Michael A. Bekos, Emilio Di Giacomo, Walter Didimo, Giuseppe Liotta, Fabrizio Montecchiani
2018 arXiv   pre-print
We prove that every set S of Δ slopes containing the horizontal slope is universal for 1-bend upward planar drawings of bitonic st-graphs with maximum vertex degree Δ, i.e., every such digraph admits a  ...  In addition, we prove that every such set S can be used to construct 2-bend upward planar drawings of n-vertex planar st-graphs with at most 4n-9 bends in total.  ...  A bitonic st-ordering of G is an st-ordering such that, for every vertex u ∈ V , S(u) is bitonic [18] . A planar st-graph G is a bitonic st-graph if it admits a bitonic st-ordering.  ... 
arXiv:1803.09949v2 fatcat:odrwbrgyp5bnxixqafded53dcy

Upward planar drawings with two slopes [article]

Jonathan Klawitter, Tamara Mchedlidze
2021 arXiv   pre-print
For the variable embedding scenario, we describe a linear-time algorithm for single-source digraphs, a quartic-time algorithm for series-parallel digraphs, and a fixed-parameter tractable algorithm for  ...  For the latter two classes, we make use of SPQR-trees and the notion of upward spirality.  ...  For the variable embedding scenario, we check whether graphs of different graph classes admit an upward planar 2-slope drawing, based on the results of see Section 3.  ... 
arXiv:2106.02839v2 fatcat:t62riog4n5hlbknlbe3v3h46uy

Parameterized Complexity in Graph Drawing (Dagstuhl Seminar 21293)

Robert Ganian, Fabrizio Montecchiani, Martin Nöllenburg, Meirav Zehavi
2021
It brought together 28 researchers from the Graph Drawing and the Parameterized Complexity research communities with the aim to discuss and explore open research questions on the interface between the  ...  This report documents the program and the outcomes of Dagstuhl Seminar 21293 "Parameterized Complexity in Graph Drawing". The seminar was held mostly in-person from July 18 to July 23, 2021.  ...  We extracted and discuss possible open directions related to k-planarity, fan-planarity and other classes of beyond-planar graphs that could be attacked during and after the workshop.  ... 
doi:10.4230/dagrep.11.6.82 fatcat:dth3fds7snd2lcqobs5dl7kfyu

Subject index volumes 1–200

1999 Theoretical Computer Science  
-, 1291 subgraph maxima1 vertex-induced -, 2772 subgraph problem highest degree -, 3217 homeomorphic -, 752 lexicographically first maximal -, 1640 subgraphs, 629,723 of planar St-graphs, 1156  ...  , 11.53 graph-oriented object data model, 3030 graph-rewrite systems, 1149 graph-rewriting formalism, 2126 graphs, set-inclusion ordering, 2008 set-Levenshtein distance, 3340 set-models, classical  ... 
doi:10.1016/s0304-3975(98)00319-3 fatcat:s22ud3iiqjht7lfbtc3zctk7zm

Dagstuhl Reports, Volume 11, Issue 6, July 2021, Complete Issue [article]

2021
We extracted and discuss possible open directions related to k-planarity, fan-planarity and other classes of beyond-planar graphs that could be attacked during and after the workshop.  ...  Furthermore we highlighted some of the methods developed on track-layout of fan-planar graphs by Biedl et al. [3].  ...  Two-page embeddings of upward planar graphs: The group studied the complexity of recognizing whether st-planar graphs admit an upward two-page book embedding. c.  ... 
doi:10.4230/dagrep.11.6 fatcat:4ojdxh5mknhx5op4bxxc7ypgna

Algorithm Engineering for fundamental Sorting and Graph Problems

Vitaly Osipov
2014
It is a set of basic techniques one can find in any (good) coursebook on algorithms and data structures.  ...  Fundamental Algorithms build a basis knowledge for every computer science undergraduate or a professional programmer.  ...  We would like to thank Irit Katriel, Rodrigo Paredes, Dominik Schultes and Jan Wassenberg for providing graph generators, instances, and source codes.  ... 
doi:10.5445/ir/1000042377 fatcat:72infiexarhixk6vxfg6b7op4i

Bifurcations of equilibria in DNA elasticity

Yoav Biton
2007
electrostatic forces are taken into account, the equations of mechanical equilibrium for a DNA molecule with N+1 [...]  ...  It takes into account the intramolecular electrostatic interactions of the negatively charged phosphate groups in the molecule and the impenetrability of the DNA molecule for cases in which theelectrostatic  ...  Each drawing illustrates one of the kinematical variables for the (artificial) case in which that variable has a positive value and the others (with the exception of ρ 3 ) are set equal to zero. negatively  ... 
doi:10.7282/t3js9qwr fatcat:tp3axv4xefgqxeg3fbasasbtrm

Problems of Drug Dependence, 1996: Proceedings of the 58th Annual Scientific Meeting of the College on Problems of Drug Dependence, Inc

:None, Universitätsbibliothek Braunschweig
1997
ACKNOWLEDGEMENTS Supported by DA 03413, K05 DA00008 and F32 DA05709 from the National Institute on Drug Abuse. ACKNOWLEDGEMENTS Supported by NIH/NIDA grants DA08254 and NS33432.  ...  WHAT KERR SAID It is possible to discern a set of themes which constituted the Kerr's framework of thinking and we can for convenience order the content of his presentation under four headings.  ...  The dose-effect curve for stimulation of locomotor activity is bitonic with maximal effects generally occurring at intermediate doses.  ... 
doi:10.24355/dbbs.084-200602280100-3 fatcat:c2hifyknjngybbgwksoimfieoq