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Efficient Generation of Different Topological Representations of Graphs Beyond-Planarity [article]

Patrizio Angelini, Michael A. Bekos, Michael Kaufmann, Thomas Schneck
2019 arXiv   pre-print
Beyond-planarity focuses on combinatorial properties of classes of non-planar graphs that allow for representations satisfying certain local geometric or topological constraints on their edge crossings  ...  Overcoming the limitations of standard combinatorial arguments, we present a technique to systematically generate all non-isomorphic topological representations of complete and complete bipartite graphs  ...  Generation Procedure Let C be a beyond-planarity class of topological graphs and let G be a graph with n ≥ 3 vertices.  ... 
arXiv:1908.03042v2 fatcat:6fpblytg75ef7bkfdy54ku2gvi

A Survey on Graph Drawing Beyond Planarity [article]

Walter Didimo, Giuseppe Liotta, Fabrizio Montecchiani
2018 arXiv   pre-print
Graph Drawing Beyond Planarity is a rapidly growing research area that classifies and studies geometric representations of non-planar graphs in terms of forbidden crossing configurations.  ...  Aim of this survey is to describe the main research directions in this area, the most prominent known results, and some of the most challenging open problems.  ...  There is a general lack of user-studies to assess the effectiveness of the beyond-planar graph models in practice.  ... 
arXiv:1804.07257v1 fatcat:xeckxilhfbbgdbfhctikymlq6m

Beyond-Planar Graphs: Algorithmics and Combinatorics (Dagstuhl Seminar 16452)

Sok-Hee Hong, Michael Kaufmann, Stephen G. Kobourov, János Pach, Marc Herbstritt
2017 Dagstuhl Reports  
The common interest was in the exploration of structural properties and the development of algorithms for so-called beyond-planar graphs, i.e., non-planar graphs with topological constraints such as specific  ...  Next we discussed and grouped together open research problems about beyond planar graphs, such as their combinatorial structures (e.g, thickness, crossing number, coloring), their topology (e.g., string  ...  are known and these properties can be used in the development of efficient algorithms for planar graphs, even where the more general problem is NP-hard.  ... 
doi:10.4230/dagrep.6.11.35 dblp:journals/dagstuhl-reports/Hong0KP16 fatcat:gmft5jywxbapza52lhj4o23ngq

Beyond trees: MRF inference via outer-planar decomposition

Dhruv Batra, A. C. Gallagher, Devi Parikh, Tsuhan Chen
2010 2010 IEEE Computer Society Conference on Computer Vision and Pattern Recognition  
We leverage a new class of graphs amenable to exact inference, called outerplanar graphs, and propose an approximate inference algorithm called Outer-Planar Decomposition (OPD).  ...  OPD is a strict generalization of BP and TRW, and contains both of them as special cases.  ...  We thank Pedro Felzenszwalb for pointing out the connections between outer-planar graphs and k-trees, and Carlos Guestrin and Ramin Zabih for helpful discussions.  ... 
doi:10.1109/cvpr.2010.5539951 dblp:conf/cvpr/BatraGPC10 fatcat:zpodxtnqabbm7c6w5ozwgfq7qe

Beyond-Planarity: Turán-Type Results for Non-Planar Bipartite Graphs

Patrizio Angelini, Michael A. Bekos, Michael Kaufmann, Maximilian Pfister, Torsten Ueckerdt, Michael Wagner
2018 International Symposium on Algorithms and Computation  
Beyond-planarity focuses on the study of geometric and topological graphs that are in some sense nearly planar.  ...  Here, we study this problem for bipartite topological graphs, considering several types of beyond-planar graphs, i.e. 1-planar, 2-planar, fan-planar, and RAC graphs.  ...  Different requirements on the crossing configurations naturally give rise to different classes of beyond-planar graphs.  ... 
doi:10.4230/lipics.isaac.2018.28 dblp:conf/isaac/AngeliniB0PU18 fatcat:x4ht6ptrrrayxfszttwctbgjo4

Computational Algorithm for Determining the Generic Mobility of Floating Planar and Spherical Linkages [chapter]

Offer Shai, Andreas Müller
2013 Mechanisms and Machine Science  
Its foundation is a novel representation of constraints by means of a constraint graph.  ...  this paper, which always finds the correct generic mobility of any planar and spherical mechanism.  ...  CONCLUSIONS AND OUTLOOK The paper introduces an efficient computational algorithm for determining the correct generic/topological mobility for any planar or spherical mechanism with higher and lower kinematic  ... 
doi:10.1007/978-94-007-7214-4_22 fatcat:dnood5et5jglrgsfz5datu4irq

Network Filtering for Big Data: Triangulated Maximally Filtered Graph [article]

Guido Previde Massara, T. Di Matteo, Tomaso Aste
2015 arXiv   pre-print
We propose a network-filtering method, the Triangulated Maximally Filtered Graph (TMFG), that provides an approximate solution to the Weighted Maximal Planar Graph problem.  ...  The method is based on local topological moves and can therefore take advantage of parallel and GPUs computing.  ...  The structure of this network is a representation of the information in the dataset and such information can be efficiently analysed by using network-theoretic tools.  ... 
arXiv:1505.02445v2 fatcat:ezk2egzdkrb6dcfkownuu5f2em

Topological Spines: A Structure-preserving Visual Representation of Scalar Fields

C. Correa, P. Lindstrom, Peer-Timo Bremer
2011 IEEE Transactions on Visualization and Computer Graphics  
Right: Two persistence parameters-noise (blue) and variation (red)-can be explored to obtain a different topological spine, highlighting different structural aspects of the scalar field, such as symmetries  ...  Middle: A topological spine is a graphical representation of the topology that preserves the relative position of extrema and also conveys the nesting structure of the surrounding contours.  ...  planar graph.  ... 
doi:10.1109/tvcg.2011.244 pmid:22034301 fatcat:wsydoqefvneajbq4nm643653jq

COMPUTING WATERTIGHT VOLUMETRIC MODELS FROM BOUNDARY REPRESENTATIONS TO ENSURE CONSISTENT TOPOLOGICAL OPERATIONS

M. W. Jahn, P. E. Bradley
2021 ISPRS Annals of the Photogrammetry, Remote Sensing and Spatial Information Sciences  
The algorithms developed for this task are presented, whereby using the philosophy of graph databases and the Property Graph Model.  ...  They ensure topologically consistent 3D models and allow the definition of proper topological operations.  ...  geo-data which in turn is more easy to be analysed in a general way, i.e. the way of topology and graphs.  ... 
doi:10.5194/isprs-annals-viii-4-w2-2021-21-2021 fatcat:apovj7qnwvabrisve23y3vspcm

Network Filtering for Big Data: Triangulated Maximally Filtered Graph

Guido Previde Massara, T. Di Matteo, Tomaso Aste
2016 Journal of Complex Networks  
We propose a network-filtering method, the Triangulated Maximally Filtered Graph (TMFG), that provides an approximate solution to the Weighted Maximal Planar Graph problem.  ...  The method is based on local topological moves and can therefore take advantage of parallel and GPUs computing.  ...  The structure of this network is a representation of the information in the dataset and such information can be efficiently analysed by using network-theoretic tools.  ... 
doi:10.1093/comnet/cnw015 fatcat:p7f7nmvssjbejcjd54wehiwtrm

Efficiency and robustness in ant networks of galleries

J. Buhl, J. Gautrais, R. V. Sol�, P. Kuntz, S. Valverde, J. L. Deneubourg, G. Theraulaz
2004 European Physical Journal B : Condensed Matter Physics  
These networks are neither small-worlds nor scale-free networks and belong to a particular class of network, i.e. embedded planar graphs emerging from a distributed growth mechanism.  ...  Recent theoretical and empirical studies have focused on the topology of large networks of communication/interactions in biological, social and technological systems.  ...  Network robustness Beyond the efficiency associated to a given network topology, an additional and complementary approach is the analysis of fragility against random failures.  ... 
doi:10.1140/epjb/e2004-00364-9 fatcat:kpr2fpdylba6jiaullzx5w4ola

Topological signatures for fast mobility analysis

Abhirup Ghosh, Benedek Rozemberczki, Subramanian Ramamoorthy, Rik Sarkar
2018 Proceedings of the 26th ACM SIGSPATIAL International Conference on Advances in Geographic Information Systems - SIGSPATIAL '18  
We define the problem of mobility prediction at different distance scales, and show that with the signatures simple k nearest neighbor based regression perform accurate prediction.  ...  The construction of signatures is based on a differential form that can be generated in a distributed setting using local communication, and a signature can be locally and inexpensively updated and communicated  ...  Constructing planar graph. The Delaunay triangulation [15] of 20000 random points in the plane make the planar graph G.  ... 
doi:10.1145/3274895.3274952 dblp:conf/gis/GhoshRRS18 fatcat:g7xxcnvzfvdu7betkx7exhf5pa

A Colloquium on Graph Theory

W. T. Tutte
1960 Canadian mathematical bulletin  
Haj6s explained to me the difference between the Hajos and Hadwiger Conjectures, which are generalizations of the Four Colour Conjecture applying to non-planar graphs.  ...  Hajos is interested in ways of representing graphs. In his lecture he gave a theory of the representation of a graph by a set of intervals on a line.  ... 
doi:10.1017/s0008439500025418 fatcat:cw7tukk6zzbknohmnlpb532mma

Selected Open Problems in Graph Drawing [chapter]

Franz Brandenburg, David Eppstein, Michael T. Goodrich, Stephen Kobourov, Giuseppe Liotta, Petra Mutzel
2004 Lecture Notes in Computer Science  
Proximity Drawability Problems Recently, much attention has been devoted to the study of the combinatorial properties of different types of proximity graphs.  ...  graph G so as to minimize the area of a numberingupward planar drawing of G (taken over all possible numberings of G)?  ...  Acknowledgements We wish to thank Emilio Di Giacomo for useful discussions and comments while preparing this collection of open problems.  ... 
doi:10.1007/978-3-540-24595-7_55 fatcat:4xhjrvq2cffufbfswpjjjtiy3a

Visualization and Measurement of the Cortical Surface

Brian A. Wandell, Suelika Chial, Benjamin T. Backus
2000 Journal of Cognitive Neuroscience  
Abstract Much of the human cortical surface is obscured from view by the complex pattern of folds, making the spatial relationship between different surface locations hard to interpret.  ...  Methods for viewing large portions of the brain's surface in a single flattened representation are described.  ...  Hence, at this point we replace the original edges with a new planar representation using the Delaunay triangulation of the nodes. This set of edges preserves the planar graph and is efficient.  ... 
doi:10.1162/089892900562561 pmid:11054917 fatcat:tcwxid4psjfgnoeee5q5mvpfza
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