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Planar Confluent Orthogonal Drawings of 4-Modal Digraphs 四模态有向图的平面合流正交图
International Symposium Graph Drawing and Network Visualization Pub Date : 2022-08-29 DOI: 10.48550/arXiv.2208.13446
Sabine Cornelsen, Gregor Diatzko
{"title":"Planar Confluent Orthogonal Drawings of 4-Modal Digraphs","authors":"Sabine Cornelsen, Gregor Diatzko","doi":"10.48550/arXiv.2208.13446","DOIUrl":"https://doi.org/10.48550/arXiv.2208.13446","url":null,"abstract":"In a planar confluent orthogonal drawing (PCOD) of a directed graph (digraph) vertices are drawn as points in the plane and edges as orthogonal polylines starting with a vertical segment and ending with a horizontal segment. Edges may overlap in their first or last segment, but must not intersect otherwise. PCODs can be seen as a directed variant of Kandinsky drawings or as planar L-drawings of subdivisions of digraphs. The maximum number of subdivision vertices in an edge is then the split complexity. A PCOD is upward if each edge is drawn with monotonically increasing y-coordinates and quasi-upward if no edge starts with decreasing y-coordinates. We study the split complexity of PCODs and (quasi-)upward PCODs for various classes of graphs.","PeriodicalId":159831,"journal":{"name":"International Symposium Graph Drawing and Network Visualization","volume":"27 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127417872","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
An FPT Algorithm for Bipartite Vertex Splitting 二部顶点分割的FPT算法
International Symposium Graph Drawing and Network Visualization Pub Date : 2022-08-27 DOI: 10.48550/arXiv.2208.12898
Abu Reyan Ahmed, S. Kobourov, Myroslav Kryven
{"title":"An FPT Algorithm for Bipartite Vertex Splitting","authors":"Abu Reyan Ahmed, S. Kobourov, Myroslav Kryven","doi":"10.48550/arXiv.2208.12898","DOIUrl":"https://doi.org/10.48550/arXiv.2208.12898","url":null,"abstract":"Bipartite graphs model the relationship between two disjoint sets of objects. They have a wide range of applications and are often visualized as a 2-layered drawing, where each set of objects is visualized as a set of vertices (points) on one of the two parallel horizontal lines and the relationships are represented by edges (simple curves) between the two lines connecting the corresponding vertices. One of the common objectives in such drawings is to minimize the number of crossings this, however, is computationally expensive and may still result in drawings with so many crossings that they affect the readability of the drawing. We consider a recent approach to remove crossings in such visualizations by splitting vertices, where the goal is to find the minimum number of vertices to be split to obtain a planar drawing. We show that determining whether a planar drawing exists after splitting at most $k$ vertices is fixed parameter tractable in $k$.","PeriodicalId":159831,"journal":{"name":"International Symposium Graph Drawing and Network Visualization","volume":"61 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129618326","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Rectilinear Planarity of Partial 2-Trees 部分2树的线性平面性
International Symposium Graph Drawing and Network Visualization Pub Date : 2022-08-26 DOI: 10.48550/arXiv.2208.12558
W. Didimo, Michael Kaufmann, G. Liotta, Giacomo Ortali
{"title":"Rectilinear Planarity of Partial 2-Trees","authors":"W. Didimo, Michael Kaufmann, G. Liotta, Giacomo Ortali","doi":"10.48550/arXiv.2208.12558","DOIUrl":"https://doi.org/10.48550/arXiv.2208.12558","url":null,"abstract":"A graph is rectilinear planar if it admits a planar orthogonal drawing without bends. While testing rectilinear planarity is NP-hard in general (Garg and Tamassia, 2001), it is a long-standing open problem to establish a tight upper bound on its complexity for partial 2-trees, i.e., graphs whose biconnected components are series-parallel. We describe a new O(n^2)-time algorithm to test rectilinear planarity of partial 2-trees, which improves over the current best bound of O(n^3 log n) (Di Giacomo et al., 2022). Moreover, for partial 2-trees where no two parallel-components in a biconnected component share a pole, we are able to achieve optimal O(n)-time complexity. Our algorithms are based on an extensive study and a deeper understanding of the notion of orthogonal spirality, introduced several years ago (Di Battista et al, 1998) to describe how much an orthogonal drawing of a subgraph is rolled-up in an orthogonal drawing of the graph.","PeriodicalId":159831,"journal":{"name":"International Symposium Graph Drawing and Network Visualization","volume":"58 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115461439","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 4
Testing Upward Planarity of Partial 2-Trees 部分2-树的上平面性检验
International Symposium Graph Drawing and Network Visualization Pub Date : 2022-08-26 DOI: 10.48550/arXiv.2208.12548
S. Chaplick, E. D. Giacomo, Fabrizio Frati, R. Ganian, Chrysanthi N. Raftopoulou, Kirill Simonov
{"title":"Testing Upward Planarity of Partial 2-Trees","authors":"S. Chaplick, E. D. Giacomo, Fabrizio Frati, R. Ganian, Chrysanthi N. Raftopoulou, Kirill Simonov","doi":"10.48550/arXiv.2208.12548","DOIUrl":"https://doi.org/10.48550/arXiv.2208.12548","url":null,"abstract":". We present an O ( n 2 )-time algorithm to test whether an n vertex directed partial 2-tree is upward planar. This result improves upon the previously best known algorithm, which runs in O ( n 4 ) time.","PeriodicalId":159831,"journal":{"name":"International Symposium Graph Drawing and Network Visualization","volume":"28 1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121384783","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 3
Arrangements of Pseudocircles: On Digons and Triangles 伪圆的排列:关于地凹形和三角形
International Symposium Graph Drawing and Network Visualization Pub Date : 2022-08-25 DOI: 10.48550/arXiv.2208.12110
S. Felsner, Sandro Roch, M. Scheucher
{"title":"Arrangements of Pseudocircles: On Digons and Triangles","authors":"S. Felsner, Sandro Roch, M. Scheucher","doi":"10.48550/arXiv.2208.12110","DOIUrl":"https://doi.org/10.48550/arXiv.2208.12110","url":null,"abstract":". In this article, we study the cell-structure of simple arrangements of pairwise intersecting pseudocircles. The focus will be on two problems from Gr¨unbaum’s monograph from the 1970’s. First, we discuss the maximum number of digons or touching points. Gr¨unbaum conjectured that there are at most 2 n − 2 digon cells or equivalently at most 2 n − 2 touchings. Agarwal et al. (2004) verified the conjecture for cylindrical arrangements. We show that the conjecture holds for any arrangement which contains three pseudocircles that pairwise form a touching. The proof makes use of the result for cylindrical arrangements. Moreover, we construct non-cylindrical arrangements which attain the maximum of 2 n − 2 touchings and have no triple of pairwise touching pseudocircles. Second, we discuss the minimum number of triangular cells (triangles) in arrangements without digons and touchings. Felsner and Scheucher (2017) showed that there exist arrangements with only (cid:100) 1611 n (cid:101) triangles, which disproved a conjecture of Gr¨unbaum. Here we provide a construction with only (cid:100) 43 n (cid:101) triangles. A corresponding lower bound was obtained by Snoeyink and Hershberger (1991).","PeriodicalId":159831,"journal":{"name":"International Symposium Graph Drawing and Network Visualization","volume":"2016 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129931685","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
The thickness of fan-planar graphs is at most three 扇形平面图的厚度最多为3
International Symposium Graph Drawing and Network Visualization Pub Date : 2022-08-25 DOI: 10.48550/arXiv.2208.12324
O. Cheong, Maximilian Pfister, Lena Schlipf
{"title":"The thickness of fan-planar graphs is at most three","authors":"O. Cheong, Maximilian Pfister, Lena Schlipf","doi":"10.48550/arXiv.2208.12324","DOIUrl":"https://doi.org/10.48550/arXiv.2208.12324","url":null,"abstract":". We prove that in any strongly fan-planar drawing of a graph G the edges can be colored with at most three colors, such that no two edges of the same color cross. This implies that the thickness of strongly fan-planar graphs is at most three. If G is bipartite, then two colors suffice to color the edges in this way.","PeriodicalId":159831,"journal":{"name":"International Symposium Graph Drawing and Network Visualization","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121788469","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Compatible Spanning Trees in Simple Drawings of Kn 在Kn的简单图纸兼容生成树
International Symposium Graph Drawing and Network Visualization Pub Date : 2022-08-25 DOI: 10.1007/978-3-031-22203-0_2
O. Aichholzer, Kristin Knorr, Wolfgang Mulzer, Nicolas El Maalouly, Johannes Obenaus, Rosna Paul, Meghana M. Reddy, B. Vogtenhuber, A. Weinberger
{"title":"Compatible Spanning Trees in Simple Drawings of Kn","authors":"O. Aichholzer, Kristin Knorr, Wolfgang Mulzer, Nicolas El Maalouly, Johannes Obenaus, Rosna Paul, Meghana M. Reddy, B. Vogtenhuber, A. Weinberger","doi":"10.1007/978-3-031-22203-0_2","DOIUrl":"https://doi.org/10.1007/978-3-031-22203-0_2","url":null,"abstract":"","PeriodicalId":159831,"journal":{"name":"International Symposium Graph Drawing and Network Visualization","volume":"51 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129016122","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
st-Orientations with Few Transitive Edges 具有少量传递边的st-取向
International Symposium Graph Drawing and Network Visualization Pub Date : 2022-08-24 DOI: 10.48550/arXiv.2208.11414
Carla Binucci, W. Didimo, M. Patrignani
{"title":"st-Orientations with Few Transitive Edges","authors":"Carla Binucci, W. Didimo, M. Patrignani","doi":"10.48550/arXiv.2208.11414","DOIUrl":"https://doi.org/10.48550/arXiv.2208.11414","url":null,"abstract":". The problem of orienting the edges of an undirected graph such that the resulting digraph is acyclic and has a single source s and a single sink t has a long tradition in graph theory and is central to many graph drawing algorithms. Such an orientation is called an st -orientation. We address the problem of computing st -orientations of undirected graphs with the minimum number of transitive edges. We prove that the problem is NP-hard in the general case. For planar graphs we describe an ILP model that is fast in practice. We experimentally show that optimum solutions dramatically reduce the number of transitive edges with respect to unconstrained st -orientations computed via classical st -numbering algorithms. Moreover, focusing on popular graph drawing algorithms that apply an st -orientation as a preliminary step, we show that reducing the number of transitive edges leads to drawings that are much more compact.","PeriodicalId":159831,"journal":{"name":"International Symposium Graph Drawing and Network Visualization","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122443466","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 2
Improved Scheduling of Morphing Edge Drawing 改进的变形边绘制调度
International Symposium Graph Drawing and Network Visualization Pub Date : 2022-08-24 DOI: 10.48550/arXiv.2208.11305
Kazuo Misue
{"title":"Improved Scheduling of Morphing Edge Drawing","authors":"Kazuo Misue","doi":"10.48550/arXiv.2208.11305","DOIUrl":"https://doi.org/10.48550/arXiv.2208.11305","url":null,"abstract":". Morphing edge drawing (MED), a graph drawing technique, is a dynamic extension of partial edge drawing (PED), where partially drawn edges (stubs) are repeatedly stretched and shrunk by morphing. Previous experimental evaluations have shown that the reading time with MED may be shorter than that with PED. The morphing scheduling method limits visual clutter by avoiding crossings between stubs. How-ever, as the number of intersections increases, the overall morphing cycle tends to lengthen in this method, which is likely to have a negative effect on the reading time. In this paper, improved scheduling methods are presented to address this issue. The first method shortens the duration of a single cycle by overlapping a part of the current cycle with the succeeding one. The second method duplicates every morph by the allowable number of times in one cycle. The third method permits a specific number of simultaneous crossings per edge. The effective performances of these methods are demonstrated through experimental evaluations.","PeriodicalId":159831,"journal":{"name":"International Symposium Graph Drawing and Network Visualization","volume":"26 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125537046","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
FORBID: Fast Overlap Removal By stochastic gradIent Descent for Graph Drawing 禁止:快速重叠去除随机梯度下降图形绘制
International Symposium Graph Drawing and Network Visualization Pub Date : 2022-08-19 DOI: 10.1007/978-3-031-22203-0_6
Loann Giovannangeli, Frédéric Lalanne, R. Giot, Romain Bourqui
{"title":"FORBID: Fast Overlap Removal By stochastic gradIent Descent for Graph Drawing","authors":"Loann Giovannangeli, Frédéric Lalanne, R. Giot, Romain Bourqui","doi":"10.1007/978-3-031-22203-0_6","DOIUrl":"https://doi.org/10.1007/978-3-031-22203-0_6","url":null,"abstract":"","PeriodicalId":159831,"journal":{"name":"International Symposium Graph Drawing and Network Visualization","volume":"73 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126423629","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
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