Book ChapterDOI
Computational Complexity of Geometric Symmetry Detection in Graphs
Joseph Manning
- pp 1-7
Reads0
Chats0
TLDR
The central results show that for general graphs, however, detecting the presence of even a single axial or rotational symmetry is NP-complete.Abstract:
Constructing a visually informative drawing of an abstract graph is a problem of considerable practical importance, and has recently been the focus of much investigation. Displaying symmetry has emerged as one of the foremost criteria for achieving good drawings. Linear-time algorithms are already known for the detection and display of symmetry in trees, outerplanar graphs, and embedded planar graphs. The central results of this paper show that for general graphs, however, detecting the presence of even a single axial or rotational symmetry is NP-complete. A number of related results are also established, including the #P-completeness of counting the axial or rotational symmetries of a graph.read more
Citations
More filters
Journal ArticleDOI
Algorithms for drawing graphs: an annotated bibliography
TL;DR: A bibliographic survey on algorithms whose goal is to produce aesthetically pleasing drawings of graphs is presented, a first attempt to encompass both theoretical and application-oriented papers from disparate areas.
Journal ArticleDOI
Area requirement and symmetry display of planar upward drawings
TL;DR: A linear-time algorithm is presented that produces drawings of planar acyclic digraphs with a small number of bends, asymptotically optimal area, and such that symmetries and isomorphisms of the digraph are displayed.
Journal ArticleDOI
Large-Graph Layout Algorithms at Work: An Experimental Study
Stefan Hachul,Michael Jünger +1 more
TL;DR: This paper investigates some of these methods that are based on force-directed or algebraic approaches in terms of running time and drawing quality on a big variety of artificial and real-world graphs.
Journal ArticleDOI
Spring algorithms and symmetry
Peter Eades,Xuemin Lin +1 more
TL;DR: This paper formalizes the concepts of graph symmetries in terms of “reflectional” and “rotational” automorphisms; and characterize the types of symmetry, which can be displayed simultaneously by a graph layout, in termsof “geometric’ automorphism groups.
Proceedings ArticleDOI
Drawing graphs in the plane with high resolution
Michael Formann,Torben Hagerup,J. Haralambides,Michael Kaufmann,Frank Thomson Leighton,A. Simvonis,Emo Welzl,Gerhard J. Woeginger +7 more
TL;DR: It is shown that the problem of deciding if R=2 pi /d for a graph is NP-hard for d=4, and a counting argument is used to show that R=O(log d/d/sup 2/) for many graphs.
References
More filters
Book
The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
Journal ArticleDOI
Some NP-Complete Problems Similar to Graph Isomorphism
TL;DR: Several altered or generalized versions of the ISOMORPHISM problem are presented and shown to be NP-complete and one of these is the problem of determining whether a given graph has a fixed-point-free automorphism.
Proceedings ArticleDOI
A method for drawing graphs
TL;DR: The authors are developing programs that draw pictures of graphs in the plane, and there are au infinite number of pictures that represent a given graph.
Geometric symmetry in graphs
TL;DR: In this article, the authors investigated the general problem of constructing meaningful drawings of abstract graphs, in particular the application of axial and rotational symmetry, collectively known as geometric symmetry, to achieving this goal.
Fast Detection and Display of Symmetry in Trees
TL;DR: An expression is obtained for the maximum number of axial symmetries of a tree which can be simultaneously displayed in a single drawing, and an algorithm is presented for constructing such a maximally-symmetric drawing.