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Drawing Graphs Nicely Using Simulated Annealing
, 1996
"... The paradigm of simulated annealing is applied to the problem of drawing graphs "nicely." Our algorithm deals with general graphs with straighline edges, and employs several simple criteria for the aesthetic quality of the result. The algorithm is flexible, in that the relative weights of ..."
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Cited by 208 (11 self)
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The paradigm of simulated annealing is applied to the problem of drawing graphs "nicely." Our algorithm deals with general graphs with straighline edges, and employs several simple criteria for the aesthetic quality of the result. The algorithm is flexible, in that the relative weights of the criteria can be changed. For graphs of modest size it produces good results, competitive with those produced by other methods, notably, the "spring method" and its variants.
Spring Algorithms and Symmetry
 Theoretical Computer Science
, 1999
"... Spring algorithms are regarded as effective tools for visualizing undirected graphs. One major feature of applying spring algorithms is to display symmetric properties of graphs. This feature has been confirmed by numerous experiments. In this paper, firstly we formalize the concepts of graph symmet ..."
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Cited by 26 (3 self)
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Spring algorithms are regarded as effective tools for visualizing undirected graphs. One major feature of applying spring algorithms is to display symmetric properties of graphs. This feature has been confirmed by numerous experiments. In this paper, firstly we formalize the concepts of graph symmetries in terms of "reflectional" and "rotational" automorphisms; and characterize the types of symmetries, which can be displayed simultaneously by a graph layout, in terms of "geometric" automorphism groups. We show that our formalization is complete. Secondly, we provide general theoretical evidence of why many spring algorithms can display graph symmetry. Finally, the strength of our general theorem is demonstrated from its application to several existing spring algorithms. 1 Introduction Graphs are commonly used in Computer Science to model relational structures such as programs, databases, and data structures. A good graph "layout" gives a clear understanding of a structural model; a ba...
Isomorphic Subgraphs
 Proc. Graph Drawing'99, LNCS 1731
, 1999
"... We are interested in finding symmetries in graphs and then use these symmetries for graph drawing algorithms. There are two general approaches to this problem, the first one is known as Geometric Symmetries on the basis of drawings, the other rests upon the graphtheoretical notion of graphs. For a ..."
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Cited by 2 (1 self)
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We are interested in finding symmetries in graphs and then use these symmetries for graph drawing algorithms. There are two general approaches to this problem, the first one is known as Geometric Symmetries on the basis of drawings, the other rests upon the graphtheoretical notion of graphs. For a given graph G the Isomorphic Subgraphs problem makes use of the second approach and tries to find the two largest disjoint isomorphic subgraphs in G. Hence, G consists of two identical copies and a remainder. There are many NPcomplete or open problems related to our problem, like Graph Isomorphism, Graph Automorphism or Largest Common Subgraph. We show that the Isomorphic Subgraphs problem is NPhard for connected outerplanar graphs, and 2connected planar graphs and is solvable in linear time when restricted to trees. Additionally we will shortly discuss the applicability of Isomorphic Subgraphs in graph drawing algorithms.