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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 the crite ..."
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Cited by 174 (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.
On Embedding an OuterPlanar Graph in a Point Set
 CGTA: Computational Geometry: Theory and Applications
, 1997
"... Given an nvertex outerplanar graph G and a set P of n points in the plane, we present an O(n log n) time and O(n) space algorithm to compute a straightline embedding of G in P , improving upon the algorithm in [GMPP91, CU96] that requires O(n ) time. Our algorithm is nearoptimal as the ..."
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Cited by 28 (1 self)
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Given an nvertex outerplanar graph G and a set P of n points in the plane, we present an O(n log n) time and O(n) space algorithm to compute a straightline embedding of G in P , improving upon the algorithm in [GMPP91, CU96] that requires O(n ) time. Our algorithm is nearoptimal as there is an\Omega (n log n) lower bound for the problem [BMS95]. We present a simpler O(nd) time and O(n) space algorithm to compute a straightline embedding of G in P where log n d 2n is the length of the longest vertex disjoint path in the dual of G. Therefore, the time complexity of the simpler algorithm varies between O(n log n) and O(n ) depending on the value of d. More efficient algorithms are presented for certain restricted cases. If the dual of G is a path, then an optimal \Theta(n log n) time algorithm is presented. If the given point set is in convex position then we show that O(n) time suffices.
Optimal Algorithms to Embed Trees in a Point Set
, 1995
"... We present optimal \Theta(n log n) time algorithms to solve two tree embedding problems whose solution previously took quadratic time or more: rooted tree embeddings and degreeconstrained embeddings. In the rooted tree embedding problem we are given a rooted tree T with n nodes and a set of n po ..."
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Cited by 20 (1 self)
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We present optimal \Theta(n log n) time algorithms to solve two tree embedding problems whose solution previously took quadratic time or more: rooted tree embeddings and degreeconstrained embeddings. In the rooted tree embedding problem we are given a rooted tree T with n nodes and a set of n points P with one designated point p and are asked to find a straightline embedding of T into P with the root at point p. In the degreeconstrained embedding problem we are given a set of n points P where each point is assigned a positive degree and the degrees sum to 2n \Gamma 2 and are asked to embed a tree in P that respects the degrees assigned to each point of P .
Where to Draw the Line
, 1996
"... Graph Drawing (also known as Graph Visualization) tackles the problem of representing graphs on a visual medium such as computer screen, printer etc. Many applications such as software engineering, data base design, project planning, VLSI design, multimedia etc., have data structures that can be rep ..."
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Cited by 2 (0 self)
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Graph Drawing (also known as Graph Visualization) tackles the problem of representing graphs on a visual medium such as computer screen, printer etc. Many applications such as software engineering, data base design, project planning, VLSI design, multimedia etc., have data structures that can be represented as graphs. With the ever increasing complexity of these and new applications, and availability of hardware supporting visualization, the area of graph drawing is increasingly getting more attention from both practitioners and researchers. In a typical drawing of a graph, the vertices are represented as symbols such as circles, dots or boxes, etc., and the edges are drawn as continuous curves joining their end points. Often, the edges are simply drawn as (straight or poly) lines joining their end points (and hence the title of this thesis), followed by an optional transformation into smooth curves. The goal of research in graph drawing is to develop techniques for constructing good...
3 Symmetric Graph Drawing
"... 3.2 Basic Concepts for Symmetric Graph Drawing........ 89 Drawing of a graph • Automorphisms of a graph • ..."
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3.2 Basic Concepts for Symmetric Graph Drawing........ 89 Drawing of a graph • Automorphisms of a graph •