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Turnregularity and optimal area drawings of orthogonal representations
, 2000
"... Given an orthogonal representation H with n vertices and bends, we study the problem of computing a planar orthogonal drawing of H with small area. This problem has direct applications to the development of practical graph drawing techniques for information visualization and VLSI layout. In this pap ..."
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Cited by 17 (5 self)
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Given an orthogonal representation H with n vertices and bends, we study the problem of computing a planar orthogonal drawing of H with small area. This problem has direct applications to the development of practical graph drawing techniques for information visualization and VLSI layout. In this paper, we introduce the concept of turnregularity of an orthogonal representation H, provide combinatorial characterizations of it, and show that if H is turnregular (i.e., all its faces are turnregular), then a planar orthogonal drawing of H with minimum area can be computed in O(n) time, and a planar orthogonal drawing of H with minimum area and minimum total edge length within that area can be computed in O(n 7/4 log n) time. We also apply our theoretical results to the design and implementation of new practical heuristic methods for constructing planar orthogonal drawings. An experimental study conducted on a test suite of orthogonal representations of randomly generated biconnected 4planar graphs shows that the percentage of turnregular faces is quite high and that our heuristic drawing methods perform better than previous ones.
Drawing Clustered Graphs on . . .
 J. GRAPH ALGORITHMS APPL
, 1999
"... Clustered graphs are graphs with recursive clustering structures over the vertices. For graphical representation, the clustering structure is represented by a simple region that contains the drawing of all the vertices which belong to that cluster. In this paper, we present an algorithm which pro ..."
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Cited by 3 (0 self)
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Clustered graphs are graphs with recursive clustering structures over the vertices. For graphical representation, the clustering structure is represented by a simple region that contains the drawing of all the vertices which belong to that cluster. In this paper, we present an algorithm which produces planar drawings of clustered graphs in a convention known as orthogonal grid rectangular cluster drawings. If the input graph has n vertices, then the algorithm produces in O(n) time a drawing with O(n²) area and at most 3 bends in each edge. This result is as good as existing results for classical planar graphs. Further, we show that our algorithm is optimal in terms of the number of bends per edge.
Accelerated bend minimization
, 2012
"... We present an O(n 3/2) algorithm for minimizing the number of bends in an orthogonal drawing of a plane graph. It has been posed as a long standing open problem at Graph Drawing 2003, whether the bound of O(n 7/4 √ log n) shown by Garg and Tamassia in 1996 could be improved. To answer this question, ..."
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Cited by 2 (1 self)
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We present an O(n 3/2) algorithm for minimizing the number of bends in an orthogonal drawing of a plane graph. It has been posed as a long standing open problem at Graph Drawing 2003, whether the bound of O(n 7/4 √ log n) shown by Garg and Tamassia in 1996 could be improved. To answer this question, we show how to solve the uncapacitated mincost flow problem on a planar bidirected graph with bounded costs and face sizes in O(n 3/2) time.
Smooth Orthogonal Layouts
"... Abstract. We study the problem of creating smooth orthogonal layouts for planar graphs. While in traditional orthogonal layouts every edge is made of a sequence of axisaligned line segments, in smooth orthogonal layouts every edge is made of axisaligned segments and circular arcs with common tange ..."
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Cited by 1 (1 self)
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Abstract. We study the problem of creating smooth orthogonal layouts for planar graphs. While in traditional orthogonal layouts every edge is made of a sequence of axisaligned line segments, in smooth orthogonal layouts every edge is made of axisaligned segments and circular arcs with common tangents. Our goal is to create such layouts with low edge complexity, measured by the number of line and circular arc segments. We show that every biconnected 4planar graph has a smooth orthogonal layout with edge complexity 3. If the input graph has a complexity2 traditional orthogonal layout we can transform it into a smooth complexity2 layout. Using the Kandinsky model for removing the degree restriction, we show that any planar graph has a smooth complexity2 layout. 1
Bend Minimization in Planar Orthogonal Drawings Using Integer Programming
, 2004
"... We consider the problem of minimizing the number of bends in a planar orthogonal graph drawing. While the problem can be solved via network flow for a given planar embedding of a graph G, it is NPhard if we consider the set of all planar embeddings of G. Our approach for biconnected graphs combines ..."
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We consider the problem of minimizing the number of bends in a planar orthogonal graph drawing. While the problem can be solved via network flow for a given planar embedding of a graph G, it is NPhard if we consider the set of all planar embeddings of G. Our approach for biconnected graphs combines an integer linear programming (ILP) formulation for the set of all embeddings of a planar graph with the network flow formulation for fixed embeddings. We report on extensive computational experiments with two benchmark sets containing a total of more than 12,000 graphs where we compared the performance of our ILPbased algorithm with a heuristic and a previously published branch & bound algorithm for solving the same problem. Our new algorithm is significantly faster than the previously published approach for the larger graphs of the benchmark graphs derived from industrial applications and almost twice as fast for the benchmark graphs from the artificially generated set of hard instances of the problem.
SUMMARY
"... A wide number of practical applications would benefit from automatically generated graphical representations of database schemas, in which tables are represented by boxes, and table attributes correspond to distinct stripes inside each table. Links, connecting attributes of two different tables, rep ..."
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A wide number of practical applications would benefit from automatically generated graphical representations of database schemas, in which tables are represented by boxes, and table attributes correspond to distinct stripes inside each table. Links, connecting attributes of two different tables, represent referential constraints or join relationships, and may attach arbitrarily to the left or to the righthand side of the stripes representing the attributes. To our knowledge no drawing technique is available to automatically produce diagrams in such a strongly constrained drawing convention. In this paper we provide a polynomial time algorithm for solving this problem, and test its efficiency and effectiveness against a large test suite. Also, we describe an implementation of a system that uses such an algorithm and we study the main methodological problems we faced in developing such a technology. Copyright © 2002 John Wiley &Sons,Ltd. KEY WORDS: graph drawing; algorithm engineering; drawing standard; orthogonal drawing; database schema visualization; upward drawing