Results 1 
9 of
9
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 ..."
Abstract

Cited by 17 (5 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 3 (0 self)
 Add to MetaCart
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.
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 ..."
Abstract

Cited by 3 (2 self)
 Add to MetaCart
(Show Context)
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
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, ..."
Abstract

Cited by 2 (1 self)
 Add to MetaCart
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.
Bounds for Orthogonal 3D . . .
 J. GRAPH ALGORITHMS APPL
, 1999
"... This paper studies 3D orthogonal grid drawings for graphs of arbitrary degree, in particular Kn , with vertices drawn as boxes. It establishes asymptotic lower bounds for the volume of the bounding box and the number of bends of such drawings and exhibits a construction that achieves these bounds. ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
This paper studies 3D orthogonal grid drawings for graphs of arbitrary degree, in particular Kn , with vertices drawn as boxes. It establishes asymptotic lower bounds for the volume of the bounding box and the number of bends of such drawings and exhibits a construction that achieves these bounds. No edge route in this construction bends more than three times. For drawings constrained to have at most k bends on any edge route, simple constructions are given for k =1andk =2.The unconstrained construction handles the k # 3cases.
BendMinimal Orthogonal Drawing of NonPlanar Graphs
, 2004
"... This thesis belongs to the field of graph drawing research. It present s a new procedure for calculatp tl bend minimal shape of nonplanar graphswit givent opology. This met9 d is anextP,,9 oft he SimplePodevsnef drawing stKBRK9 SimplePodevsnef is a simplificatPD of t9 more complex Podevsnef  ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
This thesis belongs to the field of graph drawing research. It present s a new procedure for calculatp tl bend minimal shape of nonplanar graphswit givent opology. This met9 d is anextP,,9 oft he SimplePodevsnef drawing stKBRK9 SimplePodevsnef is a simplificatPD of t9 more complex Podevsnef  also known as Kandinsky  st andard. Bot models guarant ee bendminimalit y for planar graphswit givent opology. Theygenerat ortatK9 drawings wit equal vertF size where mult,PD edges can be at hed t a single side of a node. In cont9F t t Kandinsky, SimplePodevsnef has cert, rests9BD,D on t9 split up of such bundles. The algorit9 present9 int hist hesis expandstd drawing st andard for nonplanar graphs. It tKpK crossing point of edges in a special way, and enablestbl t share identen9 grid points where appropriatK Hence it allows crossings of whole bundles of edges inst9 of single edges only. Furt,PB9EKp we show a sharp upper bound of t9 bend count fort he heuristu use of SimplePodevsnef for nonplanar graphs; we also present an ext9F ion oft he new metP d tB is ablet draw nonplanar clustus9,RDB . Clust ergraphs are an ext ension of graphs, wheret here exis t a hierarchical st,pKBp9 of clusters, in whicht he nodes oft he graph are organized.
Labeling heuristics for orthogonal drawings
 In Symposium on Graph Drawing (GD’01), volume 2265 of LNCS
, 2002
"... Abstract. This paper studies the problem of computing an orthogonal drawing of a graph with labels along the edges. Labels are not allowed to overlap with each other or with edges to which they are not assigned. The optimization goal is area minimization. We provide a unified framework that allows t ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
Abstract. This paper studies the problem of computing an orthogonal drawing of a graph with labels along the edges. Labels are not allowed to overlap with each other or with edges to which they are not assigned. The optimization goal is area minimization. We provide a unified framework that allows to easily design edge labeling heuristics. By using the frameworkwe implemented and experimentally compared several heuristics. The best performing heuristics have been embedded in the topologyshapemetrics approach. 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 ..."
Abstract
 Add to MetaCart
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.
Drawing Databbase Schemas
, 2002
"... 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 ..."
Abstract
 Add to MetaCart
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.