Results 1 
9 of
9
AreaEfficient Static and Incremental Graph Drawings
, 1997
"... In this paper, we present algorithms to produce orthogonal drawings of arbitrary graphs. As opposed to most known algorithms, we do not restrict ourselves to graphs with maximum degree 4. The best previous result gave an (m \Gamma 1) \Theta ( m 2 + 1)grid for graphs with n nodes and m edges. We p ..."
Abstract

Cited by 26 (6 self)
 Add to MetaCart
In this paper, we present algorithms to produce orthogonal drawings of arbitrary graphs. As opposed to most known algorithms, we do not restrict ourselves to graphs with maximum degree 4. The best previous result gave an (m \Gamma 1) \Theta ( m 2 + 1)grid for graphs with n nodes and m edges. We present algorithms for two scenarios. In the static scenario, the graph is given completely in advance. We produce a drawing on a grid of size at most m+n 2 \Theta m+n 2 , or on a larger grid where the aspect ratio of the nodes is bounded. Furthermore, we give upper and lower bounds for drawings of the complete graph Kn in the underlying model. In the incremental scenario, the graph is given one node at a time, and the placement of previous nodes can not be changed for later nodes. We then come close to the bounds achieved in the static case and get at most an ( m 2 + n) \Theta ( 2 3 m+ n)grid. In both algorithms, every edge gets at most one bend, thus, the total number of bends ...
Algorithms for Drawing Clustered Graphs
, 1997
"... In the mid 1980s, graphics workstations became the main platforms for software and information engineers. Since then, visualization of relational information has become an essential element of software systems. Graphs are commonly used to model relational information. They are depicted on a graphics ..."
Abstract

Cited by 25 (2 self)
 Add to MetaCart
In the mid 1980s, graphics workstations became the main platforms for software and information engineers. Since then, visualization of relational information has become an essential element of software systems. Graphs are commonly used to model relational information. They are depicted on a graphics workstation as graph drawings. The usefulness of the relational model depends on whether the graph drawings effectively convey the relational information to the users. This thesis is concerned with finding good drawings of graphs. As the amount of information that we want to visualize becomes larger and the relations become more complex, the classical graph model tends to be inadequate. Many extended models use a node hierarchy to help cope with the complexity. This thesis introduces a new graph model called the clustered graph. The central theme of the thesis is an investigation of efficient algorithms to produce good drawings for clustered graphs. Although the criteria for judging the qua...
Compact floorplanning via orderly spanning trees
 Journal of Algorithms
"... Floorplanning is a fundamental step in VLSI chip design. Based upon the concept of orderly spanning trees, we present a simple O(n)time algorithm to construct a floorplan for any nnode plane triangulation. In comparison with previous floorplanning algorithms in the literature, our solution is no ..."
Abstract

Cited by 14 (1 self)
 Add to MetaCart
Floorplanning is a fundamental step in VLSI chip design. Based upon the concept of orderly spanning trees, we present a simple O(n)time algorithm to construct a floorplan for any nnode plane triangulation. In comparison with previous floorplanning algorithms in the literature, our solution is not only simpler in the algorithm itself, but also produces floorplans which require fewer module types. An equally important aspect of our new algorithm lies in its ability to fit the floorplan area in a rectangle of size (n − 1) × ⌊ ⌋
MultiDimensional Orthogonal Graph Drawing with Small Boxes
 Proc. 7th International Symp. on Graph Drawing (GD '99
, 1999
"... In this paper we investigate the general position model for the drawing of arbitrary degree graphs in the Ddimensional (D >= 2) orthogonal grid. In this model no two vertices lie in the same grid hyperplane. ..."
Abstract

Cited by 13 (5 self)
 Add to MetaCart
In this paper we investigate the general position model for the drawing of arbitrary degree graphs in the Ddimensional (D >= 2) orthogonal grid. In this model no two vertices lie in the same grid hyperplane.
IMPROVED COMPACT VISIBILITY REPRESENTATION OF Planar Graph via Schnyder’s Realizer
 SIAM J. DISCRETE MATH. C ○ 2004 SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS VOL. 18, NO. 1, PP. 19–29
, 2004
"... Let G be an nnode planar graph. In a visibility representation of G,eachnodeofG is represented by a horizontal line segment such that the line segments representing any two adjacent nodes of G are vertically visible to each other. In the present paper we give the best known compact visibility repre ..."
Abstract

Cited by 6 (1 self)
 Add to MetaCart
Let G be an nnode planar graph. In a visibility representation of G,eachnodeofG is represented by a horizontal line segment such that the line segments representing any two adjacent nodes of G are vertically visible to each other. In the present paper we give the best known compact visibility representation of G. Given a canonical ordering of the triangulated G, our algorithm draws the graph incrementally in a greedy manner. We show that one of three canonical orderings obtained �from Schnyder’s � realizer for the triangulated G yields a visibility representation of G no wider than 22n−40. Our easytoimplement O(n)time algorithm bypasses the complicated subroutines for 15 fourconnected components and fourblock trees required by the best previously known algorithm of Kant. Our result provides a negative answer to Kant’s open question about whether � � 3n−6 is a 2 worstcase lower bound on the required width. Also, if G has no degreethree (respectively, degreefive) internal node, then our visibility representation for G is no wider than � �
FloorPlanning via Orderly Spanning Trees
, 2001
"... Floorplanning is a fundamental step in VLSI chip design. Based upon the concept of orderly spanning trees, we present a simple O(n)time algorithm to construct a oorplan for any nnode plane triangulation. In comparison with previous oorplanning algorithms in the iterature, our solution is not on ..."
Abstract

Cited by 4 (4 self)
 Add to MetaCart
Floorplanning is a fundamental step in VLSI chip design. Based upon the concept of orderly spanning trees, we present a simple O(n)time algorithm to construct a oorplan for any nnode plane triangulation. In comparison with previous oorplanning algorithms in the iterature, our solution is not only simpler in the algorithm itself, but also produces oorplans which require fewer module types. An equally important aspect of our new algorithm lies in its ability to fit the floorplan area in a rectangle of size (n1) by (2n+1)/3.
Orthogonal Drawings Based On The Stratification Of Planar Graphs
, 2000
"... Several algorithms have been proposed to draw planar graphs using 2visibility and Kandinsky Models. Here, we propose three new algorithms implementing these models in linear time using small grid sizes and few bends. These algorithms are all based on the construction of a particular layered spannin ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
Several algorithms have been proposed to draw planar graphs using 2visibility and Kandinsky Models. Here, we propose three new algorithms implementing these models in linear time using small grid sizes and few bends. These algorithms are all based on the construction of a particular layered spanning tree called Stratification. A linear time algorithm that computes a stratification is also presented.
Drawing Clustered Graphs on an Orthogonal Grid (Extended Abstract)
 J. Graph Algorithms Appl
, 1997
"... 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 produc ..."
Abstract
 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. We present an algorithm which produces such drawings with O(n 2 ) area and with at most 3 bends in each edge. This result is as good as existing results for classical planar graphs. Further, we show that the bend performance of our algorithm is optimal. (Extended Abstract) 1 Introduction Clustered graphs are graphs with recursive clustering structures over the vertices (see Figure 1). This type of clustering structure appears in many systems. Examples include CASE tools [40], management information systems [19], and VLSI design tools [15]. For graphical representation, the clust...
Drawing HighDegree Graphs With Small GridSize
, 1997
"... . In this paper, we present a general scheme to produce interactive and static orthogonal drawings of graphs. As opposed to most known algorithms, we do not restrict ourselves to graph with maximum degree 4, but allow arbitrary degrees. We show here how, with one specific implementation of the sc ..."
Abstract
 Add to MetaCart
. In this paper, we present a general scheme to produce interactive and static orthogonal drawings of graphs. As opposed to most known algorithms, we do not restrict ourselves to graph with maximum degree 4, but allow arbitrary degrees. We show here how, with one specific implementation of the scheme, we can obtain an m+n 2 \Theta m+n 2 grid for all simple connected graphs without nodes of degree 1. Furthermore, there is at most one bend per edge, and the number of bends is at most m. Th dimension of node v is at most deg(v) 2 . The algorithm works in linear time. Acknowledgements: This work was done while the first author was working at and the third author was consulting with Tom Sawyer Software. It was in part funded by the NIST under grant number 70NANB5H1162. This paper is part of a series about the orthogonal library of the Graph Layout Toolkit produced by Tom Sawyer Software. Patent on these and related results is pending. The first author would like to tha...