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A Better Heuristic for Orthogonal Graph Drawings
 COMPUT. GEOM. THEORY APPL
, 1998
"... An orthogonal drawing of a graph is an embedding in the plane such that all edges are drawn as sequences of horizontal and vertical segments. We present a linear time and space algorithm to draw any connected graph orthogonally on a grid of size n \Theta n with at most 2n + 2 bends. Each edge is ben ..."
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Cited by 81 (6 self)
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An orthogonal drawing of a graph is an embedding in the plane such that all edges are drawn as sequences of horizontal and vertical segments. We present a linear time and space algorithm to draw any connected graph orthogonally on a grid of size n \Theta n with at most 2n + 2 bends. Each edge is bent at most twice. In particular for nonplanar and nonbiconnected planar graphs, this is a big improvement. The algorithm is very simple, easy to implement, and it handles both planar and nonplanar graphs at the same time.
New Lower Bounds For Orthogonal Drawings
 J. GRAPH ALGORITHMS APPL
, 1998
"... An orthogonal drawing of a graph is an embedding of the graph in the twodimensional grid such that edges are routed along gridlines. In this paper we explore lower bounds for orthogonal graph drawings. We prove lower bounds on the number of bends and, when crossings are not allowed, also lower bou ..."
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Cited by 3 (0 self)
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An orthogonal drawing of a graph is an embedding of the graph in the twodimensional grid such that edges are routed along gridlines. In this paper we explore lower bounds for orthogonal graph drawings. We prove lower bounds on the number of bends and, when crossings are not allowed, also lower bounds on the size of the grid.
Efficient Algorithms for Drawing Planar Graphs
, 1999
"... x 1 Introduction 1 1.1 Historical Background . . .............................. 4 1.2 Drawing Styles . ................................... 4 1.2.1 Polyline drawings .............................. 5 1.2.2 Planar drawings ............................... 5 1.2.3 Straight line drawings ................. ..."
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x 1 Introduction 1 1.1 Historical Background . . .............................. 4 1.2 Drawing Styles . ................................... 4 1.2.1 Polyline drawings .............................. 5 1.2.2 Planar drawings ............................... 5 1.2.3 Straight line drawings ............................ 6 1.2.4 Orthogonal drawings . . ........................... 7 1.2.5 Grid drawings ................................ 8 1.3 Properties of Drawings ................................ 9 1.4 Scope of this Thesis .................................. 10 1.4.1 Rectangular drawings . . . ......................... 11 1.4.2 Orthogonal drawings . . ........................... 12 1.4.3 Boxrectangular drawings ........................... 14 1.4.4 Convex drawings . . ............................. 16 1.5 Summary ....................................... 16 2 Preliminaries 20 2.1 Basic Terminology .................................. 20 2.1.1 Graphs and Multigraphs ........................... 20 i CO...
Bendoptimal orthogonal graph drawing in the general position model
, 2012
"... We consider orthogonal drawings in the general position model, i.e., no two points share a coordinate. The drawings are also required to be bend minimal, i.e., each edge of a drawing in k dimensions has exactly one segment parallel to each coordinate direction that are glued together at k − 1 bends. ..."
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We consider orthogonal drawings in the general position model, i.e., no two points share a coordinate. The drawings are also required to be bend minimal, i.e., each edge of a drawing in k dimensions has exactly one segment parallel to each coordinate direction that are glued together at k − 1 bends. We provide a precise description of the class of graphs that admit an orthogonal drawing in the general position model in the plane. The main tools for the proof are Eulerian orientations of graphs and discrete harmonic functions. The tools developed for the planar case can also be applied in higher dimensions. We discuss twobend drawings in three dimensions and show that K2k+2 admits a kbend drawing in k + 1 dimensions. If we allow that a vertex is placed at infinity, we can draw K2k+3 with k bends in k + 1 dimensions.
SeparatorBased Graph Embedding into Multidimensional Grids with Small EdgeCongestion
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The Complexity of Embedding of Acyclic Graphs into Grids with Minimum Congestion
, 2000
"... It is known that the problem of determining, given a planar graph G and integers m and n, whether there exists a congestion1 embedding of G into a two dimensional mngrid is NPcomplete. In this paper, we show that the problem is still NPcomplete if G is restricted to an acyclic graph. ..."
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It is known that the problem of determining, given a planar graph G and integers m and n, whether there exists a congestion1 embedding of G into a two dimensional mngrid is NPcomplete. In this paper, we show that the problem is still NPcomplete if G is restricted to an acyclic graph.
On the Complexity of Minimum Congestion Embedding of Acyclic Graphs into Ladders
, 2001
"... It is known that the problem of determining, given a planar graph G and an integer m, whether there exists a congestion1 embedding of G into an m kgrid is NPcomplete for a xed integer k 3. It is also known that the problem for k = 3 is NPcomplete even if G is restricted to an acyclic graph. T ..."
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It is known that the problem of determining, given a planar graph G and an integer m, whether there exists a congestion1 embedding of G into an m kgrid is NPcomplete for a xed integer k 3. It is also known that the problem for k = 3 is NPcomplete even if G is restricted to an acyclic graph. The complexity of the problem for k = 2 was left open. In this paper, we show that for k = 2, the problem can be solved in polynomial time if G is restricted to a tree, while the problem is NPcomplete even if G is restricted to an acyclic graph.