Results 1  10
of
31
Competitive Online Routing in Geometric Graphs
 Theoretical Computer Science
, 2001
"... We consider online routing algorithms for finding paths between the vertices of plane graphs. ..."
Abstract

Cited by 55 (8 self)
 Add to MetaCart
We consider online routing algorithms for finding paths between the vertices of plane graphs.
Planar Minimally Rigid Graphs and PseudoTriangulations
, 2003
"... Pointed pseudotriangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (incident to an angle larger than π). In this paper we prove that the opposite statement is also true, namely that planar minimally rigid graphs always admit pointed embeddings, even under cer ..."
Abstract

Cited by 39 (15 self)
 Add to MetaCart
Pointed pseudotriangulations are planar minimally rigid graphs embedded in the plane with pointed vertices (incident to an angle larger than π). In this paper we prove that the opposite statement is also true, namely that planar minimally rigid graphs always admit pointed embeddings, even under certain natural topological and combinatorial constraints. The proofs yield efficient embedding algorithms. They also provide—to the best of our knowledge—the first algorithmically effective result on graph embeddings with oriented matroid constraints other than convexity of faces.
On Simultaneous Planar Graph Embeddings
 COMPUT. GEOM
, 2003
"... We consider the problem of simultaneous embedding of planar graphs. There are two variants ..."
Abstract

Cited by 39 (8 self)
 Add to MetaCart
(Show Context)
We consider the problem of simultaneous embedding of planar graphs. There are two variants
ThreeDimensional Orthogonal Graph Drawing
, 2000
"... vi Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Tables . . . . . . . . . . . . ..."
Abstract

Cited by 33 (13 self)
 Add to MetaCart
(Show Context)
vi Declaration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii List of Algorithms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiv I Orthogonal Graph Drawing 1 1
Layout of Graphs with Bounded TreeWidth
 2002, submitted. Stacks, Queues and Tracks: Layouts of Graph Subdivisions 41
, 2004
"... A queue layout of a graph consists of a total order of the vertices, and a partition of the edges into queues, such that no two edges in the same queue are nested. The minimum number of queues in a queue layout of a graph is its queuenumber. A threedimensional (straight line grid) drawing of a gr ..."
Abstract

Cited by 31 (23 self)
 Add to MetaCart
(Show Context)
A queue layout of a graph consists of a total order of the vertices, and a partition of the edges into queues, such that no two edges in the same queue are nested. The minimum number of queues in a queue layout of a graph is its queuenumber. A threedimensional (straight line grid) drawing of a graph represents the vertices by points in Z and the edges by noncrossing linesegments. This paper contributes three main results: (1) It is proved that the minimum volume of a certain type of threedimensional drawing of a graph G is closely related to the queuenumber of G. In particular, if G is an nvertex member of a proper minorclosed family of graphs (such as a planar graph), then G has a O(1) O(1) O(n) drawing if and only if G has O(1) queuenumber.
Strictly Convex Drawings of Planar Graphs
, 2004
"... Every threeconnected planar graph with n vertices has a drawing on an O(n7=3) \Theta O(n7=3) grid in which all faces are strictly convex polygons. ..."
Abstract

Cited by 28 (1 self)
 Add to MetaCart
Every threeconnected planar graph with n vertices has a drawing on an O(n7=3) \Theta O(n7=3) grid in which all faces are strictly convex polygons.
Pathwidth and ThreeDimensional StraightLine Grid Drawings of Graphs
"... We prove that every nvertex graph G with pathwidth pw(G) has a threedimensional straightline grid drawing with O(pw(G) n) volume. Thus for ..."
Abstract

Cited by 23 (12 self)
 Add to MetaCart
(Show Context)
We prove that every nvertex graph G with pathwidth pw(G) has a threedimensional straightline grid drawing with O(pw(G) n) volume. Thus for
Simultaneous embedding of a planar graph and its dual on the grid
, 2002
"... Abstract. Traditional representations of graphs and their duals suggest the requirement that the dual vertices be placed inside their corresponding primal faces, and the edges of the dual graph cross only their corresponding primal edges. We consider the problem of simultaneously embedding a planar ..."
Abstract

Cited by 19 (10 self)
 Add to MetaCart
(Show Context)
Abstract. Traditional representations of graphs and their duals suggest the requirement that the dual vertices be placed inside their corresponding primal faces, and the edges of the dual graph cross only their corresponding primal edges. We consider the problem of simultaneously embedding a planar graph and its dual into a small integer grid such that the edges are drawn as straightline segments and the only crossings are between primaldual pairs of edges. We provide a lineartime algorithm that simultaneously embeds a 3connected planar graph and its dual on a (2n −2) ×(2n −2) integer grid, where n is the total number of vertices in the graph and its dual. Furthermore our embedding algorithm satisfies the two natural requirements mentioned above.
GIOTTO3D: A System for Visualizing Hierarchical Structures in 3D
 Proceedings of Graph Drawing ’96), Lecture Notes in Computer Science 1190
, 1997
"... Hierarchical structures represented by directed acyclic graphs are widely used in visualization applications (e.g., class inheritance diagrams and scheduling diagrams). 3D information visualization has received increasing attention in the last few years, motivated by the advances in hardware and ..."
Abstract

Cited by 17 (1 self)
 Add to MetaCart
(Show Context)
Hierarchical structures represented by directed acyclic graphs are widely used in visualization applications (e.g., class inheritance diagrams and scheduling diagrams). 3D information visualization has received increasing attention in the last few years, motivated by the advances in hardware and software technology for 3D computer graphics.
OutputSensitive Reporting of Disjoint Paths
, 1996
"... A kpath query on a graph consists of computing k vertexdisjoint paths between two given vertices of the graph, whenever they exist. In this paper, we study the problem of performing kpath queries, with k < 3, in a graph G with n vertices. We denote with the total length of the paths reported. ..."
Abstract

Cited by 16 (3 self)
 Add to MetaCart
A kpath query on a graph consists of computing k vertexdisjoint paths between two given vertices of the graph, whenever they exist. In this paper, we study the problem of performing kpath queries, with k < 3, in a graph G with n vertices. We denote with the total length of the paths reported. For k < 3, we present an optimal data structure for G that uses O(n) space and executes kpath queries in outputsensitive O() time. For triconnected planar graphs, our results make use of a new combinatorial structure that plays the same role as bipolar (st) orientations for biconnected planar graphs. This combinatorial structure also yields an alternative construction of convex grid drawings of triconnected planar graphs.