Topic

# Dominance drawing

About: Dominance drawing is a research topic. Over the lifetime, 226 publications have been published within this topic receiving 6315 citations.

##### Papers published on a yearly basis

##### Papers

More filters

•

23 Jul 1998

TL;DR: In this paper, the authors describe fundamental algorithmic techniques for constructing drawings of graphs and provide an accurate, accessible reflection of the rapidly expanding field of graph drawing, using a reference manual.

Abstract: From the Publisher:
This book is designed to describe fundamental algorithmic techniques for constructing drawings of graphs. Suitable as a book or reference manual, its chapters offer an accurate, accessible reflection of the rapidly expanding field of graph drawing.

1,754 citations

••

TL;DR: It is shown that any setF, which can support a Fáry embedding of every planar graph of sizen, has cardinality at leastn+(1−o(1))√n which settles a problem of Mohar.

Abstract: Answering a question of Rosenstiehl and Tarjan, we show that every plane graph withn vertices has a Fary embedding (i.e., straight-line embedding) on the 2n−4 byn−2 grid and provide anO(n) space,O(n logn) time algorithm to effect this embedding. The grid size is asymptotically optimal and it had been previously unknown whether one can always find a polynomial sized grid to support such an embedding. On the other hand we show that any setF, which can support a Fary embedding of every planar graph of sizen, has cardinality at leastn+(1−o(1))√n which settles a problem of Mohar.

755 citations

••

TL;DR: This work introduces a new method to optimize the required area, minimum angle, and number of bends of planar graph drawings on a grid using a new type of ordering on the vertices and faces of triconnected planar graphs.

Abstract: We introduce a new method to optimize the required area, minimum angle, and number of bends of planar graph drawings on a grid. The main tool is a new type of ordering on the vertices and faces of triconnected planar graphs. Using this method linear-time-and-space algorithms can be designed for many graph-drawing problems. Our main results are as follows:
Every triconnected planar graphG admits a planar convex grid drawing with straight lines on a (2n−4)×(n−2) grid, wheren is the number of vertices.
Every triconnected planar graph with maximum degree 4 admits a planar orthogonal grid drawing on ann×n grid with at most [3n/2]+4 bends, and ifn>6, then every edge has at most two bends.
Every planar graph with maximum degree 3 admits a planar orthogonal grid drawing with at most [n/2]+1 bends on an [n/2]×[n/2] grid.
Every triconnected planar graphG admits a planar polyline grid drawing on a (2n−6)×(3n−9) grid with minimum angle larger than 2/d radians and at most 5n−15 bends, withd the maximum degree.

309 citations

•

[...]

01 Jan 2004

TL;DR: The book presents the important fundamental theorems and algorithms on planar graph drawing with easy-to-understand and constructive proofs and is suitable for use in advanced undergraduate and graduate level courses on algorithms, graph theory, graph drawing, information visualization and computational geometry.

Abstract: The book presents the important fundamental theorems and algorithms on planar graph drawing with easy-to-understand and constructive proofs. Extensively illustrated and with exercises included at the end of each chapter, it is suitable for use in advanced undergraduate and graduate level courses on algorithms, graph theory, graph drawing, information visualization and computational geometry. The book will also serve as a useful reference source for researchers in the field of graph drawing and software developers in information visualization, VLSI design and CAD.

191 citations

••

24 Jul 2009TL;DR: This paper studies the interplay between number of bends per edge and total number of edges in RAC drawings to establish upper and lower bounds on these quantities.

Abstract: Cognitive experiments show that humans can read graph drawings in which all edge crossings are at right angles equally well as they can read planar drawings; they also show that the readability of a drawing is heavily affected by the number of bends along the edges. A graph visualization whose edges can only cross perpendicularly is called a RAC (Right Angle Crossing) drawing . This paper initiates the study of combinatorial and algorithmic questions related with the problem of computing RAC drawings with few bends per edge. Namely, we study the interplay between number of bends per edge and total number of edges in RAC drawings. We establish upper and lower bounds on these quantities by considering two classical graph drawing scenarios: The one where the algorithm can choose the combinatorial embedding of the input graph and the one where this embedding is fixed.

163 citations