TY - GEN

T1 - Drawing with fat edges

AU - Duncan, Christian A.

AU - Efrat, Alon

AU - Kobourov, Stephen G.

AU - Wenk, Carola

N1 - Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2002

Y1 - 2002

N2 - In this paper, we introduce the problem of drawing with "fat" edges. Traditionally, graph drawing algorithms represent vertices as circles and edges as closed curves connecting the vertices. In this paper we consider the problem of drawing graphs with edges of variable thickness. The thickness of an edge is often used as a visualization cue, to indicate importance, or to convey some additional information. We present a model for drawing with fat edges and a corresponding polynomial time algorithm that uses the model. We focus on a restricted class of graphs that occur in VLSI wire routing and show how to extend the algorithm to general planar graphs. We show how to take an arbitrary wire routing and convert it into a homotopic equivalent routing such that the distance between any two wires is maximized. Moreover, the routing uses the minimum length wires. Maximizing the distance between wires is equivalent to finding the drawing in which the edges are drawn as thick as possible. To the best of our knowledge this is the first algorithm that finds the maximal distance between any two wires and allows for wires of variable thickness. The previous best known result for the corresponding decision problem with unit wire thickness is the algorithm of Gao et al, which runs in O(kn2 log(kn)) time and uses O(kn2) space, where n is the number of wires and k is the maximum of the input and output complexities. The running time of our algorithm is O(kn + n3) and the space required is O(k+n). The algorithm generalizes naturally to general planar graphs as well.

AB - In this paper, we introduce the problem of drawing with "fat" edges. Traditionally, graph drawing algorithms represent vertices as circles and edges as closed curves connecting the vertices. In this paper we consider the problem of drawing graphs with edges of variable thickness. The thickness of an edge is often used as a visualization cue, to indicate importance, or to convey some additional information. We present a model for drawing with fat edges and a corresponding polynomial time algorithm that uses the model. We focus on a restricted class of graphs that occur in VLSI wire routing and show how to extend the algorithm to general planar graphs. We show how to take an arbitrary wire routing and convert it into a homotopic equivalent routing such that the distance between any two wires is maximized. Moreover, the routing uses the minimum length wires. Maximizing the distance between wires is equivalent to finding the drawing in which the edges are drawn as thick as possible. To the best of our knowledge this is the first algorithm that finds the maximal distance between any two wires and allows for wires of variable thickness. The previous best known result for the corresponding decision problem with unit wire thickness is the algorithm of Gao et al, which runs in O(kn2 log(kn)) time and uses O(kn2) space, where n is the number of wires and k is the maximum of the input and output complexities. The running time of our algorithm is O(kn + n3) and the space required is O(k+n). The algorithm generalizes naturally to general planar graphs as well.

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U2 - 10.1007/3-540-45848-4_14

DO - 10.1007/3-540-45848-4_14

M3 - Conference contribution

AN - SCOPUS:35048835431

SN - 3540433090

SN - 9783540433095

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 162

EP - 177

BT - Graph Drawing - 9th International Symposium, GD 2001, Revised Papers

A2 - Mutzel, Petra

A2 - Junger, Michael

A2 - Leipert, Sebastian

PB - Springer-Verlag

T2 - 9th International Symposium on Graph Drawing, GD 2001

Y2 - 23 September 2001 through 26 September 2001

ER -