TY - GEN

T1 - Balanced aspect ratio trees and their use for drawing very large graphs

AU - Duncan, Christian A.

AU - Goodrich, Michael T.

AU - Kobourov, Stephen G.

N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1998.
Copyright:
Copyright 2016 Elsevier B.V., All rights reserved.

PY - 1999

Y1 - 1999

N2 - We describe a new approach for cluster-based drawing of very large graphs, which obtains clusters by using binary space partition (BSP) trees. We also introduce a novel BSP-type decomposition, called the balanced aspect ratio (BAR) tree, which guarantees that the cells produced are convex and have bounded aspect ratios. In addition, the tree depth is O(log n), and its construction takes O(n log n) time, where n is the number of points. We show that the BAR tree can be used to recursively divide a graph into subgraphs of roughly equal size, such that the drawing of each subgraph has a balanced aspect ratio. As a result, we obtain a representation of a graph as a collection of O(log n) layers, where each succeeding layer represents the graph in an increasing level of detail. The overall running time of the algorithm is O(n log n + m + D0(G)), where n and m are the number of vertices and edges of the graph G, and D0(G) is the time it takes to obtain an initial embedding of G. In particular, if the graph is planar each layer is a graph drawn with straight lines and without crossings on the n × n grid and the running time reduces to O(n log n).

AB - We describe a new approach for cluster-based drawing of very large graphs, which obtains clusters by using binary space partition (BSP) trees. We also introduce a novel BSP-type decomposition, called the balanced aspect ratio (BAR) tree, which guarantees that the cells produced are convex and have bounded aspect ratios. In addition, the tree depth is O(log n), and its construction takes O(n log n) time, where n is the number of points. We show that the BAR tree can be used to recursively divide a graph into subgraphs of roughly equal size, such that the drawing of each subgraph has a balanced aspect ratio. As a result, we obtain a representation of a graph as a collection of O(log n) layers, where each succeeding layer represents the graph in an increasing level of detail. The overall running time of the algorithm is O(n log n + m + D0(G)), where n and m are the number of vertices and edges of the graph G, and D0(G) is the time it takes to obtain an initial embedding of G. In particular, if the graph is planar each layer is a graph drawn with straight lines and without crossings on the n × n grid and the running time reduces to O(n log n).

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U2 - 10.1007/3-540-37623-2_9

DO - 10.1007/3-540-37623-2_9

M3 - Conference contribution

AN - SCOPUS:84957868512

SN - 3540654739

SN - 9783540654735

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

SP - 111

EP - 124

BT - Graph Drawing - 6th International Symposium, GD 1998, Proceedings

A2 - Whitesides, Sue H.

PB - Springer-Verlag

T2 - 6th International Symposium on Graph Drawing, GD 1998

Y2 - 13 August 1998 through 15 August 1998

ER -