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

Christian A. Duncan, Michael T. Goodrich, Stephen G. Kobourov

Research output: Chapter in Book/Report/Conference proceedingConference contribution

14 Scopus citations


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).

Original languageEnglish (US)
Title of host publicationGraph Drawing - 6th International Symposium, GD 1998, Proceedings
EditorsSue H. Whitesides
Number of pages14
ISBN (Print)3540654739, 9783540654735
StatePublished - 1999
Event6th International Symposium on Graph Drawing, GD 1998 - Montreal, Canada
Duration: Aug 13 1998Aug 15 1998

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Other6th International Symposium on Graph Drawing, GD 1998

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Computer Science(all)


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