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

11 Scopus citations

Abstract

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 publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringer Verlag
Pages111-124
Number of pages14
Volume1547
ISBN (Print)3540654739, 9783540654735
DOIs
StatePublished - 1999
Externally publishedYes
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)
Volume1547
ISSN (Print)03029743
ISSN (Electronic)16113349

Other

Other6th International Symposium on Graph Drawing, GD 1998
CountryCanada
CityMontreal
Period8/13/988/15/98

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ASJC Scopus subject areas

  • Computer Science(all)
  • Theoretical Computer Science

Cite this

Duncan, C. A., Goodrich, M. T., & Kobourov, S. G. (1999). Balanced aspect ratio trees and their use for drawing very large graphs. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1547, pp. 111-124). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 1547). Springer Verlag. https://doi.org/10.1007/3-540-37623-2_9