Drawing large graphs by low-rank stress majorization

Marc Khoury, Yifan Hu, Shankar Krishnan, Carlos Eduardo Scheidegger

Research output: Contribution to journalArticle

15 Citations (Scopus)

Abstract

Optimizing a stress model is a natural technique for drawing graphs: one seeks an embedding into Rd which best preserves the induced graph metric. Current approaches to solving the stress model for a graph with |ν| nodes and |ε| edges require the full all-pairs shortest paths (APSP) matrix, which takes O(|ν|2 log |ε|+|ν||ε|) time and O(|ν|2) space. We propose a novel algorithm based on a low-rank approximation to the required matrices. The crux of our technique is an observation that it is possible to approximate the full APSP matrix, even when only a small subset of its entries are known. Our algorithm takes time O(k|ν|+|ν| log|ν|+|ε|) per iteration with a preprocessing time of O(k3 +k(|ε|+|ν| log|ν|)+k2|ν|) and memory usage of O(k|ν|), where a user-defined parameter k trades off quality of approximation with running time and space. We give experimental results which show, to the best of our knowledge, the largest (albeit approximate) full stress model based layouts to date. Computer Graphics Forum

Original languageEnglish (US)
Pages (from-to)975-984
Number of pages10
JournalComputer Graphics Forum
Volume31
Issue number3 PART1
StatePublished - 2012
Externally publishedYes

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Computer graphics
Set theory
Data storage equipment

ASJC Scopus subject areas

  • Computer Networks and Communications

Cite this

Khoury, M., Hu, Y., Krishnan, S., & Scheidegger, C. E. (2012). Drawing large graphs by low-rank stress majorization. Computer Graphics Forum, 31(3 PART1), 975-984.

Drawing large graphs by low-rank stress majorization. / Khoury, Marc; Hu, Yifan; Krishnan, Shankar; Scheidegger, Carlos Eduardo.

In: Computer Graphics Forum, Vol. 31, No. 3 PART1, 2012, p. 975-984.

Research output: Contribution to journalArticle

Khoury, M, Hu, Y, Krishnan, S & Scheidegger, CE 2012, 'Drawing large graphs by low-rank stress majorization', Computer Graphics Forum, vol. 31, no. 3 PART1, pp. 975-984.
Khoury, Marc ; Hu, Yifan ; Krishnan, Shankar ; Scheidegger, Carlos Eduardo. / Drawing large graphs by low-rank stress majorization. In: Computer Graphics Forum. 2012 ; Vol. 31, No. 3 PART1. pp. 975-984.
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