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We introduce low-stretch trees to the visualization community with LSQT, ournovel technique that uses quasi-trees for both layout and edge bundling. Ourmethod offers strong computational speed and complexity guarantees byleveraging the convenient properties of low-stretch trees, which accuratelyreflect the topological structure of arbitrary graphs with superior fidelitycompared to arbitrary spanning trees. Low-stretch quasi-trees also haveprovable sparseness guarantees, providing algorithmic support for aggressivede-cluttering of hairball graphs. LSQT does not rely on previously computedvertex positions and computes bundles based on topological structure before anygeometric layout occurs. Edge bundles are computed efficiently and stored in anexplicit data structure that supports sophisticated visual encoding andinteraction techniques, including dynamic layout adjustment and interactivebundle querying. Our unoptimized implementation handles graphs of over 100,000edges in eight seconds, providing substantially higher performance thanprevious approaches.

LSQT: Low-Stretch Quasi-Trees for Bundling and Layout