  We introduce low-stretch trees to the visualization community with LSQT, our
novel technique that uses quasi-trees for both layout and edge bundling. Our
method offers strong computational speed and complexity guarantees by
leveraging the convenient properties of low-stretch trees, which accurately
reflect the topological structure of arbitrary graphs with superior fidelity
compared to arbitrary spanning trees. Low-stretch quasi-trees also have
provable sparseness guarantees, providing algorithmic support for aggressive
de-cluttering of hairball graphs. LSQT does not rely on previously computed
vertex positions and computes bundles based on topological structure before any
geometric layout occurs. Edge bundles are computed efficiently and stored in an
explicit data structure that supports sophisticated visual encoding and
interaction techniques, including dynamic layout adjustment and interactive
bundle querying. Our unoptimized implementation handles graphs of over 100,000
edges in eight seconds, providing substantially higher performance than
previous approaches.
