Doctor of Philosophy in Computer Science (PhD)
Optimization for Machine Learning
Low-stretch trees are spanning trees which provide approximate distance preservation for edges in the original graph by minimizing stretch. We explore the application of these trees to network visualization. In particular, we present a novel edge bundling technique, LSTB, that computes edge bundles explicitly and efficiently and does not rely on fixed vertex positions. This approach is in contrast to previous methods, which require the user to provide a layout of the input graph. We introduce an abstract framework for edge bundling methods, which provides a unifying formalization of bundling terminology and techniques, as well as a classification of such methods. Based on this framework, LSTB provides algorithmic support for sophisticated visual encodings, including dynamic layout adjustment and interactive bundle querying.In addition, we explore the use of the multiplicative weights update method to compute a distribution over low-stretch trees in order to achieve low stretch for all edges in expectation, rather than on average. We present the results of using this distribution in place of a single low-stretch tree as a routing graph for LSTB. While the distribution provides better stretch guarantees, we find that from a visual perspective a single low-stretch tree provides a better routing graph for the LSTB edge bundling application.
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