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CounterTop: little patterns in big graphs
Mawhirter, Daniel E.
Mawhirter, Daniel E.
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2023
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Abstract
Consider data. The abstract, amorphous, enigmatic concept which the Oxford English Dictionary defines as ``facts and statistics collected together for reference or analysis". This simple definition implies a world of possibilities in how we interact with data.
Before the internet, before the world became so connected, data may have taken the form of manually recorded events, measurements, or observations. Due to the manual effort involved, recording was a deliberate act, one only worth undertaking for information known to be relevant. Since then our ability to automatically record data has advanced tremendously, to the point that recording is often a side effect. But the larger contribution of the internet comes from connectivity as transactions, acquaintances, and even workplaces are no longer bound by geography.
What are we to do with this abundant resource? Data means very little in and of itself, so how do we extract useful insights from today's and tomorrow's massive datasets?
These questions may never have truly satisfactory answers. This dissertation certainly will not present comprehensive answers. But a portion of the answer necessarily involves a search for patterns: manageable slices of a dataset that exhibit similar properties. Patterns can be interesting because of being common or rare, sparse or dense, large or small, or any other property one can imagine.
In order to manage the scope of this research, it is subject to a few constraints. I chose to focus on matching patterns in graphs where edges in each direction are equivalent, known as undirected graphs. This work also implicitly considers graphs to convey only topology information, making them unlabeled. But subject to these constraints, this dissertation contains a body of work that answers the question:
How can we efficiently find little patterns in big graphs?
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