Geometry of Graph Partitions via Optimal Transport
Abstract
We define a distance metric between partitions of a graph using machinery from optimal transport. Our metric is built from a linear assignment problem that matches partition components, with assignment cost proportional to transport distance over graph edges. We show that our distance can be computed using a single linear program without precomputing pairwise assignment costs and derive several theoretical properties of the metric. Finally, we provide experiments demonstrating these properties empirically, specifically focusing on its value for new problems in ensemblebased analysis of political districting plans.
 Publication:

arXiv eprints
 Pub Date:
 October 2019
 arXiv:
 arXiv:1910.09618
 Bibcode:
 2019arXiv191009618A
 Keywords:

 Mathematics  Optimization and Control;
 Computer Science  Computers and Society;
 Computer Science  Discrete Mathematics
 EPrint:
 30 pages, 15 figures