Geometry of Graph Partitions via Optimal Transport
Name
19m1295258.pdf
Description
Published version
Size
2.42 MB
Format
Adobe PDF
Checksum (MD5)
7e4f37318a4f08ef35ae206a5baae548
Author(s)
Abrishami, Tara
Guillen, Nestor
Rule, Parker
Schutzman, Zachary
Solomon, Justin
Weighill, Thomas
Wu, Si
Date Issued
2020
Journal
SIAM Journal on Scientific Computing
Publisher
Society for Industrial & Applied Mathematics (SIAM)
Version
Final published version
Abstract
© 2020 Tara Abrishami, Nestor Guillen, Parker Rule, 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 the metric's value for new problems in ensemble-based analysis of political districting plans.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Terms of Use
Article is made available in accordance with the publisher's policy and may be subject to US copyright law. Please refer to the publisher's site for terms of use.
Persistent DSpace Link
DOI of Published Version
https://doi.org/10.1137/19M1295258
