Redistricting is the problem of partitioning a set of geographic units into a fixed number of
subsets called districts, subject to a list of rules and priorities. These districts are used for …

The American winner-take-all congressional district system empowers politicians to
engineer electoral outcomes by manipulating district boundaries. Existing computational …

States in the United States redraw their electoral district boundaries every 10 years. This
redistricting process can be contentious and has long-lasting consequences for political …

Projection robust Wasserstein (PRW) distance is recently proposed to efficiently mitigate the
curse of dimensionality in the classical Wasserstein distance. In this paper, by equivalently …

During decennial redistricting, mapmakers are often instructed to preserve political
subdivisions and prior district cores as much as possible. Political subdivisions can include …

In this work, we present the Bregman Alternating Projected Gradient (BAPG) method, a
single-loop algorithm that offers an approximate solution to the Gromov-Wasserstein (GW) …

Dimension reduction techniques typically seek an embedding of a high-dimensional point
cloud into a low-dimensional Euclidean space which optimally preserves the geometry of …

The fields of effective resistance and optimal transport on graphs are filled with rich
connections to combinatorics, geometry, machine learning, and beyond. In this article we put …

We apply persistent homology, the dominant tool from the field of topological data analysis,
to study electoral redistricting. Our method combines the geographic information from a …

Defining meaningful distances between samples in a dataset is a fundamental problem in
machine learning. Optimal Transport (OT) lifts a distance between features (the" ground …