All You Need is Resistance: On the Equivalence of Effective Resistance and Certain Optimal Transport Problems on Graphs

arXiv:2404.15261v1 Announce Type: cross
Abstract: 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 forth a bold claim: that the two fields should be understood as one and the same, up to a choice of $p$. We make this claim precise by introducing the parameterized family of $p$-Beckmann distances for probability measures on graphs and relate them sharply to certain Wasserstein distances. …

abstract article arxiv beyond bold claim combinatorics cs.dm cs.lg fields geometry graphs machine machine learning math.oc math.pr transport type