In this note, we study the expander decomposition problem in a more general setting where the input graph has positively weighted edges and nonnegative demands on its vertices. We show how to extend the techniques of Chuzhoy et al. (FOCS 2020) to this wider setting, obtaining a deterministic algorithm for the problem in almost-linear time.
@article{arxiv.2106.01567,
title = {Deterministic Weighted Expander Decomposition in Almost-linear Time},
author = {Jason Li and Thatchaphol Saranurak},
journal= {arXiv preprint arXiv:2106.01567},
year = {2021}
}