Low-Step Multi-Commodity Flow Emulators
Thatchaphol Saranurak
University of Michigan
Add to Calendar
2024-05-14 16:15:00
2024-05-14 17:15:00
America/New_York
Low-Step Multi-Commodity Flow Emulators
Abstract: We introduce the concept of low-step multi-commodity flow emulators for any undirected, capacitated graph. At a high level, these emulators contain approximate multi-commodity flows whose paths contain a small number of edges, shattering the infamous flow decomposition barrier for multi-commodity flow.We prove the existence of low-step multi-commodity flow emulators and develop efficient algorithms to compute them. We then apply them to solve constant-approximate $k$-commodity flow in $O((m+k)^{1+\epsilon})$ time. To bypass the $O(mk)$ flow decomposition barrier, we represent our output multi-commodity flow implicitly; prior to our work, even the existence of implicit constant-approximate multi-commodity flows of size $o(mk)$ was unknown.Our results generalize to the \emph{minimum cost} setting, where each edge has an associated cost and the multi-commodity flow must satisfy a cost budget. Our algorithms are also parallel.
32-G449