Deterministic Min-cut in Poly-logarithmic Max-flows release_nsgh4kakazbxtf2kvc7ps2qo3y

by Jason Li, Debmalya Panigrahi

Released as a article .

2021  

Abstract

We give a deterministic algorithm for finding the minimum (weight) cut of an undirected graph on n vertices and m edges using polylog(n) calls to any maximum flow subroutine. Using the current best deterministic maximum flow algorithms, this yields an overall running time of Õ(m ·min(√(m), n^2/3)) for weighted graphs, and m^4/3+o(1) for unweighted (multi)-graphs. This marks the first improvement for this problem since a running time bound of Õ(mn) was established by several papers in the early 1990s. To obtain this result, we introduce a new tool for finding minimum cuts of an undirected graph: *isolating cuts*. Given a set of vertices R, this entails finding cuts of minimum weight that separate (or isolate) each individual vertex v∈ R from the rest of the vertices R∖{v}. Naïvely, this can be done using |R| maxflow calls, but we show that just O(log |R|) suffice for finding isolating cuts for any set of vertices R. We call this the *isolating cut lemma*.
In text/plain format

Archived Files and Locations

application/pdf  458.4 kB
file_5clb6k2qgrbzpjhb6ukstavibe
arxiv.org (repository)
web.archive.org (webarchive)
Read Archived PDF
Preserved and Accessible
Type  article
Stage   submitted
Date   2021-11-03
Version   v1
Language   en ?
arXiv  2111.02008v1
Work Entity
access all versions, variants, and formats of this works (eg, pre-prints)
Catalog Record
Revision: e31cb2ab-b718-4966-8430-ecc631a53bf1
API URL: JSON