Searcharxiv⌕ Search
Home/Archive/arXiv

arXiv · 2409.08350

An efficient heuristic for approximate maximum flow computations

Jingyun Qian·Georg Hahn
View original source ↗Read source document ↗Export metadata ↓

Abstract

Several concepts borrowed from graph theory are routinely used to better understand the inner workings of the (human) brain. To this end, a connectivity network of the brain is built first, which then allows one to assess quantities such as information flow and information routing via shortest path and maximum flow computations. Since brain networks typically contain several thousand nodes and edges, computational scaling is a key research area. In this contribution, we focus on approximate maximum flow computations in large brain networks. By combining graph partitioning with maximum flow computations, we propose a new approximation algorithm for the computation of the maximum flow with runtime O(|V||E|^2/k^2) compared to the usual runtime of O(|V||E|^2) for the Edmonds-Karp algorithm, where $V$ is the set of vertices, $E$ is the set of edges, and $k$ is the number of partitions. We assess both accuracy and runtime of the proposed algorithm on simulated graphs as well as on graphs downloaded from the Brain Networks Data Repository (https://networkrepository.com).

Explore related subjects

cs.DSstat.ME

Keep this discovery

BibTeXRIS

Jingyun Qian, Georg Hahn. 2024-09-12. An efficient heuristic for approximate maximum flow computations. https://arxiv.org/abs/2409.08350

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

Quasi-Monte Carlo Beyond Hardy-Krause II: $(1 + \varepsilon)n$ Samples Suffice

Numerical integration studies how well one can estimate the integral of a function $f$ over $[0,1)^d$ using $n$ sample points. The two classical methods, Monte Carlo (MC) and quasi-Monte Carlo (QMC), have complementary strengths and weaknesses, and a fundamental question is to design an approach that combines the benefits of both. Recently, building on the transference principle in discrepancy theory, Bansal and Jiang~\cite{BJ25a} gave a randomized QMC method that bridges MC and QMC guarantees using only i.i.d.\ samples. Their method also goes beyond the classical Koksma--Hlawka inequality: it achieves integration error $\widetilde{O}_d(\sigma_{\mathsf{SO}}(f)/n)$, where the smoothed-out variation $\sigma_{\mathsf{SO}}(f)$ can be substantially smaller than the Hardy--Krause variation that governs the classical bound. However, their algorithm requires $n^2$ i.i.d.\ samples as input, and this quadratic blowup is inherent to any method based on the transference principle. In this work, we bypass the quadratic blowup: for any constant $\varepsilon > 0$, we show that $(1+\varepsilon)n$ i.i.d.\ samples suffice to both obtain the beyond-Hardy--Krause guarantee of~\cite{BJ25a}, resolving an open problem posed there, and to produce low-discrepancy point sequences. Our algorithms are variants of the online Haar-thinning method of Dwivedi, Feldheim, Gurel-Gurevich, and Ramdas~\cite{DFG+19}.

cs.DS↗
arXiv2026

Single-Exponential Algorithms and a Polynomial Kernel for Strong Connectivity Augmentation

Strong Connectivity Augmentation (SCA) asks whether a directed acyclic graph can be made strongly connected by adding at most $k$ prescribed links whose total weight is within a given budget. Klinkby, Misra, and Saurabh (SODA 2021) gave an $O^*(2^{O(k\log k)})$-time algorithm and asked whether the problem admits a single-exponential parameterized algorithm and a polynomial kernel. We answer both questions affirmatively: SCA can be solved in $O^*(9^k)$ time and admits a polynomial kernel with $O(k^4)$ vertices and $O(k^{16})$ bits. For unweighted SCA, we obtain $O^*(4^k)$ time and a kernel with $O(k^3)$ vertices. Our algorithms are based on a particularly simple reduction to Strongly Connected Spanning Subgraph with two edge costs.

cs.DS↗