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Related papers: A New Algorithm for Multicommodity Flow

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We provide a new algebraic technique to solve the sequential flow problem in polynomial space. The task is to maximise the flow through a graph where edge capacities can be changed over time by choosing a sequence of capacity labelings from…

Optimization and Control · Mathematics 2026-02-09 Hugo Gimbert , Corto Mascle , Patrick Totzke

We explore here surprising links between the time-cost-tradeoff problem and the minimum cost flow problem that lead to fast, strongly polynomial, algorithms for both problems. One of the main results is a new algorithm for the unit capacity…

Data Structures and Algorithms · Computer Science 2025-07-30 Dorit S. Hochbaum

When solving hard multicommodity network flow problems using an LP-based approach, the number of commodities is a driving factor in the speed at which the LP can be solved, as it is linear in the number of constraints and variables. The…

Optimization and Control · Mathematics 2021-08-16 Ahmad Kazemi , Pierre Le Bodic , Andreas Ernst , Mohan Krishnamoorthy

This article focuses on a biobjective extension of the maximum flow network interdiction problem, where each arc in the network is associated with two capacity values. Two maximum flows from a source to a sink are to be computed…

Combinatorics · Mathematics 2020-10-09 Luca E. Schäfer , Stefan Ruzika , Sven O. Krumke , Carlos M. Fonseca

The multi-commodity flow (MCF) problem is a fundamental topic in network flow and combinatorial optimization, with broad applications in transportation, communication, and logistics, etc. Nowadays, the rapid expansion of allocation systems…

Machine Learning · Computer Science 2026-02-12 Xinyu Yuan , Yan Qiao , Zonghui Wang , Wenzhi Chen

We show a deterministic constant-time local algorithm for constructing an approximately maximum flow and minimum fractional cut in multisource-multitarget networks with bounded degrees and bounded edge capacities. Locality means that the…

Data Structures and Algorithms · Computer Science 2023-11-03 Endre Csóka , András Pongrácz

In this paper, we bound the integrality gap and the approximation ratio for maximum plane multiflow problems and deduce bounds on the flow-cut-gap. Planarity means here that the union of the supply and demand graph is planar. We first prove…

Data Structures and Algorithms · Computer Science 2020-03-19 Naveen Garg , Nikhil Kumar , András Sebő

We introduce a new approach to computing an approximately maximum s-t flow in a capacitated, undirected graph. This flow is computed by solving a sequence of electrical flow problems. Each electrical flow is given by the solution of a…

Data Structures and Algorithms · Computer Science 2010-10-20 Paul Christiano , Jonathan A. Kelner , Aleksander Madry , Daniel A. Spielman , Shang-Hua Teng

Multi-label submodular Markov Random Fields (MRFs) have been shown to be solvable using max-flow based on an encoding of the labels proposed by Ishikawa, in which each variable $X_i$ is represented by $\ell$ nodes (where $\ell$ is the…

Data Structures and Algorithms · Computer Science 2017-02-21 Thalaiyasingam Ajanthan , Richard Hartley , Mathieu Salzmann

To enable fast uncertainty quantification of fluid flow in a discrete fracture network (DFN), we present two approaches to quickly compute fluid flow in DFNs using combinatorial optimization algorithms. Specifically, the presented Hanan…

Geophysics · Physics 2018-11-14 A. Hobé , D. Vogler , M. P. Seybold , A. Ebigbo , R. R. Settgast , M. O. Saar

In this paper we study minimum cut and maximum flow problems on planar graphs, both in static and in dynamic settings. First, we present an algorithm that given an undirected planar graph computes the minimum cut between any two given…

Data Structures and Algorithms · Computer Science 2010-11-23 Giuseppe F. Italiano , Piotr Sankowski

We give an information flow interpretation for multicasting using network coding. This generalizes the fluid model used to represent flows to a single receiver. Using the generalized model, we present a decentralized algorithm to minimize…

Information Theory · Computer Science 2007-07-13 Kapil Bhattad , Niranjan Ratnakar , Ralf Koetter , Krishna R. Narayanan

We present novel oblivious routing algorithms for both splittable and unsplittable multicommodity flow. Our algorithm for minimizing congestion for \emph{unsplittable} multicommodity flow is the first oblivious routing algorithm for this…

Data Structures and Algorithms · Computer Science 2017-12-07 Michael Schapira , Gal Shahaf

A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling. The main measure of progress is that within a strongly polynomial number of…

Data Structures and Algorithms · Computer Science 2016-03-01 László A. Végh

We present a new algorithm for computing balanced flows in equality networks arising in market equilibrium computations. The current best time bound for computing balanced flows in such networks requires $O(n)$ maxflow computations, where…

Data Structures and Algorithms · Computer Science 2016-05-16 Omar Darwish , Kurt Mehlhorn

It is well-known that the Ford-Fulkerson algorithm for finding a maximum flow in a network need not terminate if we allow the arc capacities to take irrational values. Every non-terminating example converges to a limit flow, but this limit…

Combinatorics · Mathematics 2015-04-17 Spencer Backman , Tony Huynh

Currently, the best known tradeoff between approximation ratio and complexity for the Sparsest Cut problem is achieved by the algorithm in [Sherman, FOCS 2009]: it computes $O(\sqrt{(\log n)/\varepsilon})$-approximation using…

Data Structures and Algorithms · Computer Science 2025-07-11 Vladimir Kolmogorov

The Maximum Flow (Max-Flow) problem is a cornerstone in graph theory and combinatorial optimization, aiming to determine the largest possible flow from a designated source node to a sink node within a capacitated flow network. It has…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-11-04 Shruthi Kannappan , Ashwina Kumar , Rupesh Nasre

In this paper, we present a general framework for efficiently computing diverse solutions to combinatorial optimization problems. Given a problem instance, the goal is to find $k$ solutions that maximize a specified diversity measure; the…

Data Structures and Algorithms · Computer Science 2025-04-25 Yuni Iwamasa , Tomoki Matsuda , Shunya Morihira , Hanna Sumita

In this work, we develop a new framework for dynamic network flow problems based on optimal transport theory. We show that the dynamic multi-commodity minimum-cost network flow problem can be formulated as a multi-marginal optimal transport…

Optimization and Control · Mathematics 2021-06-29 Isabel Haasler , Axel Ringh , Yongxin Chen , Johan Karlsson