English
Related papers

Related papers: Approximating maximum integral multiflows on bound…

200 papers

Unsplittable flow problems cover a wide range of telecommunication and transportation problems and their efficient resolution is key to a number of applications. In this work, we study algorithms that can scale up to large graphs and…

Data Structures and Algorithms · Computer Science 2023-03-29 François Lamothe , Emmanuel Rachelson , Alain Haït , Cedric Baudoin , Jean-Baptiste Dupe

Following [21, 23], the present work investigates a new relative entropy-regularized algorithm for solving the optimal transport on a graph problem within the randomized shortest paths formalism. More precisely, a unit flow is injected into…

Machine Learning · Computer Science 2021-09-21 Sylvain Courtain , Guillaume Guex , Ilkka Kivimaki , Marco Saerens

The traditional multi-commodity flow problem assumes a given flow network in which multiple commodities are to be maximally routed in response to given demands. This paper considers the multi-commodity flow network-design problem: given a…

Data Structures and Algorithms · Computer Science 2015-06-02 Samir Khuller , Balaji Raghavachari , Neal E. Young

We present a parallel algorithm for the $(1-\epsilon)$-approximate maximum flow problem in capacitated, undirected graphs with $n$ vertices and $m$ edges, achieving $O(\epsilon^{-3}\text{polylog} n)$ depth and $O(m \epsilon^{-3}…

Data Structures and Algorithms · Computer Science 2024-02-26 Arpit Agarwal , Sanjeev Khanna , Huan Li , Prathamesh Patil , Chen Wang , Nathan White , Peilin Zhong

We prove an approximate max-multiflow min-multicut theorem for bounded treewidth graphs. In particular, we show the following: Given a treewidth-$r$ graph, there exists a (fractional) multicommodity flow of value $f$, and a multicut of…

Data Structures and Algorithms · Computer Science 2022-11-14 Tobias Friedrich , Davis Issac , Nikhil Kumar , Nadym Mallek , Ziena Zeif

We have a set of processors (or agents) and a set of graph networks defined over some vertex set. Each processor can access a subset of the graph networks. Each processor has a demand specified as a pair of vertices $<u, v>$, along with a…

Data Structures and Algorithms · Computer Science 2012-10-08 Venkatesan T. Chakaravarthy , Sambuddha Roy , Yogish Sabharwal

This paper introduces a novel theoretical framework and a suite of highly efficient, parallelizable algorithms for solving the large-scale multicommodity flow (MCF) feasibility problem. We reframe the classical constraint-satisfaction…

Optimization and Control · Mathematics 2025-08-26 Pengfei Liu

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

An instance of the Connected Maximum Cut problem consists of an undirected graph G = (V, E) and the goal is to find a subset of vertices S $\subseteq$ V that maximizes the number of edges in the cut \delta(S) such that the induced graph…

Data Structures and Algorithms · Computer Science 2015-07-03 MohammadTaghi Hajiaghayi , Guy Kortsarz , Robert MacDavid , Manish Purohit , Kanthi Sarpatwar

We provide $m^{1+o(1)}k\epsilon^{-1}$-time algorithms for computing multiplicative $(1 - \epsilon)$-approximate solutions to multi-commodity flow problems with $k$-commodities on $m$-edge directed graphs, including concurrent…

Data Structures and Algorithms · Computer Science 2025-04-01 Li Chen , Andrei Graur , Aaron Sidford

We give an O(n log^3 n) algorithm that, given an n-node directed planar graph with arc capacities, a set of source nodes, and a set of sink nodes, finds a maximum flow from the sources to the sinks. Previously, the fastest algorithms known…

Discrete Mathematics · Computer Science 2011-05-12 Glencora Borradaile , Philip N. Klein , Shay Mozes , Yahav Nussbaum , Christian Wulff-Nilsen

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

We consider an undirected multi(commodity)flow demand problem in which a supply graph is planar, each source-sink pair is located on one of three specified faces of the graph, and the capacities and demands are integer-valued and Eulerian.…

Combinatorics · Mathematics 2014-10-28 Maxim A. Babenko , Alexander V. Karzanov

We improve on random sampling techniques for approximately solving problems that involve cuts and flows in graphs. We give a near-linear-time construction that transforms any graph on n vertices into an O(n\log n)-edge graph on the same…

Data Structures and Algorithms · Computer Science 2007-05-23 Andras Benczur , David R. Karger

We give the first O(m polylog(n)) time algorithms for approximating maximum flows in undirected graphs and constructing polylog(n) -quality cut-approximating hierarchical tree decompositions. Our algorithm invokes existing algorithms for…

Data Structures and Algorithms · Computer Science 2015-11-18 Richard Peng

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

We give a number of approximation metatheorems for monotone maximization problems expressible in the first-order logic, in substantially more general settings than the previously known. We obtain * constant-factor approximation algorithm in…

Discrete Mathematics · Computer Science 2021-10-12 Zdeněk Dvořák

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…

Data Structures and Algorithms · Computer Science 2024-06-21 Bernhard Haeupler , D Ellis Hershkowitz , Jason Li , Antti Roeyskoe , Thatchaphol Saranurak

Throughput is a main performance objective in communication networks. This paper considers a fundamental maximum throughput routing problem -- the all-or-nothing multicommodity flow (ANF) problem -- in arbitrary directed graphs and in the…

Data Structures and Algorithms · Computer Science 2022-07-27 Anya Chaturvedi , Chandra Chekuri , Mengxue Liu , Andréa W. Richa , Mattias Rost , Stefan Schmid , Jamison Weber

Finding a \emph{single} best solution is the most common objective in combinatorial optimization problems. However, such a single solution may not be applicable to real-world problems as objective functions and constraints are only…

Data Structures and Algorithms · Computer Science 2022-01-25 Tesshu Hanaka , Masashi Kiyomi , Yasuaki Kobayashi , Yusuke Kobayashi , Kazuhiro Kurita , Yota Otachi