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In this paper we provide new randomized algorithms with improved runtimes for solving linear programs with two-sided constraints. In the special case of the minimum cost flow problem on $n$-vertex $m$-edge graphs with integer…

Data Structures and Algorithms · Computer Science 2021-08-24 Jan van den Brand , Yin Tat Lee , Yang P. Liu , Thatchaphol Saranurak , Aaron Sidford , Zhao Song , Di Wang

We present a nearly-linear time algorithm for finding a minimum-cost flow in planar graphs with polynomially bounded integer costs and capacities. The previous fastest algorithm for this problem is based on interior point methods (IPMs) and…

Data Structures and Algorithms · Computer Science 2022-05-04 Sally Dong , Yu Gao , Gramoz Goranci , Yin Tat Lee , Richard Peng , Sushant Sachdeva , Guanghao Ye

Lov\'{a}sz et al. proved that every $6$-edge-connected graph has a nowhere-zero $3$-flow. In fact, they proved a more technical statement which says that there exists a nowhere zero $3$-flow that extends the flow prescribed on the incident…

Space complexity is a critical factor in various computational models, including streaming, parallel/distributed computing, and communication complexity. We study the space complexity of the minimum-cost flow problem, a generalization of…

Data Structures and Algorithms · Computer Science 2026-05-12 Jan van den Brand , Zhao Song , Albert Weng

Maximum flow (and minimum cut) algorithms have had a strong impact on computer vision. In particular, graph cuts algorithms provide a mechanism for the discrete optimization of an energy functional which has been used in a variety of…

Computer Vision and Pattern Recognition · Computer Science 2011-12-30 Camille Couprie , Leo Grady , Hugues Talbot , Laurent Najman

The minimum cost-flow problems have been attracted recently in optimization because of their applications in several areas of applied science and real life. Therefore, finding optima solution of these problems would be significant. Although…

Optimization and Control · Mathematics 2021-01-05 Eghbal Hosseini

Flows over time are used to model many real-world logistic and routing problems. The networks underlying such problems -- streets, tracks, etc. -- are inherently undirected and directions are only imposed on them to reduce the danger of…

Data Structures and Algorithms · Computer Science 2014-10-03 Ashwin Arulselvan , Martin Groß , Martin Skutella

Consider routing traffic on the N x N torus, simultaneously between all source-destination pairs, to minimize the cost $\sum_ec(e)f^2(e)$, where f(e) is the volume of flow across edge e and the c(e) form an i.i.d. random environment. We…

Probability · Mathematics 2011-11-09 David Aldous

We study the electrical distribution network reconfiguration problem, defined as follows. We are given an undirected graph with a root vertex, demand at each non-root vertex, and resistance on each edge. Then, we want to find a spanning…

Data Structures and Algorithms · Computer Science 2024-12-20 Takehiro Ito , Naonori Kakimura , Naoyuki Kamiyama , Yusuke Kobayashi , Yoshio Okamoto

We describe a simple deterministic near-linear time approximation scheme for uncapacitated minimum cost flow in undirected graphs with real edge weights, a problem also known as transshipment. Specifically, our algorithm takes as input a…

Data Structures and Algorithms · Computer Science 2024-06-27 Emily Fox

We consider the problem of finding a minimum edge cost subgraph of a graph satisfying both given node-connectivity requirements and degree upper bounds on nodes. We present an iterative rounding algorithm of the biset LP relaxation for this…

Data Structures and Algorithms · Computer Science 2015-08-11 Takuro Fukunaga , Zeev Nutov , R. Ravi

The minimum-cost subset $k$-connected subgraph problem is a cornerstone problem in the area of network design with vertex connectivity requirements. In this problem, we are given a graph $G=(V,E)$ with costs on edges and a set of terminals…

Data Structures and Algorithms · Computer Science 2013-01-21 Bundit Laekhanukit

The paper focuses on two problems: (i) how to orient the edges of an undirected graph in order to maximize the number of ordered vertex pairs (x,y) such that there is a directed path from x to y, and (ii) how to orient the edges so as to…

Data Structures and Algorithms · Computer Science 2015-06-02 S. L. Hakimi , E. Schmeichel , Neal E. Young

We present a parallel algorithm for computing $(1+\epsilon)$-approximate mincost flow on an undirected graph with $m$ edges, where capacities and costs are assigned to both edges and vertices. Our algorithm achieves $\hat{O}(m)$ work and…

Data Structures and Algorithms · Computer Science 2025-10-24 Bernhard Haeupler , Yonggang Jiang , Yaowei Long , Thatchaphol Saranurak , Shengzhe Wang

Tutte's $3$-flow conjecture states that every $4$-edge-connected graph admits a nowhere-zero $3$-flow. In this paper, we characterize all graphs with independence number at most $4$ that admit a nowhere-zero $3$-flow. The characterization…

Combinatorics · Mathematics 2017-07-24 Jiaao Li , Rong Luo , Yi Wang

We investigate the time-complexity of the All-Pairs Max-Flow problem: Given a graph with $n$ nodes and $m$ edges, compute for all pairs of nodes the maximum-flow value between them. If Max-Flow (the version with a given source-sink pair…

Data Structures and Algorithms · Computer Science 2019-07-11 Amir Abboud , Robert Krauthgamer , Ohad Trabelsi

Motivated by the challenge of analyzing data sets with periodic boundary conditions to investigate transportation properties, we introduce a concept of circular max-flow for graphs mapped onto the circle. Unlike classical max-flow…

Algebraic Topology · Mathematics 2024-12-18 Matteo Pegoraro , Lisbeth Fajstrup

We combine the well known Shortest Paths (SP) problem and the Bottleneck Paths (BP) problem to introduce a new problem called the Shortest Paths for All Flows (SP-AF) problem that has relevance in real life applications. We first solve the…

Data Structures and Algorithms · Computer Science 2013-11-21 Tong-Wook Shinn , Tadao Takaoka

A $3$-dimensional nowhere-zero flow on a graph $G$ is a flow where each edge is assigned a $3$-dimensional vector with unit norm (which corresponds to the points of a $2$-dimensional unit sphere $S^2$). K. Jain posed two conjectures related…

Combinatorics · Mathematics 2026-03-25 Nikolay Ulyanov

Klinz and Woeginger (1995) prove that the minimum cost quickest flow problem is NP-hard. On the other hand, the quickest minimum cost flow problem can be solved efficiently via a straightforward reduction to the quickest flow problem…

Discrete Mathematics · Computer Science 2023-03-07 Martin Skutella