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In this paper we provide an algorithm which given any $m$-edge $n$-vertex directed graph with integer capacities at most $U$ computes a maximum $s$-$t$ flow for any vertices $s$ and $t$ in $m^{11/8+o(1)}U^{1/4}$ time with high probability.…

Data Structures and Algorithms · Computer Science 2019-11-01 Yang P. Liu , Aaron Sidford

Minimum cost homomorphism problems can be viewed as a generalization of list homomorphism problems. They also extend two well-known graph colouring problems: the minimum colour sum problem and the optimum cost chromatic partition problem.…

Computational Complexity · Computer Science 2016-08-23 Pavol Hell , Mayssam Mohammadi Nevisi

We present formalisations of the correctness of executable algorithms to solve minimum-cost flow problems in Isabelle/HOL. Two of the algorithms are based on the technique of scaling, most notably Orlin's algorithm, which has the fastest…

Logic in Computer Science · Computer Science 2026-02-04 Mohammad Abdulaziz , Thomas Ammer

An algorithm is presented which produces the minimum cost bipartite matching between two sets of M points each, where the cost of matching two points is proportional to the minimum distance by which a particle could reach one point from the…

Data Structures and Algorithms · Computer Science 2013-11-20 Kyle Treleaven , Josh Bialkowski , Emilio Frazzoli

We consider a constrained version of the shortest path problem on the complete graphs whose edges have independent random lengths and costs. We establish the asymptotic value of the minimum length as a function of the cost-budget within a…

Combinatorics · Mathematics 2021-11-16 Alan Frieze , Tomasz Tkocz

This paper deals with robust optimization applied to network flows. Two robust variants of the minimum-cost integer flow problem are considered. Thereby, uncertainty in problem formulation is limited to arc unit costs and expressed by a…

Artificial Intelligence · Computer Science 2020-02-27 Marko Špoljarec , Robert Manger

The minimum-cost flow problem is a classic problem in combinatorial optimization with various applications. Several pseudo-polynomial, polynomial, and strongly polynomial algorithms have been developed in the past decades, and it seems that…

Data Structures and Algorithms · Computer Science 2015-09-16 Tobias Brunsch , Kamiel Cornelissen , Bodo Manthey , Heiko Röglin , Clemens Rösner

We study the problem of finding the cycle of minimum cost-to-time ratio in a directed graph with $ n $ nodes and $ m $ edges. This problem has a long history in combinatorial optimization and has recently seen interesting applications in…

Data Structures and Algorithms · Computer Science 2018-03-02 Karl Bringmann , Thomas Dueholm Hansen , Sebastian Krinninger

In this paper we provide an algorithm for maintaining a $(1-\epsilon)$-approximate maximum flow in a dynamic, capacitated graph undergoing edge additions. Over a sequence of $m$-additions to an $n$-node graph where every edge has capacity…

Data Structures and Algorithms · Computer Science 2022-12-14 Jan van den Brand , Yang P. Liu , Aaron Sidford

The support of a flow $x$ in a network is the subdigraph induced by the arcs $uv$ for which $x(uv)>0$. We discuss a number of results on flows in networks where we put certain restrictions on structure of the support of the flow. Many of…

Discrete Mathematics · Computer Science 2024-05-16 Stéphane Bessy , Jørgen Bang-Jensen , Lucas Picasarri-Arrieta

Flows and colorings are disparate concepts in graph algorithms -- the former is tractable while the latter is intractable. Tutte introduced the concept of nowhere-zero flows to unify these two concepts. Jaeger showed that nowhere-zero flows…

Data Structures and Algorithms · Computer Science 2025-04-29 Karthekeyan Chandrasekaran , Siyue Liu , R. Ravi

In this paper we consider generalized flow problems where there is an $m$-edge $n$-node directed graph $G = (V,E)$ and each edge $e \in E$ has a loss factor $\gamma_e >0$ governing whether the flow is increased or decreased as it crosses…

Data Structures and Algorithms · Computer Science 2025-10-21 Shunhua Jiang , Michael Kapralov , Lawrence Li , Aaron Sidford

We combine the work of Garg and Konemann, and Fleischer with ideas from dynamic graph algorithms to obtain faster (1-eps)-approximation schemes for various versions of the multicommodity flow problem. In particular, if eps is moderately…

Data Structures and Algorithms · Computer Science 2015-03-13 Aleksander Madry

We give polynomial time logarithmic approximation guarantees for the budget minimization, as well as for the profit maximization versions of minimum spanning tree interdiction. In this problem, the goal is to remove some edges of an…

Data Structures and Algorithms · Computer Science 2025-07-28 Rafail Ostrovsky , Yuval Rabani , Yoav Siman Tov

In this paper we study the min-cost flow problem in planar networks. We start with the min-cost flow problem and apply two transformations, one is based on geometric duality of planar graphs and the other on linear programming duality. The…

Discrete Mathematics · Computer Science 2013-07-01 Haim Kaplan , Yahav Nussbaum

Network flow interdiction analysis studies by how much the value of a maximum flow in a network can be diminished by removing components of the network constrained to some budget. Although this problem is strongly NP-complete on general…

Discrete Mathematics · Computer Science 2008-01-14 Rico Zenklusen

We consider approximation algorithms for the problem of finding $x$ of minimal norm $\|x\|$ satisfying a linear system $\mathbf{A} x = \mathbf{b}$, where the norm $\|\cdot \|$ is arbitrary and generally non-Euclidean. We show a simple…

Data Structures and Algorithms · Computer Science 2016-06-28 Jonah Sherman

The present work studies a kind of Maximum Concurrent Flow Problem, called as Extended Maximum Concurrent Flow Problem with Saturated Capacity. Our major contributions are as follows: (A) Propose the definition of Extensive Maximum…

Optimization and Control · Mathematics 2013-11-12 Congdian Cheng

This paper bridges discrete and continuous optimization approaches for decomposable submodular function minimization, in both the standard and parametric settings. We provide improved running times for this problem by reducing it to a…

Data Structures and Algorithms · Computer Science 2021-03-08 Kyriakos Axiotis , Adam Karczmarz , Anish Mukherjee , Piotr Sankowski , Adrian Vladu

In this paper, we investigate the problem of finding minimal graphs in $M^n\times\mathbb R$ with general boundary conditions using a variational approach. We look at so called generalized solutions of the Dirichlet Problem that minimize a…

Differential Geometry · Mathematics 2013-11-18 Matthew McGonagle , Ling Xiao