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Related papers: Integer Plane Multiflow Maximisation : Flow-Cut Ga…

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Cutting planes for mixed-integer linear programs (MILPs) are typically computed in rounds by iteratively solving optimization problems, the so-called separation. Instead, we reframe the problem of finding good cutting planes as a continuous…

Optimization and Control · Mathematics 2023-07-10 Didier Chételat , Andrea Lodi

We give an $O(n^{1.5}\log n)$ time algorithm for finding the maximum flow in a directed planar graph with multiple sources and a single sink. The techniques generalize to a subquadratic time algorithm for bounded genus graphs.

Discrete Mathematics · Computer Science 2010-09-03 Glencora Borradaile , Christian Wulff-Nilsen

We give an algorithm that computes exact maximum flows and minimum-cost flows on directed graphs with $m$ edges and polynomially bounded integral demands, costs, and capacities in $m^{1+o(1)}$ time. Our algorithm builds the flow through a…

Data Structures and Algorithms · Computer Science 2022-04-26 Li Chen , Rasmus Kyng , Yang P. Liu , Richard Peng , Maximilian Probst Gutenberg , Sushant Sachdeva

We discuss the extension of the maximal-unitarity method to two loops, focusing on the example of the planar double box. Maximal cuts are reinterpreted as contour integrals, with the choice of contour fixed by the requirement that integrals…

High Energy Physics - Theory · Physics 2012-12-11 Henrik Johansson , David A. Kosower , Kasper J. Larsen

In a multihop wireless network, wireless interference is crucial to the maximum multiflow (MMF) problem, which studies the maximum throughput between multiple pairs of sources and sinks. In this paper, we observe that network coding could…

Information Theory · Computer Science 2012-02-15 Jin-Yi Zhou , Shu-Tao Xia , Yong Jiang , Hai-Tao Zheng

Many problems of interest for cyber-physical network systems can be formulated as Mixed Integer Linear Programs in which the constraints are distributed among the agents. In this paper we propose a distributed algorithm to solve this class…

Optimization and Control · Mathematics 2017-12-06 Andrea Testa , Alessandro Rucco , Giuseppe Notarstefano

Let $G=(V,E)$ be a graph with four distinguished vertices, two sources $s_1, s_2$ and two sinks $t_1,t_2$, let $c:\, E \rightarrow \mathbb Z_+$ be a capacity function, and let ${\cal P}$ be the set of all simple paths in $G$ from $s_1$ to…

Combinatorics · Mathematics 2024-07-26 Guoli Ding , Rongchuan Tao , Mengxi Yang , Wenan Zang

Network coding (NC), when combined with multipath routing, enables a linear programming (LP) formulation for a multi-source multicast with intra-session network coding (MISNC) problem. However, it is still hard to solve using conventional…

Networking and Internet Architecture · Computer Science 2020-12-29 Jianwei Zhang

We consider offline scheduling algorithms that incorporate speed scaling to address the bicriteria problem of minimizing energy consumption and a scheduling metric. For makespan, we give linear-time algorithms to compute all non-dominated…

Data Structures and Algorithms · Computer Science 2007-05-23 David P. Bunde

One issue limiting the adaption of large-scale multi-region segmentation is the sometimes prohibitive memory requirements. This is especially troubling considering advances in massively parallel computing and commercial graphics processing…

Computer Vision and Pattern Recognition · Computer Science 2015-02-02 John S. H. Baxter , Martin Rajchl , Jing Yuan , Terry M. Peters

Co-flows model a modern scheduling setting that is commonly found in a variety of applications in distributed and cloud computing. In co-flow scheduling, there are $m$ input ports and $m$ output ports. Each co-flow $j \in J$ can be…

Data Structures and Algorithms · Computer Science 2018-12-04 Sungjin Im , Manish Purohit

The coflow scheduling problem is considered: given an input/output switch with each port having a fixed capacity, find a scheduling algorithm that minimizes the weighted sum of the coflow completion times respecting the port capacities,…

Data Structures and Algorithms · Computer Science 2020-04-14 Akhil Bhimaraju , Debanuj Nayak , Rahul Vaze

We prove the NP-completeness of the integer multiflow problem in planar graphs, with the following restrictions: there are only two demand edges, both lying on the infinite face of the routing graph. This was one of the open challenges…

Discrete Mathematics · Computer Science 2009-11-17 Guyslain Naves

All-Pairs Minimum Cut (APMC) is a fundamental graph problem that asks to find a minimum $s,t$-cut for every pair of vertices $s,t$. A recent line of work on fast algorithms for APMC has culminated with a reduction of APMC to…

Data Structures and Algorithms · Computer Science 2026-04-07 Yotam Kenneth-Mordoch , Robert Krauthgamer

We introduce a stochastic version of the cutting-plane method for a large class of data-driven Mixed-Integer Nonlinear Optimization (MINLO) problems. We show that under very weak assumptions the stochastic algorithm is able to converge to…

Optimization and Control · Mathematics 2021-03-04 Dimitris Bertsimas , Michael Lingzhi Li

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

We consider a routing problem which plays an important role in several applications, primarily in communication network planning and VLSI layout design. The original underlying graph algorithmic task is called Disjoint Paths problem. In…

Data Structures and Algorithms · Computer Science 2018-09-19 Rupei Xu , András Faragó

We consider the problem of scheduling a set of jobs on a set of identical parallel machines, with the aim of minimizing the total weighted completion time. The problem has been solved in the literature with a number of mathematical…

Data Structures and Algorithms · Computer Science 2020-06-24 Arthur Kramer , Mauro Dell'Amico , Manuel Iori

There is a long history of approximation schemes for the problem of scheduling jobs on identical machines to minimize the makespan. Such a scheme grants a $(1+\epsilon)$-approximation solution for every $\epsilon > 0$, but the running time…

Data Structures and Algorithms · Computer Science 2021-07-30 Sebastian Berndt , Max A. Deppert , Klaus Jansen , Lars Rohwedder

The (non-uniform) sparsest cut problem is the following graph-partitioning problem: given a "supply" graph, and demands on pairs of vertices, delete some subset of supply edges to minimize the ratio of the supply edges cut to the total…

Data Structures and Algorithms · Computer Science 2021-06-01 Vincent Cohen-Addad , Anupam Gupta , Philip N. Klein , Jason Li