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Related papers: On Weighted Multicommodity Flows in Directed Netwo…

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Consider a routing problem consisting of a demand graph H and a supply graph G. If the pair obeys the cut condition, then the flow-cut gap for this instance is the minimum value C such that there is a feasible multiflow for H if each edge…

Discrete Mathematics · Computer Science 2010-08-16 Chandra Chekuri , F. Bruce Shepherd , Christophe Weibel

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

This paper researches combinatorial algorithms for the multi-commodity flow problem. We relax the capacity constraints and introduce a penalty function $h$ for each arc. If the flow exceeds the capacity on arc $a$, arc $a$ would have a…

Optimization and Control · Mathematics 2020-10-08 Pengfei Liu

Given a graph $G=(V,E)$ with two distinguished vertices $s,t\in V$ and an integer $L$, an {\em $L$-bounded flow} is a flow between $s$ and $t$ that can be decomposed into paths of length at most $L$. In the {\em maximum $L$-bounded flow…

Data Structures and Algorithms · Computer Science 2019-02-21 Kateřina Altmanová , Petr Kolman , Jan Voborník

Generative Adversarial Networks have been shown to be powerful in generating content. To this end, they have been studied intensively in the last few years. Nonetheless, training these networks requires solving a saddle point problem that…

Machine Learning · Computer Science 2019-10-09 Jingrong Lin , Keegan Lensink , Eldad Haber

A seminal result of [Fleischer et al. and Karakostas and Kolliopulos, both FOCS 2004] states that system optimal multi-commodity static network flows are always implementable as tolled Wardrop equilibrium flows even if users have…

Computer Science and Game Theory · Computer Science 2025-03-11 Lukas Graf , Tobias Harks , Julian Schwarz

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

We study a variant of Min Cost Flow in which the flow needs to be connected. Specifically, in the Connected Flow problem one is given a directed graph $G$, along with a set of demand vertices $D \subseteq V(G)$ with demands $\mathsf{dem}: D…

Data Structures and Algorithms · Computer Science 2021-07-21 Isja Mannens , Jesper Nederlof , Céline Swennenhuis , Krisztina Szilágyi

We study single commodity network flows with suitable robustness and efficiency specs. An original use of a maximum entropy problem for distributions on the paths of the graph turns this problem into a steering problem for Markov chains…

Mathematical Physics · Physics 2017-09-28 Yongxin Chen , Tryphon T. Georgiou , Michele Pavon , Allen Tannenbaum

There has been intensive work on the parameterized complexity of the typically NP-hard task to edit undirected graphs into graphs fulfilling certain given vertex degree constraints. In this work, we lift the investigations to the case of…

Discrete Mathematics · Computer Science 2018-02-01 Robert Bredereck , Vincent Froese , Marcel Koseler , Marcelo Garlet Millani , André Nichterlein , Rolf Niedermeier

A cut tree (or Gomory-Hu tree) of an undirected weighted graph G=(V,E) encodes a minimum s-t-cut for each vertex pair {s,t} \subseteq V and can be iteratively constructed by n-1 maximum flow computations. They solve the multiterminal…

Data Structures and Algorithms · Computer Science 2013-10-02 Tanja Hartmann , Dorothea Wagner

In this paper we consider random access wireless multi-hop mesh networks with multi-packet reception capabilities where multiple flows are forwarded to the gateways through node disjoint paths. We address the issue of aggregate…

Networking and Internet Architecture · Computer Science 2016-11-15 Manolis Ploumidis , Nikolaos Pappas , Apostolos Traganitis

The multicommodity flow problem is a classic problem in network flow and combinatorial optimization, with applications in transportation, communication, logistics, and supply chain management, etc. Existing algorithms often focus on…

Data Structures and Algorithms · Computer Science 2023-04-25 Li Chen , Mingquan Ye

The dual of a planar graph $G$ is a planar graph $G^*$ that has a vertex for each face of $G$ and an edge for each pair of adjacent faces of $G$. The profound relationship between a planar graph and its dual has been the algorithmic basis…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-10-23 Yaseen Abd-Elhaleem , Michal Dory , Merav Parter , Oren Weimann

We consider single-sink network flow problems. An instance consists of a capacitated graph (directed or undirected), a sink node $t$ and a set of demands that we want to send to the sink. Here demand $i$ is located at a node $s_i$ and…

Data Structures and Algorithms · Computer Science 2015-05-18 F. Bruce Shepherd , Adrian Vetta

We consider the all-pairs multicommodity network flow problem on a network with capacitated edges. The usual treatment keeps track of a separate flow for each source-destination pair on each edge; we rely on a more efficient formulation in…

Optimization and Control · Mathematics 2025-04-04 Fangzhao Zhang , Stephen Boyd

We introduce a new approach to the maximum flow problem in undirected, capacitated graphs using $\alpha$-\emph{congestion-approximators}: easy-to-compute functions that approximate the congestion required to route single-commodity demands…

Data Structures and Algorithms · Computer Science 2013-04-09 Jonah Sherman

Minimum cuts have been closely related to shortest paths in planar graphs via planar duality - so long as the graphs are undirected. Even maximum flows are closely related to shortest paths for the same reason - so long as the source and…

Data Structures and Algorithms · Computer Science 2013-05-27 Glencora Borradaile , Anna Harutyunyan

Stable flows generalize the well-known concept of stable matchings to markets in which transactions may involve several agents, forwarding flow from one to another. An instance of the problem consists of a capacitated directed network, in…

Discrete Mathematics · Computer Science 2018-12-27 Ágnes Cseh , Jannik Matuschke

We show fixed-parameter tractability of the Directed Multicut problem with three terminal pairs (with a randomized algorithm). This problem, given a directed graph $G$, pairs of vertices (called terminals) $(s_1,t_1)$, $(s_2,t_2)$, and…

Data Structures and Algorithms · Computer Science 2024-01-11 Meike Hatzel , Lars Jaffke , Paloma T. Lima , Tomáš Masařík , Marcin Pilipczuk , Roohani Sharma , Manuel Sorge