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Related papers: Congestion in planar graphs with demands on faces

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We consider the problem of multicommodity flows in planar graphs. Okamura and Seymour showed that if all the demands are incident on one face, then the cut-condition is sufficient for routing demands. We consider the following…

Discrete Mathematics · Computer Science 2025-01-13 Nikhil Kumar

We give an algorithm with complexity $O(f(R)^{k^2} k^3 n)$ for the integer multiflow problem on instances $(G,H,r,c)$ with $G$ an acyclic planar digraph and $r+c$ Eulerian. Here, $f$ is a polynomial function, $n = |V(G)|$, $k = |E(H)|$ and…

Discrete Mathematics · Computer Science 2010-08-24 Guyslain Naves

In this paper we show an O(n^(3/2) log^2 n) time algorithm for finding a maximum flow in a planar graph with multiple sources and multiple sinks. This is the fastest algorithm whose running time depends only on the number of vertices in the…

Discrete Mathematics · Computer Science 2010-12-30 Yahav Nussbaum

Emerging reconfigurable optical communication technologies allow to enhance datacenter topologies with demand-aware links optimized towards traffic patterns. This paper studies the algorithmic problem of jointly optimizing topology and…

Performance · Computer Science 2024-01-10 Wenkai Dai , Michael Dinitz , Klaus-Tycho Foerster , Long Luo , Stefan Schmid

Given an undirected, edge-weighted graph G together with pairs of vertices, called pairs of terminals, the minimum multicut problem asks for a minimum-weight set of edges such that, after deleting these edges, the two terminals of each pair…

Data Structures and Algorithms · Computer Science 2016-11-24 Éric Colin de Verdière

We consider the approximability of the maximum edge-disjoint paths problem (MEDP) in undirected graphs, and in particular, the integrality gap of the natural multicommodity flow based relaxation for it. The integrality gap is known to be…

Discrete Mathematics · Computer Science 2013-03-21 Chandra Chekuri , Guyslain Naves , F. Bruce Shepherd

We study the problem of enumerating the $k$-arc-connected orientations of a graph $G$, i.e., generating each exactly once. A first algorithm using submodular flow optimization is easy to state, but intricate to implement. In a second…

Combinatorics · Mathematics 2020-07-29 Sarah Blind , Kolja Knauer , Petru Valicov

We give an iterative algorithm for finding the maximum flow between a set of sources and sinks that lie on the boundary of a planar graph. Our algorithm uses only O(n) queries to simple data structures, achieving an O(n log n) running time…

Data Structures and Algorithms · Computer Science 2013-06-25 Glencora Borradaile , Anna Harutyunyan

Given $k$ pairs of terminals $\{(s_{1}, t_{1}), \ldots, (s_{k}, t_{k})\}$ in a graph $G$, the min-sum $k$ vertex-disjoint paths problem is to find a collection $\{Q_{1}, Q_{2}, \ldots, Q_{k}\}$ of vertex-disjoint paths with minimum total…

Data Structures and Algorithms · Computer Science 2015-07-23 Glencora Borradaile , Amir Nayyeri , Farzad Zafarani

This paper deals with the problem of computing, in an online fashion, a maximum benefit multi-commodity flow (\ONMCF), where the flow demands may be bigger than the edge capacities of the network. We present an online, deterministic,…

Data Structures and Algorithms · Computer Science 2012-04-24 Guy Even , Moti Medina

We study traffic flow on roads with a localized periodic inhomogeneity such as traffic signals, using a stochastic car-following model. We find that in cases of congestion, traffic flow can be optimized by controlling the inhomogeneity's…

Statistical Mechanics · Physics 2007-05-23 Elad Tomer , Leonid Safonov , Nilly Madar , Shlomo Havlin

We investigate the terminal-pairability problem in the case when the base graph is a complete bipartite graph, and the demand graph is a (not necessarily bipartite) multigraph on the same vertex set. In computer science, this problem is…

Combinatorics · Mathematics 2020-04-22 Lucas Colucci , Péter L. Erdős , Ervin Győri , Tamás Róbert Mezei

The relationship between the sparsest cut and the maximum concurrent multi-flow in graphs has been studied extensively. For general graphs with $k$ terminal pairs, the flow-cut gap is $O(\log k)$, and this is tight. But when topological…

Data Structures and Algorithms · Computer Science 2018-11-08 Robert Krauthgamer , James R. Lee , Havana Rika

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

Given a graph $G$, a set $T$ of terminal vertices, and a demand graph $H$ on $T$, the \textsc{Multicut} problem asks for a set of edges of minimum weight that separates the pairs of terminals specified by the edges of $H$. The…

Computational Complexity · Computer Science 2026-01-27 Florian Hörsch , Dániel Marx

We give an $O(n^{1.5} \log n)$ algorithm that, given a 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.

Discrete Mathematics · Computer Science 2010-12-30 Shay Mozes

We devise a constant-factor approximation algorithm for the maximization version of the edge-disjoint paths problem if the supply graph together with the demand edges form a planar graph. By planar duality this is equivalent to packing cuts…

Data Structures and Algorithms · Computer Science 2021-12-14 Chien-Chung Huang , Mathieu Mari , Claire Mathieu , Kevin Schewior , Jens Vygen

Given finitely many connected polygonal obstacles $O_1,\dots,O_k$ in the plane and a set $P$ of points in general position and not in any obstacle, the {\em visibility graph} of $P$ with obstacles $O_1,\dots,O_k$ is the (geometric) graph…

Combinatorics · Mathematics 2017-09-08 John Gimbel , Patrice Ossona de Mendez , Pavel Valtr

introduce {\sc Planar Disjoint Paths Completion}, a completion counterpart of the Disjoint Paths problem, and study its parameterized complexity. The problem can be stated as follows: given a, not necessarily connected, plane graph $G,$ $k$…

Data Structures and Algorithms · Computer Science 2015-11-18 Isolde Adler , Stavros G. Kolliopoulos , Dimitrios M. Thilikos

We consider the following "multiway cut packing" problem in undirected graphs: we are given a graph G=(V,E) and k commodities, each corresponding to a set of terminals located at different vertices in the graph; our goal is to produce a…

Data Structures and Algorithms · Computer Science 2008-10-06 Siddharth Barman , Shuchi Chawla