相关论文: On duality and fractionality of multicommodity flo…

Let $G = (VG, AG)$ be a directed graph with a set $S \subseteq VG$ of terminals and nonnegative integer arc capacities $c$. A feasible multiflow is a nonnegative real function $F(P)$ of "flows" on paths $P$ connecting distinct terminals…

In this paper, we study fractional multiflows in undirected graphs. A fractional multiflow in a graph G with a node subset T, called terminals, is a collection of weighted paths with ends in T such that the total weights of paths traversing…

The Max-Flow Min-Cut theorem is the classical duality result for the Max-Flow problem, which considers flow of a single commodity. We study a multiple commodity generalization of Max-Flow in which flows are composed of real-valued k-vectors…

Motivated by scheduling in Geo-distributed data analysis, we propose a target location problem for multi-commodity flow (LoMuF for short). Given commodities to be sent from their resources, LoMuF aims at locating their targets so that the…

We consider the capacity problem for wireless networks. Networks are modeled as random unit-disk graphs, and the capacity problem is formulated as one of finding the maximum value of a multicommodity flow. In this paper, we develop a proof…

We consider an undirected graph $G = (VG, EG)$ with a set $T \subseteq VG$ of terminals, and with nonnegative integer capacities $c(v)$ and costs $a(v)$ of nodes $v\in VG$. A path in $G$ is a \emph{$T$-path} if its ends are distinct…

Designing and optimizing different flows in networks is a relevant problem in many contexts. While a number of methods have been proposed in the physics and optimal transport literature for the one-commodity case, we lack similar results…

This paper introduces a novel theoretical framework and a suite of highly efficient, parallelizable algorithms for solving the large-scale multicommodity flow (MCF) feasibility problem. We reframe the classical constraint-satisfaction…

We consider multicommodity flow and cut problems in {\em polymatroidal} networks where there are submodular capacity constraints on the edges incident to a node. Polymatroidal networks were introduced by Lawler and Martel and Hassin in the…

The traditional multi-commodity flow problem assumes a given flow network in which multiple commodities are to be maximally routed in response to given demands. This paper considers the multi-commodity flow network-design problem: given a…

The Integer Multicommodity Flow problem has been studied extensively in the literature. However, from a parameterised perspective, mostly special cases, such as the Disjoint Paths problem, have been considered. Therefore, we investigate the…

In this paper we study a variant of the branched transportation problem, that we call multi-material transport problem. This is a transportation problem, where distinct commodities are transported simultaneously along a network. The cost of…

In this paper, we address the minimum-cost node-capacitated multiflow problem in an undirected network. For this problem, Babenko and Karzanov (2012) showed strongly polynomial-time solvability via the ellipsoid method. Our result is the…

The multicommodity flow problem is NP-hard already for two commodities over bipartite graphs. Nonetheless, using our recent theory of n-fold integer programming and extensions developed herein, we are able to establish the surprising…

The maximum multicommodity flow problem is a natural generalization of the maximum flow problem to route multiple distinct flows. Obtaining a $1-\epsilon$ approximation to the multicommodity flow problem on graphs is a well-studied problem.…

We study a class of dynamical multi-commodity flow networks in transportation networks. These are modeled as dynamical systems describing the evolution of the densities of a number of different commodities across the cells of a…

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…

The multicast capacity of a directed network is closely related to the $s$-$t$ maximum flow, which is equal to the $s$-$t$ minimum cut capacity due to the max-flow min-cut theorem. If the topology of a network (or link capacities) is…

We consider the robust version of a multi-commodity network flow problem. The robustness is defined with respect to the deletion, or failure, of edges. While the flow problem itself is a polynomially-sized linear program, its robust version…

We derive a monotonicity property for general, transient flows of a commodity transferred throughout a network, where the flow is characterized by density and mass flux dynamics on the edges with density continuity and mass balance…