Related papers: On the Multi-Commodity Flow with convex objective …
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…
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…
Multi-band transmission is a promising technical direction for spectrum and capacity expansion of existing optical networks. Due to the increase in the number of usable wavelengths in multi-band optical networks, the complexity of resource…
We study a multi-commodity Freeway Network Control (FNC) problem aiming at achieving optimal operation of a transportation network through the use of ramp metering and variable speed limits. Straightforward formulations of both single- and…
We introduce a tree-based formulation for the minimum-cost multi-commodity flow problem that addresses large-scale instances. The method decomposes the source-based model by representing flows as convex combinations of trees rooted at…
In light of the need for design and analysis of intermodal transportation systems, we propose an algorithmic framework to determine the system optimum of an intermodal transportation system. To this end, we model an intermodal…
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…
Column generation is often used to solve multi-commodity flow problems. A program for column generation always includes a module that solves a linear equation. In this paper, we address three major issues in solving linear problem during…
We introduce a general framework for flow problems over hypergraphs. In our problem formulation, which we call the convex flow problem, we have a concave utility function for the net flow at every node and a concave utility function for…
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…
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…
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…
Telecommunication networks frequently face technological advancements and need to upgrade their infrastructure. Adapting legacy networks to the latest technology requires synchronized technicians responsible for migrating the equipment. The…
The concave utility in the Network Utility Maximization (NUM) problem is only suitable for elastic flows. However, the networks with the multiclass traffic, the utility of inelastic traffic is usually represented by the sigmoidal function…
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,…
We study the minimum-concave-cost flow problem on a two-dimensional grid. We characterize the computational complexity of this problem based on the number of rows and columns of the grid, the number of different capacities over all arcs,…
We propose a new algorithm to obtain max flow for the multicommodity flow. This algorithm utilizes the max-flow min-cut theorem and the well known labeling algorithm due to Ford and Fulkerson [1]. We proceed as follows: We select one…
The multi-commodity flow (MCF) problem is a fundamental topic in network flow and combinatorial optimization, with broad applications in transportation, communication, and logistics, etc. Nowadays, the rapid expansion of allocation systems…
Collaborative edge computing (CEC) is an emerging paradigm where heterogeneous edge devices collaborate to fulfill computation tasks, such as model training or video processing, by sharing communication and computation resources.…
In a wide range of applications it is desirable to optimally control a dynamical system with respect to concurrent, potentially competing goals. This gives rise to a multiobjective optimal control problem where, instead of computing a…