Related papers: Multicommodity Flow in Polynomial Time
The three-way table problem is to decide if there exists an l x m x n table satisfying given line sums, and find a table if there is one. It is NP-complete already for l=3 and every bounded integer program can be isomorphically represented…
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…
This article focuses on a biobjective extension of the maximum flow network interdiction problem, where each arc in the network is associated with two capacity values. Two maximum flows from a source to a sink are to be computed…
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,…
Dynamic network flows, sometimes called flows over time, extend the notion of network flows to include a transit time for each edge. While Ford and Fulkerson showed that certain dynamic flow problems can be solved via a reduction to static…
We investigate the complexity and approximability of the budget-constrained minimum cost flow problem, which is an extension of the traditional minimum cost flow problem by a second kind of costs associated with each edge, whose total value…
The paper is concerned with the two-machine flow shop, where each job requires an additional resource (referred to as storage space) from the start of its first operation till the end of its second operation. The storage requirement of a…
We consider the robust permutation flowshop problem under the budgeted uncertainty model, where at most a given number of job processing times may deviate on each machine. We show that solutions for this problem can be determined by solving…
The graph packing problem is a well-known area in graph theory. We consider a bipartite version and give almost tight conditions on the packability of two bipartite sequences.
Since the development of efficient linear program solvers in the 80s, all major improvements for solving multi-commodity flows to high accuracy came from improvements to general linear program solvers. This differs from the single commodity…
Network flows over time are a fascinating generalization of classical (static) network flows, introducing an element of time. They naturally model problems where travel and transmission are not instantaneous and flow may vary over time. Not…
The non-uniform demand network coding problem is posed as a single-source and multiple-sink network transmission problem where the sinks may have heterogeneous demands. In contrast with multicast problems, non-uniform demand problems are…
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…
We introduce the concept of low-step multi-commodity flow emulators for any undirected, capacitated graph. At a high level, these emulators contain approximate multi-commodity flows whose paths contain a small number of edges, shattering…
Production and inventory planning have become crucial and challenging in nowadays competitive industrial and commercial sectors, especially when multiple plants or warehouses are involved. In this context, this paper addresses the…
We study the computational complexity of scheduling jobs on a single speed-scalable processor with the objective of capturing the trade-off between the (weighted) flow time and the energy consumption. This trade-off has been extensively…
The determination of the computational complexity of multi-agent pathfinding on directed graphs has been an open problem for many years. For undirected graphs, solvability can be decided in polynomial time, as has been shown already in the…
We study the warehouse problem, arising in the area of inventory management and production planning. Here, a merchant wants to decide an optimal trading policy that computes quantities of a single commodity to purchase, store and sell…
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…
Throughput is a main performance objective in communication networks. This paper considers a fundamental maximum throughput routing problem -- the all-or-nothing multicommodity flow (ANF) problem -- in arbitrary directed graphs and in the…