We analyze the asymptotic behavior of the Flow Deviation Method, first presented in 1971 by Fratta, Gerla and Kleinrock, and show that when applied to packing linear programs such as the maximum concurrent flow problem, it yields a fully polynomial-time approximation scheme.

For k ≥ 1, the k-commodity flow problem is, we are given k pairs of vertices in a graph G, and we ask whether there exist k flows in the graph, where • the ith flow is between the ith pair of vertices, and has total value one; and • for each edge e, the sum of absolute values of the flows along e is at most one. We prove that for all k there exists n(k) such that if G is connected, and contract...

We explore here surprising links between the time-cost-tradeoff problem and the minimum cost flow problem that lead to faster, strongly polynomial, algorithms for both problems. One of the main results is a new algorithm for the unit capacity min cost flow that culminates decades of efforts to match the complexity of the fastest strongly polynomial algorithm known for the assignment problem. Th...

The main goal of this project is to investigate the network flow allocation (routing) problem, and devise a practical algorithm for its solution. Particularly, we plan to investigate the trade-off between the algorithm’s optimality and its implementability; therefore, obtaining an 2-suboptimal solution would be sufficient, if this will speed-up convergence or simplify the overall algorithm. Thi...

In order to solve problems such as low resources utilization of data center backbone bandwidth and expensive daily expenses caused by the tidal effect in the transition of large-scale network data, the new optimization method of bandwidth resource for bulk data transfer is proposed. This method finishes the bulk data transfer by taking full advantage of the idle channel bandwidth. Firstly, the ...

Research on the location-routing problem (LRP) is very active, producing a good number of effective exact and approximated solution approaches. It is noteworthy that most of the contributions present in the literature address the single-commodity LRP, whereas the multi-commodity case has been scarcely investigated. Yet, this issue assumes an important role in many LRP applications, particularly...

in static scheduling problem, where there is no change in situation, the challenge is that the large problems can be solved in a short time. in this paper, the static scheduling problem of automated guided vehicles in container terminal is solved by the network simplex algorithm (nsa). the algorithm is based on graph model and their performances are at least 100 times faster than traditional si...

Given a directed graph with capacities on each arc and given a set of commodities, the QoS constrained Routing Problem (QCRP) consists in routing each commodity while respecting a endto-end upper bound on the delay for each packet. This problem is NP-hard and we propose an augmented Lagrangean approach to solve it. A flow deviation algorithm as well as a projected gradient method are proposed t...

We consider the solution of the single commodity strictly convex network flow problem in a distributed asynchronous computation environment. The dual of this problem is unconstrained, differentiable, and well suited for solution via Gauss-Seidel relaxation. We show that the structure of the dual allows the successful application of a distributed asynchronous method whereby relaxation iterations...

We consider a survivable network design problem known as the 2-NodeConnected Steiner Network Problem (2NCON): we are given a weighted undirected graph with a node partition into two sets of customer nodes and one set of Steiner nodes. We ask for the minimum weight connected subgraph containing all customer nodes, in which the nodes of the second customer set are nodewise 2-connected. This probl...