The constrained maximum flow problem is to send the maximum possible flow from a source node s to a sink node t in a directed network subject to a budget constraint that the cost of flow is no more than D. In this paper, we consider two versions of this problem: (i) when the cost of flow on each arc is a linear function of the amount of flow; and (ii) when the cost of flow is a convex function ...

We present a method for solving the transshipment problem—also known as uncapacitated minimum cost flow—up to a multiplicative error of 1 + in undirected graphs with polynomially bounded integer edge weights using a tailored gradient descent algorithm. An important special case of the transshipment problem is the single-source shortest paths (SSSP) problem. Our gradient descent algorithm takes ...

The paper deals with nonlinear multicommodity flow problems with convex costs. A decomposition method is proposed to solve them. The approach applies a potential reduction algorithm to solve the master problem approximately and a column generation technique to define a sequence of primal linear programming problems. Each subproblem consists of finding a minimum cost flow between an origin and a...

Wireless mesh networks (WMNs) provide a reliable and a scalable solution for multicasting. This paper proposes a framework called Multicast Framework for Bandwidth management in WMN (MFBW) which combines the advantages of Shortest Path Tree (SPT) and Minimum Cost Tree (MCT) algorithm for efficient multicasting with optimal use of

A path-integral formalism is proposed for studying the dynamical evolution in time of patterns in an artificial neural network in the presence of noise. An effective cost function is constructed which determines the unique global minimum of the neural network system. The perturbative method discussed also provides a way for determining the storage capacity of the network.

This paper presents a new algorithm for identifying all the supported nondominated vectors (or outcomes) in the objective space, as well as the corresponding efficient solutions in the decision space, for the multi-objective integer network flow problem. Identifying the set of supported non-dominated vectors is of the utmost importance for obtaining a first approximation of the whole set of non...

Flow in planar graphs has been extensively studied, and very efficient algorithms have been developed to compute max-flows, min-cuts, and circulations. Intimate connections between solutions to the planar circulation problem and with "consistent" potential functions in the dual graph are shown. It is also shown that the set of integral circulations in a planar graph very naturally forms a distr...

This paper presents two new scaling algorithms for the minimum cost network flow problem, one a primal cycle canceling algorithm, the other a dual cut canceling algorithm. Both algorithms scale a relaxed optimality parameter, and create a second, inner relaxation. The primal algorithm uses the inner relaxation to cancel a most negative node-disjoint family of cycles w.r.t. the scaled parameter,...

Dantzig’s pivoting rule is one of the most studied pivoting rules for the simplex algorithm. Whilethe simplex algorithm with Dantzig’s rule may require an exponential number of pivoting stepson general linear programs, and even on min cost flow problems, Orlin showed that O(mn log n)Dantzig’s pivoting steps suffice to solve shortest paths problems (we denote the number of vertices<l...