We propose a new set of preconditioners for the iterative solution, via a Preconditioned Conjugate Gradient (PCG) method, of the KKT systems that must be solved at each iteration of an Interior Point (IP) algorithm for the solution of linear Min Cost Flow (MCF) problems. These preconditioners are based on the idea of extracting a proper triangulated subgraph of the original graph which strictly...

968 A Fuzzy Residual Network Approach to Minimum Cost Flow Problem with Fuzzy Parameters M. Bagherian Department of Applied Mathematics, Faculty of Mathematical Science, University of Guilan, Rasht, Iran. [email protected] . ABSTRACT The Minimum Cost Flow (MCF) problem has been defined as to determine a least cost shipment of a commodity through a network in order to satisfy demands at ce...

We consider approximation algorithms for the problem of finding x of minimal norm ‖x‖ satisfying a linear system Ax = b, where the norm ‖ · ‖ is arbitrary and generally non-Euclidean. We show a simple general technique for composing solvers, converting iterative solvers with residual error ‖Ax−b‖ ≤ t−Ω(1) into solvers with residual error exp(−Ω(t)), at the cost of an increase in ‖x‖, by recursi...

Motivated by an application in image processing, we introduce the grid-leveling problem. It turns out to be the dual of a minimum cost flow problem for an apex graph with a grid graph as its basis. We present an O(n) algorithm for this problem. The optimum solution recovers missing DC coefficients from image and video coding by Discrete Cosine Transform used in popular standards like JPEG and M...

Developing a polynomial time algorithm for the minimum cost flow problem has been a long standing open problem. In this paper, we develop one such algorithm that runs in O(min(n 2m log nC, n2m 2 log n)) time, where n is the number of nodes in the network, m is the number of arcs, and C denotes the maximum absolute arc costs if arc costs are integer and 0 otherwise. We first introduce a pseudopo...

Many emerging sensor network applications require sensor node deployment in challenging environments that are remote and inaccessible. In such applications, it is not always possible to deploy base stations in or near the sensor field to collect sensory data. Therefore, the overflow data generated by some nodes is first offloaded to other nodes inside the network to be preserved, then gets coll...

We present an algorithm to compute a complete set of efficient solutions for the biobjective integer minimum cost flow problem. We use the two phase method with a parametric network simplex algorithm in phase 1 to compute all supported non-dominated extreme points. In phase 2, the remaining nondominated points (non-extreme supported and non-supported) are computed using a k best flow algorithm ...

An M-convex function is a nonlinear discrete function defined on integer points introduced by Murota in 1996, and the M-convex submodular flow problem is one of the most general frameworks of efficiently solvable combinatorial optimization problems. It includes the minimum cost flow and the submodular flow problems as its special cases. In this paper, we first devise a successive shortest path ...

This paper presents two fast cycle canceling algorithms for the submodular flow problem. The first uses an assignment problem whose optimal solution identifies most negative node-disjoint cycles in an auxiliary network. Canceling these cycles lexicographically makes it possible to obtain an optimal submodular flow in O(nh log(nC)) time, which almost matches the current fastest weakly polynomial...

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 ...