We show that it is impossible, in NC, to approximate the value of the minimum-cost maximum ow unless P = NC.

This paper presents efficient implementations of several algorithms for solving the minimum-cost network flow problem. Various practical heuristics and other important implementation aspects are also discussed. A novel result of this work is the application of Goldberg’s recent partial augment-relabel method in the cost-scaling algorithm. The presented implementations are available as part of t...

An extensive computational analysis of several algorithms for solving the minimum-cost network flow problem is conducted. Some of the considered implementations were developed by the author and are available as part of an open-source C++ optimization library called LEMON (http://lemon.cs. elte.hu/). These codes are compared to other publicly available solvers: CS2, MCF, RelaxIV, PDNET, MCFSimpl...

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...

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...

Low Power Design has become a significant requirement when the CMOS technology entered the nanometer era. Multiple-Supply Voltage (MSV) is a popular and effective method for both dynamic and static power reduction while maintaining performance. Level shifters may cause area and Interconnect Length Overhead(ILO), and should be considered at both floorplanning and post-floorplanning stages. In th...

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...

Given an instance of the minimum cost flow problem, a version of the corresponding inverse problem, called the capacity inverse problem, is to modify the upper and lower bounds on arc flows as little as possible so that a given feasible flow x becomes optimal to the modified minimum cost flow problem. The modifications can be measured by different distances. Here, we consider the capacity inver...

We present a column generation algorithm for solving the bi-objective multicommodity minimum cost flow problem. This method is based on the biobjective simplex method and Dantzig-Wolfe decomposition. The method is initialised by optimising the problem with respect to the first objective, a single objective multi-commodity flow problem, which is solved using DantzigWolfe decomposition. Then, sim...

The pull-push hybrid P2P streaming, as an emerging and promising approach, has achieved some success in delivering live video traffic. The substream scheduling problem is a key design issue in a hybrid system. In this paper, we propose a max-flow model for unifying this sub-stream scheduling problem. We find that the sub-stream scheduling problem in GridMedia, CoolStreaming+ and LStreaming can ...