Solving the undirected minimum cost flow problem with arbitrary costs
نویسندگان
چکیده
MINIMUM COST FLOW PROBLEM WITH ARBITRARY COSTS A. Sedeño-Noda, C. González-Martín, S. Alonso Departamento de Estadística, Investigación Operativa y Computación (DEIOC) Universidad de La Laguna, 38271 La Laguna, Tenerife (Spain). Abstract We address the undirected minimum cost flow problem with arbitrary arcs costs. The optimal solutions for this problem is characterized proving that the flow of all arc with negative cost must be equal its capacity. That is, the flow can be non-zero in both directions. This situation implies that the flow can take values that are integer multiple of 1⁄2. Therefore, this single commodity flow problem does not satisfy the unimodularity property. However, using a reformulation of the original problem, we develop an easy method for solving it using any classic minimum-cost flow problem algorithm.
منابع مشابه
Capacity Inverse Minimum Cost Flow Problem under the Weighted Hamming Distances
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 becomes optimal to the modified minimum cost flow problem. The modifications can be measured by different distances. In this article, we consider the capac...
متن کاملA Novel Experimental Analysis of the Minimum Cost Flow Problem
In the GA approach the parameters that influence its performance include population size, crossover rate and mutation rate. Genetic algorithms are suitable for traversing large search spaces since they can do this relatively fast and because the mutation operator diverts the method away from local optima, which will tend to become more common as the search space increases in size. GA’s are base...
متن کاملGeneralized Preconditioning and Network Flow Problems
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...
متن کاملTítulo: An implicit enumerative algorithm for solving the min-degree constrained minimum spanning tree problem
Given a weighted undirected graph G=(V,E) with positive costs on the edges and a positive constant d, the min-degree constrained minimum spanning tree problem is to find a minimum cost spanning tree T of G where each node I of T either has degree at least d or is a leaf node. Thus, the goal is to find a spanning tree T where all its non-leaf nodes (or central nodes) have degree at least d. Thes...
متن کاملDeenition 1 given a Graph G = ( V E ) and a Subset S of V , the Cut (s) Induced
1 Minimum Cuts In this lecture we will describe an algorithm that computes the minimum cut (or simply mincut) in an undirected graph. A c u t is deened as follows. by S is the subset of edges (ii j) 2 E such that jfii jg \ Sj = 1. That is, (S) consists of all those edges with exactly one endpoint in S. Given an undirected graph G = (V E) and for each edge e 2 E a nonnegative cost (or capacity) ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Networks
دوره 45 شماره
صفحات -
تاریخ انتشار 2005