On the Complexity and Approximability of Budget-Constrained Minimum Cost Flows
Abstract
We investigate the complexity and approximability of the budget-constrained minimum cost flow problem, which is an extension of the traditional minimum cost flow problem by a second kind of costs associated with each edge, whose total value in a feasible flow is constrained by a given budget B. This problem can, e.g., be seen as the application of the {\epsilon}-constraint method to the bicriteria minimum cost flow problem. We show that we can solve the problem exactly in weakly polynomial time , where C, U, and M are upper bounds on the largest absolute cost, largest capacity, and largest absolute value of any number occuring in the input, respectively, and MCF(m,n,C,U) denotes the complexity of finding a traditional minimum cost flow. Moreover, we present two fully polynomial-time approximation schemes for the problem on general graphs and one with an improved running-time for the problem on acyclic graphs.
Cite
@article{arxiv.1607.02282,
title = {On the Complexity and Approximability of Budget-Constrained Minimum Cost Flows},
author = {Michael Holzhauser and Sven O. Krumke and Clemens Thielen},
journal= {arXiv preprint arXiv:1607.02282},
year = {2016}
}