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arXiv · 1607.02282

On the Complexity and Approximability of Budget-Constrained Minimum Cost Flows

Michael Holzhauser·Sven O. Krumke·Clemens Thielen
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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 $O(\log M \cdot MCF(m,n,C,U))$, 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.

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Michael Holzhauser, Sven O. Krumke, Clemens Thielen. 2016-07-08. On the Complexity and Approximability of Budget-Constrained Minimum Cost Flows. https://arxiv.org/abs/1607.02282

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