Hardness and Approximation for Network Flow Interdiction

TL;DR

This paper establishes the first approximation hardness for Network Flow Interdiction, showing it is as hard to approximate as Densest k-Subgraph, and provides the first approximation algorithm with ratio 2(n-1).

Contribution

It proves the first approximation hardness for Network Flow Interdiction and introduces the first approximation algorithm, linking it to the Budgeted Minimum s-t-Cut problem.

Findings

Approximation hardness similar to Densest k-Subgraph.

First approximation algorithm with ratio 2(n-1).

Equivalence between Network Flow Interdiction and Budgeted Minimum s-t-Cut.

Abstract

In the Network Flow Interdiction problem an adversary attacks a network in order to minimize the maximum s-t-flow. Very little is known about the approximatibility of this problem despite decades of interest in it. We present the first approximation hardness, showing that Network Flow Interdiction and several of its variants cannot be much easier to approximate than Densest k-Subgraph. In particular, any $n^{o(1)}$-approximation algorithm for Network Flow Interdiction would imply an $n^{o(1)}$-approximation algorithm for Densest k-Subgraph. We complement this hardness results with the first approximation algorithm for Network Flow Interdiction, which has approximation ratio 2(n-1). We also show that Network Flow Interdiction is essentially the same as the Budgeted Minimum s-t-Cut problem, and transferring our results gives the first approximation hardness and algorithm for that problem, as well.