Hardness and approximation for network flow interdiction

Hardness and approximation for network flow interdiction

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 parti...

Network flow interdiction on planar graphs

Optimal Interdiction of Illegal Network Flow

Large scale smuggling of illegal goods is a longstanding problem, with $1.4b and thousands of agents assigned to protect the borders from such activity in the US-Mexico border alone. Illegal smuggling activities are usually blocked via inspection stations or ad-hoc checkpoints/roadblocks. Security resources are insufficient to man all stations at all times; furthermore, smugglers regularly cond...

Algorithms for Discrete and Continuous Multicommodity Flow Network Interdiction Problems

We consider a network interdiction problem on a multicommodity flow network, in which an attacker disables a set of network arcs in order to minimize the maximum profit that can be obtained from shipping commodities across the network. The attacker is assumed to have some budget for destroying (or “interdicting”) arcs, and each arc is associated with a positive interdiction expense. In this pap...

Improved Hardness for Cut, Interdiction, and Firefighter Problems

We study variants of the classic s-t cut problem and prove the following improved hardness results assuming the Unique Games Conjecture (UGC). • For any constant k ≥ 2 and ǫ > 0, we show that Directed Multicutwith k source-sink pairs is hard to approximate within a factor k − ǫ. This matches the trivial k-approximation algorithm. By a simple reduction, our result for k = 2 implies that Directed...