Extensions to Network Flow Interdiction on Planar Graphs

Network flow interdiction on planar graphs

Interdiction Problems on Planar Graphs

We introduce approximation algorithms and strong NP-completeness results for interdiction problems on planar graphs. Interdiction problems are leader-follower games in which the leader is allowed to delete a certain number of edges from the graph in order to maximally impede the follower, who is trying to solve an optimization problem on the impeded graph. We give a multiplicative (1+ǫ)-approxi...

A Note on the Integrality Gap in the Nodal Interdiction Problem

In the maximum flow network interdiction problem, an attacker attempts to minimize the maximum flow by interdicting flow on the arcs of network. In this paper, our focus is on the nodal interdiction for network instead of the arc interdiction. Two path inequalities for the node-only interdiction problem are represented. It has been proved that the integrality gap of relaxation of the maximum fl...

Markovian Network Interdiction and the Four Color Theorem

The Unreactive Markovian Evader Interdiction Problem (UME) asks to optimally place sensors on a network to detect Markovian motion by one or more evaders . It was previously proved that nding the optimal sensor placement is NP-hard if the number of evaders is unbounded. Here we show that the problem is NP-hard with just 2 evaders using a connection to coloring of planar graphs. The results sugg...

On DDoS Attack Related Minimum Cut Problems

In this paper, we study two important extensions of the classical minimum cut problem, called Connectivity Preserving Minimum Cut (CPMC) problem and Threshold Minimum Cut (TMC) problem, which have important applications in largescale DDoS attacks. In CPMC problem, a minimum cut is sought to separate a of source from a destination node and meanwhile preserve the connectivity between the source a...