Efficient Formulations for Multiple Allocation Hub Network Interdiction Problems

In this paper, we study a network interdiction problem on a multiple allocation, uncapacitated hub network. The problem is formulated as a bilevel Stackelberg game between an attacker and a defender, where the attacker identifies r out of p hubs to interdict so as to maximize the worst-case post-interdiction performance of the system with the … Read more

Interdicting Low-Diameter Cohesive Subgroups in Large-Scale Social Networks

The s-clubs model cohesive social subgroups as vertex subsets that induce subgraphs of diameter at most s. In defender-attacker settings, for low values of s, they can represent tightly-knit communities whose operation is undesirable for the defender. For instance, in online social networks, large communities of malicious accounts can effectively propagate undesirable rumors. In this … Read more

Integer Programming Formulations for Minimum Spanning Tree Interdiction

We consider a two-player interdiction problem staged over a graph where the leader’s objective is to minimize the cost of removing edges from the graph so that the follower’s objective, i.e., the weight of a minimum spanning tree in the residual graph, is increased up to a predefined level $r$. Standard approaches for graph interdiction … Read more

The Maximum Clique Interdiction Problem

Given a graph G and an interdiction budget k, the Maximum Clique Interdiction Problem asks to find a subset of at most k vertices to remove from G so that the size of the maximum clique in the remaining graph is minimized. This problem has applications in many areas, such as crime detection, prevention of … Read more

New solution approaches for the maximum-reliability stochastic network interdiction problem

We investigate methods to solve the maximum-reliability stochastic network interdiction problem (SNIP). In this problem, a defender interdicts arcs on a directed graph to minimize an attacker’s probability of undetected traversal through the network. The attacker’s origin and destination are unknown to the defender and assumed to be random. SNIP can be formulated as a … Read more

Equilibrium Strategies for Multiple Interdictors on a Common Network

In this work, we introduce multi-interdictor games, which model interactions among multiple interdictors with differing objectives operating on a common network. As a starting point, we focus on shortest path multi-interdictor (SPMI) games, where multiple interdictors try to increase the shortest path lengths of their own adversaries attempting to traverse a common network. We first … Read more

The Maximum Flow Network Interdiction Problem: Valid Inequalities, Integrality Gaps, and Approximability

We study the Maximum Flow Network Interdiction Problem (MFNIP). We present two classes of polynomially separable valid inequalities for Cardinality MFNIP. We also prove the integrality gap of the LP relaxation of Wood’s (1993) integer program is not bounded by a constant factor, even when the LP relaxation is strengthened by our valid inequalities. Finally, … Read more