Defending against Contagious Attacks on a Network with Resource Reallocation

Rufan Bai, Haoxing LIN, Xinyu Yang, Xiaowei Wu, Minming Li, Weijia Jia

Abstract:

In classic network security games, the defender distributes defending resources to the nodes of the network, and the attacker attacks a node, with the objective to maximize the damage caused.
Existing models assume that the attack at node $u$ causes damage only at $u$.
However, in many real-world security scenarios, the attack at a node $u$ spreads to the neighbors of $u$ and can cause damage at multiple nodes, e.g., for the outbreak of a virus.
In this paper, we consider the network defending problem against contagious attacks.

Existing works that study shared resources assume that the resource allocated to a node can be shared or duplicated between neighboring nodes.
However, in real world, sharing resource naturally leads to a decrease in defending power of the source node, especially when defending against contagious attacks.
To this end, we study the model in which resources allocated to a node can only be transferred to its neighboring nodes, which we refer to as a reallocation process.

We show that this more general model is difficult in two aspects: (1) even for a fixed allocation of resources, we show that computing the optimal reallocation is \NP-hard; (2) for the case when reallocation is not allowed, we show that computing the optimal allocation (against contagious attack) is also \NP-hard.
For positive results, we give a mixed integer linear program formulation for the problem and a bi-criteria approximation algorithm.
Our experimental results demonstrate that the allocation and reallocation strategies our algorithm computes perform well in terms of minimizing the damage due to contagious attacks.