Abstraction Methods for Solving Graph-Based Security Games

Abstract

Many real-world security problems can be modeled using Stackelberg security games (SSG), which model the interactions between defender and attacker. Green security games focus on environmental crime, such as preventing poaching, illegal logging, or detecting pollution. A common problem in green security games is to optimize patrolling strategies for a large physical area such as a national park or other protected area. Patrolling strategies can be modeled as paths in a graph that represents the physical terrain. However, having a detailed graph to represent possible movements in a very large area typically results in an intractable computational problem due to the extremely large number of potential paths. While a variety of algorithmic approaches have been explored in the literature to solve security games based on large graphs, the size of games that can be solved is still quite limited. Here, we introduce abstraction methods for solving large graph-based security games. We demonstrate empirically that these abstraction methods can result in dramatic improvements in solution time with modest impact on solution quality.