A graph-theoretic approach to protect static and moving targets from adversaries

The static asset protection problem (SAP) in a road network is that of allocating resources to protect vertices, given any possible behavior by an adversary determined to attack those assets. The dynamic asset protection (DAP) problem is a version of SAP where the asset is following a fixed and widely known route (e.g., a parade route) and needs to be protected. We formalize what it means for a given allocation of resources to be "optimal" for protecting a desired set of assets, and show that randomly allocating resources to a single edge cut in the road network solves this problem. Unlike SAP, we show that DAP is not only an NP-complete problem, but that approximating DAP is also NP-hard. We provide the GreedyDAP heuristic algorithm to solve DAP and show experimentally that it works well in practice, using road network data for real cities.