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.

[1]  Curt Jones,et al.  Finding Good Approximate Vertex and Edge Partitions is NP-Hard , 1992, Inf. Process. Lett..

[2]  Sarit Kraus,et al.  Adversarial Uncertainty in Multi-Robot Patrol , 2009, IJCAI.

[3]  Nils J. Nilsson,et al.  A Formal Basis for the Heuristic Determination of Minimum Cost Paths , 1968, IEEE Trans. Syst. Sci. Cybern..

[4]  E. A. Dinic.  Algorithm for solution of a problem of maximal flow in a network with power estimation , 1970 .

[5]  Clifford Stein,et al.  Introduction to Algorithms, 2nd edition. , 2001 .

[6]  David P. Morton,et al.  Stochastic Network Interdiction , 1998, Oper. Res..

[7]  T. E. Harris,et al.  Fundamentals of a Method for Evaluating Rail Net Capacities , 1955 .

[8]  Ronald L. Rivest,et al.  Introduction to Algorithms , 1990 .

[9]  Sarit Kraus,et al.  Security in multiagent systems by policy randomization , 2006, AAMAS '06.

[10]  A. Gibbons.  Algorithmic Graph Theory , 1985 .

[11]  D. R. Fulkerson,et al.  On the Max Flow Min Cut Theorem of Networks. , 1955 .

[12]  Sarit Kraus,et al.  Multi-robot perimeter patrol in adversarial settings , 2008, 2008 IEEE International Conference on Robotics and Automation.

[13]  Ronald L. Rivest,et al.  Introduction to Algorithms, Second Edition , 2001 .

[14]  Milind Tambe,et al.  Security and Game Theory: IRIS – A Tool for Strategic Security Allocation in Transportation Networks , 2011, AAMAS 2011.

[15]  R. Kevin Wood,et al.  Deterministic network interdiction , 1993 .

[16]  Milind Tambe,et al.  Effective solutions for real-world Stackelberg games: when agents must deal with human uncertainties , 2009, AAMAS 2009.

[17]  Alan Washburn,et al.  Two-Person Zero-Sum Games for Network Interdiction , 1995, Oper. Res..