A multiresolution approach for optimal defense against random attacks

Azaiez, M., Bier, V.M.: Optimal resource allocation for security in reliability systems. Eur. J. Oper. Res. 181(2), 773–786 (2007). doi:10.1016/j.ejor.2006.03.057. http://www.sciencedirect.com/science/article/pii/S0377221706004747 Bier, V.: Game-theoretic and reliability methods in counterterrorism and security. In: Wilson, G.A., Wilson, D.G., Olwell, D.H. (eds.) Statistical Methods in Counterterrorism, pp. 23–40. Springer, New York (2006) Bier, V., Oliveros, S., Samuelson, L.: Choosing what to protect: strategic defensive allocation against an unknown attacker. J. Public Econ. Theory 9(4), 563–587 (2007). doi:10.1111/j.1467-9779.2007.00320.x Bier, V.M., Nagaraj, A., Abhichandani, V.: Protection of simple series and parallel systems with components of different values. Reliab. Eng. Syst. Saf. 87(3), 315–323 (2005). doi:10.1016/j.ress.2004.06.003. http://www.sciencedirect.com/science/article/pii/S0951832004001309 Brown, D., Efendiev, Y., Hoang, V.: An efficient hierarchical multiscale finite element method for stokes equations in slowly varying media. Multiscale Model. Simul. 11(1), 30–58 (2013). doi:10.1137/110858525 Carin, L., Cybenko, G., Hughes, J.: Cybersecurity strategies: the queries methodology. Computer 41(8), 20–26 (2008). doi:10.1109/MC.2008.295 Drewry, D.T., Reynolds, P.F., Emanuel, W.R.: An optimization-based multi-resolution simulation methodology.In: Winter Simulation Conference. San Diego, California, USA (2002) Garland, M.: Multiresolution modeling: survey & future opportunities. In: Seidel, H.P., Coquillart, S. (eds.) 1999 STAR Proc. Eurographics, pp. 111–131. Eurographics Association, Milano, Italy (1999) George, A.L., Smoke, R.: Deterrence in American Foreign Policy: Theory and practice, Chap. 1. Columbia University Press, New York (1974) Golany, B., Kress, M., Penn, M., Rothblum, U.G.: Network optimization models for resource allocation in developing military countermeasures. Oper. Res. 60(1), 48–63 (2012). doi:10.1287/opre.1110.1002 Golany, B., Kress, M., Penn, M., Rothblum, U.G.: Resource allocation in an asymmetric technology race with temporary advantages. Nav. Res. Logist. (NRL) 59(2), 128–145 (2012). doi:10.1002/nav.21477 Goswami, P., Erol, F., Mukhi, R., Pajarola, R., Gobbetti, E.: An efficient multi-resolution framework for high quality interactive rendering of massive point clouds using multi-way kd-trees. Vis. Comput. 29(1), 69–83 (2013). doi:10.1007/s00371-012-0675-2 Hausken, K.: Probabilistic risk analysis and game theory. Risk Anal. 22(1), 17–27 (2002). doi:10.1111/0272-4332.t01-1-00002 Hausken, K.: Strategic defense and attack for series and parallel reliability systems: simultaneous moves by defender and attacker. Tech. Rep. 6, University of Stavanger, N-4036 Stavanger, Norway (2007) Hausken, K.: Strategic defense and attack for reliability systems. Reliab. Eng. Syst. Saf. 93(11), 1740–1750 (2008). doi:10.1016/j.ress.2007.11.002. http://www.sciencedirect.com/science/article/pii/S0951832007002578 Hausken, K.: Strategic defense and attack for series and parallel reliability systems. Eur. J. Oper. Res. 186(2), 856–881 (2008). doi:10.1016/j.ejor.2007.02.013. http://www.sciencedirect.com/science/article/pii/S0377221707002214 Hausken, K.: Strategic defense and attack of complex networks. Int. J. Perform. Eng. 5(1), 13–30 (2009) Hausken, K.: Defense and attack of complex and dependent systems. Reliab. Eng. Syst. Saf. 95(1), 29–42 (2010). doi:10.1016/j.ress.2009.07.006. http://www.sciencedirect.com/science/article/pii/S0951832009001914 Hausken, K.: Defense and attack of two-component multi-state systems. Int. J. Perform. Eng. 7(3), 205–216 (2011) Hausken, K.: Protecting complex infrastructures against multiple strategic attackers. Int. J. Syst. Sci. 42, 11–29 (2011) Hausken, K.: Strategic defense and attack of series systems when agents move sequentially. IIE Trans. 43(7), 483–504 (2011). doi:10.1080/0740817X.2010.541178 Hausken, K., Bier, V.M.: Defending against multiple different attackers. Eur. J. Oper. Res. 211(2), 370–384 (2011) Hausken, K., Bier, V.M., Azaiez, M.N.: Defending against terrorism, natural disaster, and all hazards. In: Bier, V.M., Azaiez, M.N. (eds.) Game Theor. Risk Anal. of Secur. Threats, Int. Ser. Oper. Res. & Manag. Sci. chap. 4, vol. 128, pp. 1–33. Springer, New York (2009). doi:10.1007/978-0-387-87767-94 Hausken, K., Levitin, G.: Efficiency of even separation of parallel elements with variable contest intensity. Risk Anal. 28(5), 1477–1486 (2008). doi:10.1111/j.1539-6924.2008.01090.x Hausken, K., Levitin, G.: Minmax defense strategy for complex multi-state systems. Reliab. Eng. Syst. Saf. 94(2), 577–587 (2009). doi:10.1016/j.ress.2008.06.005. http://www.sciencedirect.com/science/article/pii/S0951832008001841 Hausken, K., Levitin, G.: Protection vs. false targets in series systems. Reliab. Eng. Syst. Saf. 94(5), 973–981 (2009). doi:10.1016/j.ress.2008.11.003. http://www.sciencedirect.com/science/article/pii/S0951832008002664 Hausken, K., Levitin, G.: Protection vs. separation in parallel non-homogeneous systems. Int. J. Reliab. Qual. Perform. 1(1), 54–65 (2009) Hausken, K., Levitin, G.: Defence of homogeneous parallel multi-state systems subject to two sequential attacks. Proc. Inst. Mech. Eng. Part O J. Risk Reliab. 224(3), 171–183 (2010) Hausken, K., Levitin, G.: Review of systems defense and attack models. Int. J. Perform. Eng. 8(4), 355–366 (2012) Hausken, K., Zhuang, J.: Defending against a terrorist who accumulates resources. Mil. Oper. Res. 16(1), 21–39 (2011). doi:10.5711/1082598316121. http://www.ingentaconnect.com/content/mors/mor/2011/00000016/00000001/art00003 Hausken, K., Zhuang, J.: Governments’ and terrorists’ defense and attack in a t-period game. Decis. Anal. 8(1), 46–70 (2011). doi:10.1287/deca.1100.0194 Hausken, K., Zhuang, J.: The timing and deterrence of terrorist attacks due to exogenous dynamics. J. Oper. Res. Soc. 63(6), 725–726 (2012). doi:10.1057/jors.2011.79 Hsu, S.P., Arapostathis, A.: Competitive markov decision processes with partial observation. In: 2004 IEEE Int. Conf. Syst. Man & Cybern., vol. 1, pp. 236–241. The Hague, The Netherlands (2004). doi:10.1109/ICSMC.2004.1398303 Irnich, S., Desaulniers, G.: Shortest path problems with resource constraints. In: Desaulniers, G., Desrosiers, J., Solomon, M. (eds.) Column Generation, pp. 33–65. Springer, US (2005). doi:10.1007/0-387-25486-22 Jia, H., Skaperdas, S., Vaidya, S.: Contest functions: theoretical foundations and issues in estimation. Int. J. Ind. Organ. 31(3), 211–222 (2013). doi:10.1016/j.ijindorg.2012.06.007. http://www.sciencedirect.com/science/article/pii/S0167718712000811 Kobbelt, L., Campagna, S., Vorsatz, J., Seidel, H.P.: Interactive multi-resolution modeling on arbitrary meshes. In: Proc. the 25th Annual Conf. on Comput. Graph. and Interact. tech., SIGGRAPH ’98, pp. 105–114. ACM, New York (1998). doi:10.1145/280814.280831 Levitin, G.: Optimal defense strategy against intentional attacks. IEEE Trans. Reliab. 56(1), 148–157 (2007). doi:10.1109/TR.2006.884599 Levitin, G.: False targets in defence strategies against intentional attacks. Int. J. Perform. Eng. 5(5), 433–446 (2009) Levitin, G.: Optimal distribution of constrained resources in bi-contest detection-impact game. Int. J. Perform. Eng. 5(1), 45–54 (2009) Levitin, G.: Optimizing defense strategies for complex multi-state systems. In: Bier, V.M., Azaiez, M.N. (eds.) Game Theoretic Risk Analysis of Security Threats, International Series in Operations Research & Management Science, vol. 128, pp. 1–32. Springer, US (2009). doi:10.1007/978-0-387-87767-93 Levitin, G., Ben-Haim, H.: Importance of protections against intentional attacks. Reliab. Eng. Syst. Saf. 93(4), 639–646 (2008). doi:10.1016/j.ress.2007.03.016. http://www.sciencedirect.com/science/article/pii/S0951832007001160 Levitin, G., Hausken, K.: Protection vs. redundancy in homogeneous parallel systems. Reliab. Eng. Syst. Saf. 93(10), 1444–1451 (2008). doi:10.1016/j.ress.2007.10.007. http://www.sciencedirect.com/science/article/pii/S0951832007002530 Levitin, G., Hausken, K.: Intelligence and impact contests in systems with redundancy, false targets, and partial protection. Reliab. Eng. Syst. Saf. 94(12), 1927–1941 (2009). doi:10.1016/j.ress.2009.06.010. http://www.sciencedirect.com/science/article/pii/S0951832009001616 Levitin, G., Hausken, K.: Parallel systems under two sequential attacks. Reliab. Eng. Syst. Saf. 94(3), 763–772 (2009). doi:10.1016/j.ress.2008.08.006. http://www.sciencedirect.com/science/article/pii/S0951832008002147 Levitin, G., Hausken, K.: Separation in homogeneous systems with independent identical elements. Eur. J. Oper. Res. 203(3), 625–634 (2010). doi:10.1016/j.ejor.2009.08.016. http://www.sciencedirect.com/science/article/pii/S037722170900558X Luenberger, D.G., Ye, Y.: Linear and Nonlinear Programming, Int. Ser. Oper. Res. & Manag. Sci., vol. 116. Springer Science+Business Media, LLC, New York (2008) Luo, Y., Al-Nashif, Y., Szidarovszky, F., Hariri, S.: Game tree based partially observable stochastic game model for intrusion defense systems (IDS). In: IIE Annual Conf. & EXPO (IERC 2009). Miami (2009) Luo, Y., Szidarovszky, F., Al-Nashif, Y., Hariri, S.: A game theory based risk and impact analysis method for intrusion defense systems. In: 2009 IEEE/ACS International Conference on Computer Systems and Applications (AICCSA), pp. 975–982. IEEE (2009) Luo, Y., Szidarovszky, F., Al-Nashif, Y., Hariri, S.: Game theory based network security. J. Inf. Secur. 1, 41–44 (2010) Luo, Y., Szidarovszky, F., Al-Nashif, Y., Hariri, S.: A fictitious play approach for multi-stage intrusion defense systems. Int. J. Inf. Secur. (2011, in press) Mansoor, P.: Linking doctrine to action: a new coin center-of-gravity analysis. Tech. rep, DTIC Document (2007) Park, D., Ramanan, D., Fowlkes, C.: Multiresolution models for object detection. In: Comput. Vis.-ECCV 2010, pp. 241–254. Springer, Berlin Heidelberg (2010) Peng, R., Levitin, G., Xie, M., Ng, S.: Defending simple series and parallel systems with imperfect false targets. Reliab. Eng. Syst. Saf. 95(6), 679–688 (2010). doi:10.1016/j.ress.2010.02.008. http://www.sciencedirect.com/science/article/pii/S0951832010000438 Penrose, R., Todd, J.A.: On best approximate solutions of linear matrix equations. Math. Proc. Camb. Philos. Soc. 52, 17–19 (1956). doi:10.1017/S0305004100030929. http://journals.cambridge.org/article_S0305004100030929 Raab, M., Steger, A.: “Balls into bins”—a simple and tight analysis. In: Luby, M., Rolim, J.D., Serna, M. (eds.) Randomization and Approximation Techniques in Computer Science. Lecture Notes in Computer Science, vol. 1518, pp. 159–170. Springer, Berlin Heidelberg (1998). doi:10.1007/3-540-49543-613 Reynolds Jr, P.F., Natrajan, A., Srinivasan, S.: Consistency maintenance in multi-resolution simulations. ACM Trans. Model. Comput. Sim. 7(3), 368–392 (1997). doi:10.1145/259207.259235 Samuelson, P.A.: The fundamental approximation theorem of portfolio analysis in terms of means, variances and higher moments. Rev. Econ. Stud. 37(4), 537–542 (1970). http://www.jstor.org/stable/2296483 Sandler, T., Arce, M.D.G.: Counterterrorism a game-theoretic analysis. J. Confl. Resolut. 49(2), 183–200 (2005) Sandler, T., Siqueira, K.: Games and terrorism: recent developments. Sim. Gaming 40(2), 164–192 (2009). doi:10.1177/1046878108314772. http://sag.sagepub.com/content/40/2/164.abstract Sargent, T.J.: Macroeconomic Theory. Academic Press, New York (1979). ISBN:0-12-619750-4 Shen, D., Chen, G., Blasch, E., Tadda, G.: Adaptive markov game theoretic data fusion approach for cyber network defense. In: Mil. Commun. Conf., 2007. MILCOM 2007. IEEE, pp. 1–7. Orlando (2007). doi:10.1109/MILCOM.2007.4454758 Szidarovszky, F., Luo, Y.: Optimal protection against random attacks. Reliab. Eng. Syst. Saf. (2013). Submitted for publication Valenzuela, M., Rozenblit, J., Suantak, L.: Decision support using deterministic equivalents of probabilistic game trees. In: Proc. the 2012 19th IEEE Int. Conf. and Workshops Eng. Comput.-Based Syst. (ECBS), pp. 142–149. Novi Sad (2012). doi:10.1109/ECBS.2012.22 Wang, L., Ren, S., Yue, K., Kwiaty, K.: Optimal resource allocation for protecting system availability against random cyber attacks. In: Proc. the 2011 3rd Int. Conf. Comput. Res. & Dev. (ICCRD), vol. 1, pp. 477–482. Shanghai (2011). doi:10.1109/ICCRD.2011.5764062 Zeigler, B.P., Hu, J.H., Rozenblit, J.W.: Hierarchical, modular modelling in DEVS-scheme. In: 1989 Proc. the 21st Conf. on Winter Simul., WSC ’89, pp. 84–89. ACM, New York, Capital Hilton Hotel, Washington, DC (1989). doi:10.1145/76738.76749 Zhang, Z., Ho, P.H.: Janus: A dual-purpose analytical model for understanding, characterizing and countermining multi-stage collusive attacks in enterprise networks. J. Netw. Comput. Appl. 32(3), 710–720 (2009) Zhuang, J., Bier, V.M.: Balancing terrorism and natural disasters–defensive strategy with endogenous attacker effort. Oper. Res. 55(5), 976–991 (2007) Zhuang, J., Bier, V.M., Alagoz, O.: Modeling secrecy and deception in a multiple-period attacker/defender signaling game. Eur. J. Oper. Res. 203(2), 409–418 (2010). doi:10.1016/j.ejor.2009.07.028. http://www.sciencedirect.com/science/article/pii/S0377221709005384 Zonouz, S., Khurana, H., Sanders, W., Yardley, T.: RRE: a game-theoretic intrusion response and recovery engine. In: 2009 DSN IEEE/IFIP International Conference on Dependable Systems Networks, pp. 439–448. Lisbon (2009). doi:10.1109/DSN.2009.5270307