Abstract
We show several hardness results for the Minimum Hacking problem, which roughly can be described as the problem of finding the best way to compromise a target node given a few initial compromised nodes in a network. We give several reductions to show that Minimum Hacking is not approximable to within \(2^{(\log n)^{1-\delta}}\) where δ = 1−\(\frac{1}{{log}{log}}\) c n, for any c < 1/2. We also analyze some heuristics on this problem.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
M. Alekhnovich, S. Buss, S. Moran, and T. Pitassi, “Minimum propositional proof length is NP-hard to linearly approximate,” J. Symbolic Logic, vol. 66, pp. 171–191, 2001.
S. Arora, L. Babai, J. Stern, and Z. Sweedyk, “The hardness of approximate optima in lattices, codes, and systems of linear equations,” J. Comput. System Sci., vol. 54, pp. 317–331, 1997. 34th Annual Symposium on Foundations of Computer Science (Palo Alto, CA, 1993).
S. Arora and C. Lund, “Hardness of approximation,” in Approximation Algorithms for NP-Hard Problems, D. Hochbaum, (ed.), PWS Publishing Company, 1997, pp. 399–346.
R. Chinchani, A. Iyer, H.Q. Ngo, and S. Upadhyaya, “Towards a theory of insider threat assessment,” in Proceedings of the International Conference on Dependable Systems and Networks (DSN 2005, Yokohama, Japan), IEEE, 2005.
P. Crescenzi, V. Kann, R. Silvestri, and L. Trevisan, “Structure in approximation classes,” SIAM J. Comput., vol. 28, pp. 1759–1782, 1999 (electronic).
I. Dinur, E. Fischer, G. Kindler, R. Raz, and S. Safra, “PCP characterizations of NP: Towards a polynomially-small error-probability,” in Annual ACM Symposium on Theory of Computing Atlanta, GA, ACM: New York, 1999, pp. 29–40 (electronic).
I. Dinur and S. Safra, “On the hardness of approximating label-cover,” Inform. Process. Lett., vol. 89, pp. 247–254, 2004.
D.S. Hochbaum (ed.), Approximation Algorithms for NP Hard Problems, PWS Publishing Company: Boston, MA, 1997.
C. Lund and M. Yannakakis, “On the hardness of approximating minimization problems,” J. Assoc. Comput. Mach., vol. 41, pp. 960–981, 1994.
C.H. Papadimitriou, Computational Complexity, Addison-Wesley Publishing Company: Reading, MA, 1994.
V.V. Vazirani, Approximation Algorithms, Springer-Verlag: Berlin, 2001.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Chinchani, R., Ha, D., Iyer, A. et al. On the Hardness of Approximating the Min-Hack Problem. J Comb Optim 9, 295–311 (2005). https://doi.org/10.1007/s10878-005-1413-8
Received:
Revised:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/s10878-005-1413-8