On the Hardness of Approximating the Min-Hack Problem

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-δ where δ = 1− 1/loglog c n, for any c < 1/2. We also analyze some heuristics on this problem.