Safest Path Adversarial Coverage : Proofs and Algorithm Details Technical Report SMART 2014 / 01

Proof. Clearly, this problem is in NP, since one can easily guess the coverage path of the robot and then verify its probability of surviving it in polynomial time. To prove its NP-hardness, we use a reduction from the Hamiltonian path problem on grid graphs. A grid graph is a finite node-induced subgraph of the infinite two-dimensional integer grid (see Figure 1 for an example of a general grid graph). The Hamiltonian path problem on grid graphs (i.e., the construction of a path that visits every node of the grid graph precisely once) has been proven to be NP-complete in [2].