Abstract: The Safety Net Problem is a variation on the Minimum Spanning Tree algorithm. Given an arbitrarily weighted grid graph, G, and an arbitrarily selected set of vertices, R, what is the low-cost path that connects every vertex and ensures that if an edge is deleted every vertex in R would still have a path to get to every other vertex in R? We analyze two different approaches to this problem. The "MST-First" algorithm first finds a minimum spanning tree on G, then adds edges to the tree to form a Hamiltonian circuit that includes all required nodes. The "Path-First" algorithm starts by finding the Hamiltonian circuit and then finds the MST of G, treating the set of edges in the circuit as a singular component.