Before revision: In the Minimum Activation Path problem, we are given a graph G with edge weights w(.) and two vertices s,t of G. We want to assign a non-negative power p(v) to each vertex v of G so that the edges uv such that p(u)+p(v) is at least w(uv) contain some s-t-path, and minimize the sum of assigned powers.
After revision: In the Minimum Installation Path problem, we are given a graph G with edge weights w(.) and two vertices s,t of G. We want to assign a non-negative power p(v) to each vertex v of G so that the edges uv such that p(u)+p(v) is at least w(uv) contain some s-t-path, and minimize the sum of assigned powers.