Prove, without any possibility of refutation, the necessary and sufficient condition for the decidability of the following problem: Given a computer network represented by a weighted graph, where the weights of the edges represent the maximum theoretical transfer speeds of the connections between nodes, determine whether the network can still achieve a specified global transfer speed if one given edge fails and no communication can occur along that connection. Additionally, establish the computational complexity $($worst$-$case asymptotic lower bound$)$ of this problem.

Furthermore, design an optimal algorithm to solve this problem and prove, without any possibility of refutation, the computational complexity $($worst$-$case asymptotic upper bound$)$ of this algorithm.