Does the algorithm keep a classical reference to the end node? If so, it sounds like that would be an O(sqrt(m)) classical speedup as now you can do a double-en

Does the algorithm keep a classical reference to the end node? If so, it sounds like that would be an O(sqrt(m)) classical speedup as now you can do a double-ended search which reduces depth by 1/2 -> O(2^(x/2)) in classical performance.