I have a graph-problem which seems to be not very exotic but I do not know its proper name.
As given in the heading I am looking for a path between two given vertices that maximises the product of weights along the path, were all weights are in [0,1].
Coverstory is that vertices are states and weights denote the probability of a transition along that edge. Since the probabilities are independent, the product is the probability that this path will happen.
Any help with this would be appreciated especially the name of the problem or related google keywords, possible transformations into well known problems and/or an intuition about its complexity.