This thesis considers a problem of finding the quickest path set for data transmission on telecommunication networks, which is a routing path set requiring the minimum time for transmitting a given amount of data units from the source to the sink. It is assumed in the problem that the data can be partitioned into smaller parts. Some solution properties are characterized, and then used to exploit a branching algorithm for the optimal solution. And another algorithm is also exploited easily to account for marginal variations on the given problem data treated by the branching algorithm. Heuristic aproaches are investigated in addition and some computational experiences are discussed.