  We consider the problem of optimising the achievable EPR-pair distribution
rate between multiple source-destination pairs in a quantum internet, where the
repeaters may perform a probabilistic bell-state measurement and we may impose
a minimum end-to-end fidelity as a requirement. We construct an efficient
linear programming formulation that computes the maximum total achievable
entanglement distribution rate, satisfying the end-to-end fidelity constraint
in polynomial time (in the number of nodes in the network). We also propose an
efficient algorithm that takes the output of the linear programming solver as
an input and runs in polynomial time (in the number of nodes) to produce the
set of paths to be used to achieve the entanglement distribution rate.
Moreover, we point out a practical entanglement generation protocol which can
achieve those rates.
