Open Gromov-Witten invariants and mirror maps for semi-Fano toric   manifolds
  We prove that for a compact toric manifold whose anti-canonical divisor is numerically effective, the Lagrangian Floer superpotential defined by Fukaya-Oh-Ohto-Ono is equal to the superpotential written down by using the toric mirror map under a convergence assumption. This gives a method to compute open Gromov-Witten invariants using mirror symmetry. 
Kwokwai Chan, Siu-Cheong Lau, Naichung Conan Leung, Hsian-Hua Tseng
math.SG math.AG