  We formulate a conjecture which describes the Fukaya category of an exact
Lefschetz fibration defined by a Laurent polynomial in two variables in terms
of a pair consisting of a consistent dimer model and a perfect matching on it.
We prove this conjecture in some cases, and obtain homological mirror symmetry
for quotient stacks of toric del Pezzo surfaces by finite subgroups of the
torus as a corollary.
