  The weighted star discrepancy of point sets appears in the weighted
Koksma-Hlawka inequality and thus is a measure for the quality of point sets
with respect to their performance in quasi-Monte Carlo algorithms. A special
choice of point sets are lattice point sets whose generating vector can be
obtained one component at a time such that the resulting lattice point set has
a small weighted star discrepancy.
  In this paper we consider a reduced fast component-by-component algorithm
which significantly reduces the construction cost for such generating vectors
provided that the weights decrease fast enough.
