  Seminal works on light spanners over the years have provided spanners with
optimal lightness in various graph classes, such as general graphs, Euclidean
spanners, and minor-free graphs. Three shortcomings of previous works on light
spanners are: (i) The runtimes of these constructions are almost always
sub-optimal and usually far from optimal. (ii) These constructions are optimal
in the standard and crude sense but not in a refined sense that takes into
account a wider range of involved parameters. (iii) The techniques are ad hoc
per graph class and thus can't be applied broadly.
  This work aims at addressing these shortcomings by presenting a unified
framework of light spanners in a variety of graph classes. Informally, the
framework boils down to a transformation from sparse spanners to light
spanners; since the state-of-the-art for sparse spanners is much more advanced
than that for light spanners, such a transformation is powerful. First, we
apply our framework to design fast constructions with optimal lightness for
several graph classes. Second, we apply our framework to achieve more refined
optimality bounds for several graph classes, i.e., the bounds remain optimal
when taking into account a wider range of involved parameters, most notably
$\epsilon$. Our new constructions are significantly better than the
state-of-the-art for every examined graph class.
