  Intersection graphs of planar geometric objects such as intervals, disks,
rectangles and pseudo-disks are well studied. Motivated by various
applications, Butman et al. in SODA 2007 considered algorithmic questions in
intersection graphs of $t$-intervals. A $t$-interval is a union of at most $t$
distinct intervals (here $t$ is a parameter) -- these graphs are referred to as
Multiple-Interval Graphs. Subsequent work by Kammer et al. in Approx 2010 also
considered $t$-disks and other geometric shapes. In this paper we revisit some
of these algorithmic questions via more recent developments in computational
geometry. For the minimum weight dominating set problem, we give a simple $O(t
\log t)$ approximation for Multiple-Interval Graphs, improving on the
previously known bound of $t^2$ . We also show that it is NP-hard to obtain an
$o(t)$-approximation in this case. In fact, our results hold for the
intersection graph of a set of t-pseudo-disks which is a much larger class. We
obtain an ${\Omega}(1/t)$-approximation for the maximum weight independent set
in the intersection graph of $t$-pseudo-disks. Our results are based on simple
reductions to existing algorithms by appropriately bounding the union
complexity of the objects under consideration.
