  We develop a framework for algorithms finding the diameter in graphs of
bounded distance Vapnik-Chervonenkis dimension, in (parameterized) subquadratic
time complexity. The class of bounded distance VC-dimension graphs is wide,
including, e.g. all minor-free graphs.
  We build on the work of Ducoffe et al. [SODA'20, SIGCOMP'22], improving their
technique. With our approach the algorithms become simpler and faster, working
in $\mathcal{O}(k \cdot n^{1-1/d} \cdot m \cdot \mathrm{polylog}(n))$ time
complexity for the graph on $n$ vertices and $m$ edges, where $k$ is the
diameter and $d$ is the distance VC-dimension of the graph. Furthermore, it
allows us to use the improved technique in more general setting. In particular,
we use this framework for geometric intersection graphs, i.e. graphs where
vertices are identical geometric objects on a plane and the adjacency is
defined by intersection. Applying our approach for these graphs, we partially
answer a question posed by Bringmann et al. [SoCG'22], finding an
$\mathcal{O}(n^{7/4} \cdot \mathrm{polylog}(n))$ parameterized diameter
algorithm for unit square intersection graph of size $n$, as well as a more
general algorithm for convex polygon intersection graphs.
