  We show the first near-linear time randomized algorithms for listing all
minimum vertex cuts of polylogarithmic size that separate the graph into at
least three connected components (also known as shredders) and for finding the
most shattering one, i.e., the one maximizing the number of connected
components. Our algorithms break the quadratic time bound by Cheriyan and
Thurimella (STOC'96) for both problems that has stood for more than two
decades. Our work also removes a bottleneck to near-linear time algorithms for
the vertex connectivity augmentation problem (Jordan '95). Note that it is
necessary to list only minimum vertex cuts that separate the graph into at
least three components because there can be an exponential number of minimum
vertex cuts in general.
  To obtain near-linear time algorithms, we have extended techniques in local
flow algorithms developed by Forster et al. (SODA'20) to list shredders on a
local scale. We also exploit fast queries to a pairwise vertex connectivity
oracle subject to vertex failures (Long and Saranurak FOCS'22, Kosinas ESA'23).
This is the first application of connectivity oracles subject to vertex
failures to speed up a static graph algorithm.
