  Encke-type comet 332P/Ikeya-Murakami is experiencing cascading fragmentation
events during its 2016 apparition. It is likely the first splitting Encke-type
comet ever being observed. A nongravitational solution to the astrometry
reveals a statistical detection of the radial and transverse nongravitational
parameters, $A_{1} = \left(1.54 \pm 0.39\right) \times 10^{-8}$ AU day$^{-2}$,
and $A_{2} = \left(7.19 \pm 1.92\right) \times 10^{-9}$ AU day$^{-2}$,
respectively, which implies a nucleus erosion rate of $\left(0.91 \pm
0.17\right)$% per orbital revolution. The mass-loss rate likely has to be
supported by a much larger fraction of an active surface area than known cases
of short-period comets; it may be relevant to the ongoing fragmentation. We
failed to detect any serendipitous pre-discovery observations of the comet in
archival data from major sky surveys, whereby we infer that 332P used to be
largely inactive, and is perhaps among the few short-period comets which have
been reactivated from weakly active or dormant states. We therefore constrain
an upper limit to the nucleus size as $2.0 \pm 0.2$ km in radius. A search for
small bodies in similar orbits to that of 332P reveals comet P/2010 B2 (WISE)
as the best candidate. From an empirical generalised Jupiter-family (Encke-type
included) comet population model, we estimate the likelihood of chance
alignment of the 332P--P/2010 B2 pair to be 1 in 33, a small number indicative
of a genetic linkage between the two comets on a statistical basis. The pair
possibly originated from a common progenitor which underwent a disintegration
event well before the twentieth century.
