  The relatively rapid spatial and temporal variability of the X-ray radiation
from some molecular clouds near the Galactic center shows that this emission
component is due to the reflection of X-rays generated by a source that was
luminous in the past, most likely the central supermassive black hole,
Sagittarius A*. Studying the evolution of the molecular cloud reflection
features is therefore a key element to reconstruct Sgr A*'s past activity. The
aim of the present work is to study this emission on small angular scales in
order to characterize the source outburst on short time scales. We use Chandra
high-resolution data collected from 1999 to 2011 to study the most rapid
variations detected so far, those of clouds between 5' and 20' from Sgr A*
towards positive longitudes. Our systematic spectral-imaging analysis of the
reflection emission, notably of the Fe Kalpha line at 6.4 keV and its
associated 4-8 keV continuum, allows us to characterize the variations down to
15" angular scale and 1-year time scale. We reveal for the first time abrupt
variations of few years only and in particular a short peaked emission, with a
factor of 10 increase followed by a comparable decrease, that propagates along
the dense filaments of the Bridge cloud. This 2-year peaked feature contrasts
with the slower 10-year linear variations we reveal in all the other molecular
structures of the region. Based on column density constraints, we argue that
these two different behaviors are unlikely to be due to the same illuminating
event. The variations are likely due to a highly variable active phase of Sgr
A* sometime within the past few hundred years, characterized by at least two
luminous outbursts of a few-year time scale and during which the Sgr A*
luminosity went up to at least 10^39 erg/s.
