  We consider a set of k autonomous robots that are endowed with visibility
sensors (but that are otherwise unable to communicate) and motion actuators.
Those robots must collaborate to reach a sin- gle vertex that is unknown
beforehand, and to remain there hereafter. Previous works on gathering in
ring-shaped networks suggest that there exists a tradeoff between the size of
the set of potential initial configurations, and the power of the sensing
capabilities of the robots (i.e. the larger the initial configuration set, the
most powerful the sensor needs to be). We prove that there is no such trade
off. We propose a gathering protocol for an odd number of robots in a
ring-shaped network that allows symmetric but not periodic configurations as
initial configurations, yet uses only local weak multiplicity detection. Robots
are assumed to be anonymous and oblivious, and the execution model is the
non-atomic CORDA model with asynchronous fair scheduling. Our protocol allows
the largest set of initial configurations (with respect to impossibility
results) yet uses the weakest multiplicity detector to date. The time
complexity of our protocol is O(n2), where n denotes the size of the ring.
Compared to previous work that also uses local weak multiplicity detection, we
do not have the constraint that k < n/2 (here, we simply have 2 < k < n - 3).
