This can be solved by the following modification to the
protocol. The failure detection protocol at member Mi
works by maintaining a list (intuitively, an array) of the
known elements of the current membership list, and selecting
ping targets not randomly from this list, but in a roundrobin
fashion. Instead, a newly joining member is inserted
in the membership list at a position that is chosen uniformly
at random. On completing a traversal of the entire list, Mi
rearranges the membership list to a random reordering.
