  The literature on communication-induced checkpointing presents a family of
protocols that use logical clocks to control whether forced checkpoints must be
taken. Efficiency of these protocols is measured by how many forced checkpoints
are needed to ensure no checkpoint will be useless to the application; the
fewer forced checkpoints the better. For many years, HMNR, also called Fully
Informed (FI), was the most complex and efficient protocol of this family. The
Lazy-FI protocol applies a lazy strategy that defers the increase of logical
clocks, resulting in a protocol with better efficiency for distributed systems
where processes can take basic checkpoints at different rates. Recently, the
Fully Informed aNd Efficient (FINE) protocol was proposed using the same
control structures as FI, but with a stronger and, presumably better,
checkpoint-inducing condition. FINE and its lazy version, called Lazy-FINE,
would now be the most efficient checkpointing protocols based on logical
clocks. This paper reviews this family of protocols, proves a theorem on a
condition that must be enforced by all stronger versions of FI, and proves that
both FINE and Lazy-FINE do not guarantee the absence of useless checkpoints. As
a consequence, FI and Lazy-FI can be rolled back to the position of most
efficient protocols of this family of index-based checkpointing protocols.
