  Self-stabilization is an versatile approach to fault-tolerance since it
permits a distributed system to recover from any transient fault that
arbitrarily corrupts the contents of all memories in the system. Byzantine
tolerance is an attractive feature of distributed system that permits to cope
with arbitrary malicious behaviors. We consider the well known problem of
constructing a maximum metric tree in this context. Combining these two
properties prove difficult: we demonstrate that it is impossible to contain the
impact of Byzantine nodes in a self-stabilizing context for maximum metric tree
construction (strict stabilization). We propose a weaker containment scheme
called topology-aware strict stabilization, and present a protocol for
computing maximum metric trees that is optimal for this scheme with respect to
impossibility result.
