  We present results on the last topic we collaborate with our late friend,
Professor Ajoy Kumar Datta (1958-2019).
  In this work, we shed new light on a self-stabilizing wave algorithm proposed
by Colette Johnen in 1997. This algorithm constructs a BFS spanning tree in any
connected rooted network. Nowadays, it is still the best existing
self-stabilizing BFS spanning tree construction in terms of memory requirement,
{\em i.e.}, it only requires $\Theta(1)$ bits per edge. However, it has been
proven assuming a weakly fair daemon. Moreover, its stabilization time was
unknown.
  Here, we study the slightly modified version of this algorithm, still keeping
the same memory requirement. We prove the self-stabilization of this variant
under the distributed unfair daemon and show a stabilization time in $O(D.n^2)$
rounds, where $D$ is the network diameter and $n$ the number of processes.
