Periodic Gossiping in Back-to-back Trees

The d-ary back-to-back tree of height k, BBT k d , consists of two complete d-ary trees of height k the leaves of which are identiied. For a proper coloring of the edges of BBT k d with c d + 1 colors, we consider periodic gossiping, i.e. full-duplex all-to-all broadcasting in the 1-port model where communication is made on a link of color i at any time (round) i mod c. We present a coloring for which this process nishes within k periods, where a period is the collection of c consecutive rounds. We prove that this is optimal for c = d + 1.