Optimal broadcasting in the back to back d-ary trees

Abstract

We show that, in the constant time and processor bound models (Fraigniaud and Lazard, 1994), the broadcast time in the back to back d-ary tree BB(d, n) (Barth, 1994) is $\text{b(BB(d, n)) = IL}\text{(d + 3)n}\text{2}\text{⌋}$. In particular, to prove this result, we propose an algorithm for broadcasting in BB(d, n).