  An independent broadcast on a connected graph $G$ is a function $f:V(G)\to
\mathbb{N}_0$ such that, for every vertex $x$ of $G$, the value $f(x)$ is at
most the eccentricity of $x$ in $G$, and $f(x)>0$ implies that $f(y)=0$ for
every vertex $y$ of $G$ within distance at most $f(x)$ from $x$. The broadcast
independence number $\alpha_b(G)$ of $G$ is the largest weight
$\sum\limits_{x\in V(G)}f(x)$ of an independent broadcast $f$ on $G$.
  We describe an efficient algorithm that determines the broadcast independence
number of a given tree. Furthermore, we show NP-hardness of the broadcast
independence number for planar graphs of maximum degree four, and hardness of
approximation for general graphs. Our results solve problems posed by Dunbar,
Erwin, Haynes, Hedetniemi, and Hedetniemi (2006), Hedetniemi (2006), and
Ahmane, Bouchemakh, Sopena (2018).
