Table 1.

Notation: network setting.

Notation	Description
$\mathcal{V}$	set of nodes
$\mathcal{S},\mathcal{D},\mathcal{Q}$	sensors, destinations, transit nodes, respectively
$\mathcal{A}$	set of directed radio links (arcs); $a=\left(b\right(a),e(a\left)\right)$
${\delta }^{+}\left(v\right)$	set of nodes connected with v by its outgoing arcs
${\delta }^{-}\left(v\right)$	set of nodes connected with v by its incoming arcs
$p(v,w)$	power received at node w from transmitting node v
$\eta$	noise power
m	modulation and coding scheme
$\mathcal{M}$	set of MCSs ($\mathcal{M}:=\{1,2,\dots ,M\}$)
$\gamma \left(m\right)$	SINR threshold for MCS m
$B\left(m\right)$	bitrate in (Mbps) for MCS m
c	compatible set (c-set in short)
$m(c,w)$	number of the MCS assigned to node w in c-set c
$\widehat{\mathcal{C}}$	family of all c-sets
$\mathcal{W}\left(c\right)$	set of nodes transmitting when c-set c is used
$\mathcal{U}(c,w)$	set of nodes that receive signal from $w\in \mathcal{W}\left(c\right)$
$\mathcal{C}$	selected subfamily of $\widehat{\mathcal{C}}$
$\mathcal{C}\left(a\right)$	subset of c-sets in C broadcasting over arc a $\mathcal{C}\left(a\right)=\mathcal{C}\left(b\right(a),e(a\left)\right)$
$\mathcal{D}\left(s\right)$	set of destination nodes of sensor s ($\mathcal{D}\left(s\right)\subseteq \mathcal{D}$)
$\mathcal{B}\left(s\right)$	multicast routing tree rooted at s with leaves $\mathcal{D}\left(s\right)$
$\mathcal{V}\left(s\right),\mathcal{A}\left(s\right)$	set of nodes and arcs, respectively, of $\mathcal{B}\left(s\right)$
$\mathbb{B},\mathbb{Z},{\mathbb{R}}_{+}$	$\mathbb{B}=\{0,1\}$, $\mathbb{Z}$ integers, ${\mathbb{R}}_{+}$ non-negative real numbers