  We introduce the problem of finding a spanning tree along with a partition of
the tree edges into fewest number of feasible sets, where constraints on the
edges define feasibility. The motivation comes from wireless networking, where
we seek to model the irregularities seen in actual wireless environments. Not
all node pairs may be able to communicate, even if geographically close ---
thus, the available pairs are modeled with a link graph $\mathcal{L}=(V,E)$.
Also, signal attenuation need not follow a nice geometric formulas --- hence,
interference is modeled by a conflict (hyper)graph $\mathcal{C}=(E,F)$ on the
links. The objective is to maximize the efficiency of the communication, or
equivalently minimizing the length of a schedule of the tree edges in the form
of a coloring.
  We find that in spite of all this generality, the problem can be approximated
linearly in terms of a versatile parameter, the inductive independence of the
interference graph. Specifically, we give a simple algorithm that attains a
$O(\rho \log n)$-approximation, where $n$ is the number of nodes and $\rho$ is
the inductive independence, and show that near-linear dependence on $\rho$ is
also necessary. We also treat an extension to Steiner trees, modeling
multicasting, and obtain a comparable result.
  Our results suggest that several canonical assumptions of geometry,
regularity and "niceness" in wireless settings can sometimes be relaxed without
a significant hit in algorithm performance.
