  We consider scheduling problems in wireless networks with respect to flexible
data rates. That is, more or less data can be transmitted per time depending on
the signal quality, which is determined by the
signal-to-interference-plus-noise ratio (SINR). Each wireless link has a
utility function mapping SINR values to the respective data rates. We have to
decide which transmissions are performed simultaneously and (depending on the
problem variant) also which transmission powers are used.
  In the capacity-maximization problem, one strives to maximize the overall
network throughput, i.e., the summed utility of all links. For arbitrary
utility functions (not necessarily continuous ones), we present an O(log
n)-approximation when having n communication requests. This algorithm is built
on a constant-factor approximation for the special case of the respective
problem where utility functions only consist of a single step. In other words,
each link has an individual threshold and we aim at maximizing the number of
links whose threshold is satisfied. On the way, this improves the result in
[Kesselheim, SODA 2011] by not only extending it to individual thresholds but
also showing a constant approximation factor independent of assumptions on the
underlying metric space or the network parameters.
  In addition, we consider the latency-minimization problem. Here, each link
has a demand, e.g., representing an amount of data. We have to compute a
schedule of shortest possible length such that for each link the demand is
fulfilled, that is the overall summed utility (or data transferred) is at least
as large as its demand. Based on the capacity-maximization algorithm, we show
an O(log^2 n)-approximation for this problem.
