Approximation Algorithms for Wireless Link Scheduling with Flexible Data   Rates
  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. 
Thomas Kesselheim
cs.NI cs.DS