A log-linear $(2+5/6)$-approximation algorithm for parallel machine scheduling with a single orthogonal resource

As the gap between compute and I/O performance tends to grow, modern High-Performance Computing (HPC) architectures include a new resource type: an intermediate persistent fast memory layer, called burst buffers. This is just one of many kinds of renewable resources which are orthogonal to the processors themselves, such as network bandwidth or software licenses. Ignoring orthogonal resources while making scheduling decisions just for processors may lead to unplanned delays of jobs of which resource requirements cannot be immediately satisfied. We focus on a classic problem of makespan minimization for parallel-machine scheduling of independent sequential jobs with additional requirements on the amount of a single renewable orthogonal resource. We present an easily-implementable log-linear algorithm that we prove is $2\frac56$-approximation. In simulation experiments, we compare our algorithm to standard greedy list-scheduling heuristics and show that, compared to LPT, resource-based algorithms generate significantly shorter schedules.