An improved algorithm for online machine minimization

The online machine minimization problem seeks to design a preemptive scheduling algorithm on multiple machines — each job $j$ arrives at its release time $r_j$, has to be processed for $p_j$ time units, and must be completed by its deadline $d_j$. The goal is to minimize the number of machines the algorithm uses. We improve the $O(logm)$-competitive algorithm by Chen, Megow and Schewior (SODA 2016) and provide an $O\left(\frac{logm}{loglogm}\right)$-competitive algorithm.