Improved approximation algorithms for multiprocessor indivisible coflow scheduling

Coflow scheduling is a challenging optimization problem that underlies many data transmission and parallel computing applications. In this paper, we study the indivisible coflow scheduling problem on parallel identical machines with the objective to minimize the makespan, i.e., the completion time of the last flow. In our problem setting, the number of the input/output ports in each machine is a fixed constant, each port has a unit capacity, and all the flows inside a coflow should be scheduled on the same machine. We present a \((2 + \epsilon )\)-approximation algorithm for the problem, for any \(\epsilon > 0\), in which the number of machines can be either a fixed constant or part of the input.