On the Approximability of Related Machine Scheduling under Arbitrary Precedence

Distributed computing systems often need to consider the scheduling problem involving a collection of highly dependent data-processing tasks that must work in concert achieve mission-critical objectives. This paper considers unrelated machine for minimizing weighted sum completion time under arbitrary precedence constraints and on heterogeneous machines with different processing speeds. The is known be strongly NP-hard even single setting. By making use Queyranne’s constraint set constructing novel Linear Programming relaxation constraints, our results this advance state art. We develop 2(1 + ( ${m}$ –1)/ ${D}$ )-approximation algorithm (and ) 1-approximation) zero release time), where number servers task-skewness product. can efficiently computed polynomial using Ellipsoid method achieves nearly optimal performance practice as ${D} > {O}$ when per job schedule sufficiently larger than available. Our implementation evaluation testbed real-world benchmarks confirms significant improvement tasks.