We consider online scheduling to minimize weighted completion time on related machines, where each job consists of several tasks that can be concurrently executed. A job gets completed when all its component tasks finish. We obtain an O(K3log2K)-competitive algorithm in the non-clairvoyant setting, where K denotes the number of distinct machine speeds. The analysis is based on dual-fitting on a precedence-constrained LP relaxation that may be of independent interest.
@article{arxiv.2107.06216,
title = {Bag-of-Tasks Scheduling on Related Machines},
author = {Anupam Gupta and Amit Kumar and Sahil Singla},
journal= {arXiv preprint arXiv:2107.06216},
year = {2021}
}