arXiv:2508.04953v1 Announce Type: cross Abstract: Training deep learning (DL) models has become a dominant workload in data-centers and improving resource utilization is a key goal of DL cluster schedulers. In order to do this, schedulers typically incorporate placement policies that govern where jobs are placed on the cluster. Existing placement policies are either designed as ad-hoc heuristics or incorporated as constraints within a complex optimization problem and thus either suffer from suboptimal performance or poor scalability. Our key insight is that many placement constraints can be formulated as graph matching problems and based on that we design novel placement policies for minimizing job migration overheads and job packing. We integrate these policies into Tesserae and describe how our design leads to a scalable and effective GPU cluster scheduler. Our experimental results show that Tesserae improves average JCT by up to 1.62x and the Makespan by up to 1.15x compared with the existing schedulers.