# Non-clairvoyant Precedence Constrained Scheduling

arXiv: https://arxiv.org/abs/1905.02133 · HTML: https://mlsanity.com/paper/1905.02133/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 May 2019.

## Built on by (most cited first, 3 of 3)

- [Online Scheduling for LLM Inference with KV Cache Constraints](https://mlsanity.com/paper/2502.07115/) (2025)
- [Minimalistic Predictions to Schedule Jobs with Online Precedence Constraints](https://mlsanity.com/paper/2301.12863/) (2023)
- [LLM Serving Optimization with Variable Prefill and Decode Lengths](https://mlsanity.com/paper/2508.06133/) (2025)

## Abstract (arXiv)

We consider the online problem of scheduling jobs on identical machines, where jobs have precedence constraints. We are interested in the demanding setting where the jobs sizes are not known up-front, but are revealed only upon completion (the non-clairvoyant setting). Such precedence-constrained scheduling problems routinely arise in map-reduce and large-scale optimization. In this paper, we make progress on this problem. For the objective of total weighted completion time, we give a constant-competitive algorithm. And for total weighted flow-time, we give an O(1/ε2)-competitive algorithm under (1+ε)-speed augmentation and a natural ``no-surprises'' assumption on release dates of jobs (which we show is necessary in this context). Our algorithm proceeds by assigning em virtual rates to all the waiting jobs, including the ones which are dependent on other uncompleted jobs, and then use these virtual rates to decide on the actual rates of minimal jobs (i.e., jobs which do not have dependencies and hence are eligible to run). Interestingly, the virtual rates are obtained by allocating time in a fair manner, using a Eisenberg-Gale-type convex program (which we can also solve optimally using a primal-dual scheme). The optimality condition of this convex program allows us to show dual-fitting proofs more easily, without having to guess and hand-craft the duals. We feel that this idea of using fair virtual rates should have broader applicability in scheduling problems.