SELFISHMIGRATE: A Scalable Algorithm for Non-clairvoyantly Scheduling Heterogeneous Processors

We consider the classical problem of minimizing the total weighted flow-time for unrelated machines in the online \emph{non-clairvoyant} setting. In this problem, a set of jobs $J$ arrive over time to be scheduled on a set of $M$ machines. Each job $j$ has processing length $p_j$, weight $w_j$, and is processed at a rate of $\ell_{ij}$ when scheduled on machine $i$. The online scheduler knows the values of $w_j$ and $\ell_{ij}$ upon arrival of the job, but is not aware of the quantity $p_j$. We present the {\em first} online algorithm that is {\em scalable} ((1+\eps)-speed $O(\frac{1}{\epsilon^2})$-competitive for any constant \eps > 0) for the total weighted flow-time objective. No non-trivial results were known for this setting, except for the most basic case of identical machines. Our result resolves a major open problem in online scheduling theory. Moreover, we also show that no job needs more than a logarithmic number of migrations. We further extend our result and give a scalable algorithm for the objective of minimizing total weighted flow-time plus energy cost for the case of unrelated machines and obtain a scalable algorithm. The key algorithmic idea is to let jobs migrate selfishly until they converge to an equilibrium. Towards this end, we define a game where each job's utility which is closely tied to the instantaneous increase in the objective the job is responsible for, and each machine declares a policy that assigns priorities to jobs based on when they migrate to it, and the execution speeds. This has a spirit similar to coordination mechanisms that attempt to achieve near optimum welfare in the presence of selfish agents (jobs). To the best our knowledge, this is the first work that demonstrates the usefulness of ideas from coordination mechanisms and Nash equilibria for designing and analyzing online algorithms

LIPIcs, Volume 261, ICALP 2023, Complete Volume

LIPIcs, Volume 261, ICALP 2023, Complete Volum

Online Scalable Scheduling for the ℓk-norms of Flow Time Without Conservation of Work

We address the scheduling model of arbitrary speed-up curves and the broadcast scheduling model. The former occurs when jobs are scheduled in a multi-core system or on a cloud of machines. Here jobs can be sped up when given more processors or machines. However, the parallelizability of the jobs may vary and the algorithm is required to be oblivious of the parallelizability of a job. The latter model is natural in wireless and LAN networks where requests (or jobs) can be simultaneously satisfied together. Both settings are similar in that two schedules can do different amounts of work to satisfy all the jobs. We focus on optimizing the ℓk- norms of flow time. Recently, Gupta et al. [24] gave a (k + ɛ)-speed O(1)competitive algorithm for the ℓk norms of flow time in both scheduling settings for fixed k. Inspired by this work, we give the first analysis of a scalable algorithm, i.e. (1 + ɛ)-speed O(1)-competitive, for all ℓk-norms of flow time in both settings for fixed k and 0 < ɛ ≤ 1. Both problems have a strong lower bound without resource augmentation, so this is the best result that can be shown in the worst case setting up to a constant factor in the competitive ratio

LIPIcs, Volume 251, ITCS 2023, Complete Volume

LIPIcs, Volume 251, ITCS 2023, Complete Volum

LIPIcs, Volume 244, ESA 2022, Complete Volume

LIPIcs, Volume 244, ESA 2022, Complete Volum

LIPIcs, Volume 274, ESA 2023, Complete Volume

LIPIcs, Volume 274, ESA 2023, Complete Volum

LIPIcs, Volume 277, GIScience 2023, Complete Volume

LIPIcs, Volume 277, GIScience 2023, Complete Volum

12th International Conference on Geographic Information Science: GIScience 2023, September 12–15, 2023, Leeds, UK

No abstract available