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Scheduling Splittable Jobs on Configurable Machines

Authors Matthew Casey , Rajmohan Rajaraman , David Stalfa, Cheng Tan

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  • Theory of computation → Scheduling algorithms
Keywords
  • Scheduling algorithms
  • Approximation algorithms
  • Configurable machines
  • Splittable jobs
  • Linear programming

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Abstract

Motivated by modern architectures allowing for the partitioning of a GPU into hardware separated instances, we initiate the study of scheduling splittable jobs on configurable machines. We consider machines that can be configured into smaller instances, which we call blocks, in multiple ways, each of which is referred to as a configuration. We introduce the Configurable Machine Scheduling (cms) problem, where we are given n jobs and a set C of configurations. A schedule consists of a set of machines, each assigned some configuration in C with each block in the configuration assigned to process one job. The amount of a job’s demand that is satisfied by a block is given by an arbitrary function of the job and block. The objective is to construct a schedule using as few machines as possible. We provide a tight logarithmic factor approximation algorithm for this problem in the general setting, a factor (3 + ε) approximation algorithm for arbitrary ε > 0 when there are O(1) input configurations, and a polynomial time approximation scheme when both the number and size of configurations are O(1). Finally, we utilize a technique for finding conic integer combinations in fixed dimension to develop an optimal polynomial time algorithm in the case with O(1) jobs, O(1) blocks, and every configuration up to a given size.

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Matthew Casey, Rajmohan Rajaraman, David Stalfa, and Cheng Tan. Scheduling Splittable Jobs on Configurable Machines. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 22:1-22:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.22

Author Details

Matthew Casey
  • Northeastern University, Boston MA 02115, USA
Rajmohan Rajaraman
  • Northeastern University, Boston MA 02115, USA
David Stalfa
  • Northeastern University, Boston MA 02115, USA
Cheng Tan
  • Northeastern University, Boston MA 02115, USA

Funding

  • Casey, Matthew: Partially supported by NSF grant CCF-1909363.
  • Rajaraman, Rajmohan: Partially supported by NSF grants CCF-1909363 and CCF-2335187.
  • Stalfa, David: Partially supported by NSF grant CCF-1909363.
  • Tan, Cheng: Partially supported by NSF CAREER Award #2237295

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