Bag-Of-Tasks Scheduling on Related Machines

Authors Anupam Gupta, Amit Kumar, Sahil Singla

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Author Details

Anupam Gupta
  • Computer Science Department, Carnegie Mellon University, Pittsburgh, PA, USA
Amit Kumar
  • Computer Science and Engineering Department, Indian Institute of Technology, Delhi, India
Sahil Singla
  • Department of Computer Science, Princeton University, NJ, USA

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Anupam Gupta, Amit Kumar, and Sahil Singla. Bag-Of-Tasks Scheduling on Related Machines. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 207, pp. 3:1-3:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)


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(K³ log² K)-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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Online algorithms
  • Theory of computation → Scheduling algorithms
  • approximation algorithms
  • scheduling
  • bag-of-tasks
  • related machines


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