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Computer Science > Data Structures and Algorithms

arXiv:2210.07639 (cs)
[Submitted on 14 Oct 2022]

Title:Parallel solutions for ordinal scheduling with a small number of machines

Authors:Leah Epstein
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Abstract:We study ordinal makespan scheduling on small numbers of identical machines, with respect to two parallel solutions. In ordinal scheduling, it is known that jobs are sorted by non-increasing sizes, but the specific sizes are not known in advance. For problems with two parallel solutions, it is required to design two solutions, and the performance of algorithm is tested for each input using the best solution of the two. We find tight results for makespan minimization on two and three machines, and algorithms that have strictly better competitive ratios than the best possible algorithm with a single solution also for four and five machines. To prove upper bounds, we use a new approach of considering pairs of machines from the two solutions.
Subjects: Data Structures and Algorithms (cs.DS); Discrete Mathematics (cs.DM); Combinatorics (math.CO); Optimization and Control (math.OC)
Cite as: arXiv:2210.07639 [cs.DS]
  (or arXiv:2210.07639v1 [cs.DS] for this version)
  https://doi.org/10.48550/arXiv.2210.07639

Submission history

From: Leah Epstein [view email]
[v1] Fri, 14 Oct 2022 08:40:04 UTC (46 KB)
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