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 an 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.
Bibliographical notePublisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature.
- Competitive analysis
- Ordinal scheduling
- Semi-online algorithms
ASJC Scopus subject areas
- Computer Science Applications
- Discrete Mathematics and Combinatorics
- Control and Optimization
- Computational Theory and Mathematics
- Applied Mathematics