## Abstract

We consider a scheduling problem on identical machines, where the cost for each machine is the total size of jobs assigned to it, excluding its largest job. The objective is to minimize the cost of the schedule, which is the maximum cost over all machines. We study online algorithms with and without migration. We design an algorithm with competitive ratio 3 for the purely online variant and provide a lower bound of 2.26953 on the competitive ratio of any online algorithm. For two machines, we find tight bounds of 2 on the competitive ratio. Additionally, we design a polynomial time approximation scheme for the variant with migration. We also briefly discuss the same online problem on uniformly related machines.

Original language | English |
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Pages (from-to) | 79-87 |

Number of pages | 9 |

Journal | Discrete Applied Mathematics |

Volume | 307 |

DOIs | |

State | Published - 30 Jan 2022 |

### Bibliographical note

Funding Information:Partially supported by Grant Number 308/18 of ISF - Israeli Science Foundation.

Publisher Copyright:

© 2021 Elsevier B.V.

## Keywords

- Competitive analysis
- Load balancing
- Multiprocessor
- Scheduling

## ASJC Scopus subject areas

- Discrete Mathematics and Combinatorics
- Applied Mathematics