In online load balancing problems, jobs arrive over a list. Upon arrival of a job, the algorithm is required to assign it immediately and irrevocably to a machine. We consider such a makespan minimization problem with an additional cardinality constraint, i.e., at most k jobs may be assigned to each machine, where k is a parameter of the problem. We present both upper and lower bounds on the competitive ratio of online algorithms for this problem with identical machines.
Bibliographical noteFunding Information:
L. Epstein and A. Levin were partially supported by GIF – the German-Israeli Foundation for Scientific Research and Development (grant number I-1366-407.6/2016 ). A. Lassota was supported by the Swiss National Science Foundation within the project Lattice algorithms and Integer Programming ( 200021_185030/1 ). A. Levin was also partially supported by grants from ISF – Israel Science Foundation (grant numbers 308/18 and 1467/22 ). M. Maack was partially supported by the German Research Foundation (DFG) within the Collaborative Research Centre “On-The-Fly Computing” under the project number 160364472 — SFB 901/3 .
© 2023 Elsevier B.V.
- Competitive analysis
- Load balancing
- Online algorithms
ASJC Scopus subject areas
- Management Science and Operations Research
- Industrial and Manufacturing Engineering
- Applied Mathematics