Minimizing Makespan in Sublinear Time via Weighted Random Sampling

Authors

• Bin Fu, The University of Texas Rio Grande ValleyFollow
• Yumei Huo, College of Staten Island
• Hairong Zhao, Purdue University Northwest

Document Type

Conference Proceeding

Publication Date

6-7-2026

Abstract

We consider the classical makespan minimization scheduling problem where n jobs must be scheduled on m identical machines. Using weighted random sampling, we develop two sublinear time approximation schemes: one for the case where n is known and one for the case where n is unknown. Both algorithms not only give a (1+3ϵ)-approximation to the optimal makespan but also generate a sketch schedule. Our first algorithm, which targets the case where n is known and draws samples in a single round under weighted random sampling, has a running time of O~(m⁵ϵ⁴n+A(mϵ,ϵ)), where A(N,α) is the time complexity of any (1+α)-approximation scheme for the makespan minimization of N jobs. The second algorithm addresses the case where n is unknown. It uses adaptive weighted random sampling, and runs in sublinear time O~m⁵ϵ⁴n+A(mϵ,ϵ).

Recommended Citation

Fu, Bin, Yumei Huo, and Hairong Zhao. "Minimizing Makespan in Sublinear Time via Weighted Random Sampling." In International Workshop on Combinatorial Algorithms, pp. 531-545. Springer, Cham, 2026. https://doi.org/10.1007/978-3-032-27732-9_37

First Page

531

Last Page

545

Publication Title

Lecture Notes in Computer Science

DOI

https://doi.org/10.1007/978-3-032-27732-9_37