Sublinear time approximation schemes for makespan minimization on parallel machines - Fu, Bin; Huo, Yumei; Zhao, Hairong (Mathematical methods of operations research (Heidelberg, Germany), 2025)
We study sublinear time algorithms for the classical makespan minimization problem of scheduling n jobs on m parallel machines. Under uniform random sampling setting, we consider the problem with constrained processing times, which remains NP-hard. We first consider the problem where the processing times of all jobs differ by no more than a constant factor c . We develop the first sublinear time approximation scheme for this problem when the number of machines m is at most . We then extend our algorithm to the more general problem where the largest jobs have processing times that differ by no more than c factor for some constant , . When , our algorithm is a randomized -approximation scheme that runs in sublinear time. We further generalize our algorithms to the scheduling problems with precedence constraints where the precedence graph has a bounded depth h . Our work not only provides an algorithmic solution to the studied scheduling problem under big data environment, but also gives a methodological framework for designing sublinear time approximation algorithms for other scheduling problems.