A PTAS for multiprocessor scheduling with rejection under a machine cost constraint
Mingyang Gong, Brendan Mumey
Published: 2025/7/16
Abstract
We study the multiprocessor scheduling with rejection problem under a machine cost constraint. In this problem, each job is either rejected with a rejection penalty or; accepted and scheduled on one of the machines for processing. The machine cost is proportional to the total processing time of the jobs scheduled on it. The problem aims to minimize the makespan of the accepted jobs plus the total rejection penalty of the rejected jobs while the total machine cost does not exceed a given upper bound. We present a simple $2$-approximation algorithm for the problem and we achieve a PTAS even when the number $m$ of machines is part of the input.