In generalized malleable scheduling, jobs can be allocated and processed simultaneously on multiple machines so as to reduce the overall makespan of the schedule. The required processing time for each job is determined by the joint processing speed of the allocated machines. We study the case that processing speeds are job-dependent \(M ^{\natural }\)-concave functions and provide a constant-factor approximation for this setting, significantly expanding the realm of functions for which such an approximation is possible. Further, we explore the connection between malleable scheduling and the problem of fairly allocating items to a set of agents with distinct utility functions, devising a black-box reduction that allows to obtain resource-augmented approximation algorithms for the latter.

在广义可延展调度中，作业可以在多台机器上同时分配和处理，以减少调度的总体完成时间。每个作业所需的处理时间由分配的机器的联合处理速度决定。我们研究了处理速度依赖于作业\(M ^{\natural }\)凹函数的情况，并为此设置提供了常数因子近似值，显着扩展了可以进行这种近似的函数范围。此外，我们探索了可塑性调度与将项目公平分配给一组具有不同效用函数的代理的问题之间的联系，设计了一种黑盒简化方法，允许为后者获得资源增强的近似算法。