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.

翻译：在普遍可支配的日程安排中,可同时在多台机器上分配和处理工作,以减少整个日程安排的范围;每项工作的所需处理时间由所分配的机器的共同处理速度决定;我们研究一个案例,即处理速度是取决于工作而需要的 $M ⁇ natural$-conve 函数,为这一环境提供一个不变因素的近似值,大大扩展了近似可能达到的职能范围;此外,我们探讨可移动日程安排与将物品公平分配给一组具有不同功能的代理商的问题之间的联系,设计一个黑盒削减,以便能够为后者获得资源强化的近似算法。