  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.
