In this paper, we propose three generic models of capacitated coverage and,
more generally, submodular maximization to study task-worker assignment
problems that arise in a wide range of gig economy platforms. Our models
incorporate the following features: (1) Each task and worker can have an
arbitrary matching capacity, which captures the limited number of copies or
finite budget for the task and the working capacity of the worker; (2) Each
task is associated with a coverage or, more generally, a monotone submodular
utility function. Our objective is to design an allocation policy that
maximizes the sum of all tasks' utilities, subject to capacity constraints on
tasks and workers. We consider two settings: offline, where all tasks and
workers are static, and online, where tasks are static while workers arrive
dynamically. We present three LP-based rounding algorithms that achieve optimal
approximation ratios of 1−1/e∼0.632 for offline coverage
maximization, competitive ratios of (19−67/e3)/27∼0.580 and
0.436 for online coverage and online monotone submodular maximization,
respectively.Comment: This paper was accepted to the 19th Conference on Web and Internet
Economics (WINE), 202