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 $1-1/\mathsf{e} \sim 0.632$ for offline coverage maximization, competitive ratios of $(19-67/\mathsf{e}^3)/27\sim 0.580$ and $0.436$ for online coverage and online monotone submodular maximization, respectively.

翻译：本文提出三种通用容量覆盖模型（更广泛地，子模最大化模型），用于研究各类零工经济平台中普遍存在的任务-工人分配问题。这些模型包含以下特征：(1) 每个任务和工人可具有任意匹配容量约束，分别对应任务有限副本数或预算限制，以及工人的工作容量限制；(2) 每个任务关联一个覆盖函数，更一般地，一个单调子模效用函数。我们的目标是设计满足任务与工人容量约束的分配策略，最大化所有任务效用之和。本文考虑两种场景：离线场景（所有任务与工人均为静态）与在线场景（任务静态而工人动态到达）。我们提出三种基于线性规划松弛的舍入算法：在离线覆盖最大化问题中达到最优近似比 $1-1/\mathsf{e} \sim 0.632$；在线覆盖与在线单调子模最大化问题中分别获得 $(19-67/\mathsf{e}^3)/27\sim 0.580$ 和 $0.436$ 的竞争比。