Two-Sided Capacitated Submodular Maximization in Gig Platforms

TL;DR

This paper introduces models and algorithms for task-worker assignment in gig platforms, optimizing submodular utility functions under capacity constraints in both offline and online settings.

Contribution

It develops LP-based algorithms with provable approximation and competitive ratios for capacitated submodular maximization in gig economy scenarios.

Findings

Achieves a 0.632 approximation ratio for offline coverage maximization.

Provides a 0.580 competitive ratio for online coverage maximization.

Offers a 0.436 competitive ratio for online monotone submodular maximization.

Abstract

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.