Optimal Assignments with Supervisions
Adi Niv, Marie Maccaig, and Sergei Sergeev

TL;DR
This paper introduces a novel graph-theoretic proof of the tropical Jacobi identity and applies it to optimize task assignments involving supervision, enhancing understanding of complex assignment problems.
Contribution
It provides a new proof of the tropical Jacobi identity and applies it to develop optimal assignment strategies with supervision constraints.
Findings
New graph-theoretic proof of the tropical Jacobi identity
Application to optimal assignment problems with supervision
Improved understanding of task assignment optimization
Abstract
In this paper we provide a new graph theoretic proof of the tropical Jacobi identity, recently obtained in [AGN16]. We also develop an application of this theorem to optimal assignments with supervisions. That is, optimally assigning multiple tasks to one team, or daily tasks to multiple teams, where each team has a supervisor task or a supervised task.
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