Optimal assignments with supervisions

Adi Niv; Marie Maccaig; Sergeĭ Sergeev

doi:10.1016/j.laa.2020.02.032

Optimal assignments with supervisions

Adi Niv, Marie Maccaig, Sergeĭ Sergeev

Mathematics

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Abstract

In this paper we provide a new graph theoretic proof of the tropical Jacobi identity, recently obtained in [1]. 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.

Original language	English
Pages (from-to)	72-100
Number of pages	29
Journal	Linear Algebra and its Applications
Volume	595
Early online date	29 Feb 2020
DOIs	https://doi.org/10.1016/j.laa.2020.02.032
Publication status	Published - 15 Jun 2020

Keywords

Compound matrix
Optimal assignment problem
Permanent
Tropical algebra
Weighted graphs

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10.1016/j.laa.2020.02.032Licence: None: All rights reserved

A_Niv_et_al_Optimal_assignments_with_supervisions_Linear_Algebra_and_its_Applications_2020Accepted author manuscript, 704 KBLicence: Creative Commons: Attribution-NonCommercial-NoDerivs (CC BY-NC-ND)

https://www.sciencedirect.com/science/article/pii/S002437952030104XLicence: None: All rights reserved

Tropical Optimisation
Sergeev, S.
Engineering & Physical Science Research Council
1/04/17 → 31/08/19
Project: Research Councils

Cite this

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AU - Maccaig, Marie

AU - Sergeev, Sergeĭ

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AB - In this paper we provide a new graph theoretic proof of the tropical Jacobi identity, recently obtained in [1]. 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.

KW - Compound matrix

KW - Optimal assignment problem

KW - Permanent

KW - Tropical algebra

KW - Weighted graphs

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JO - Linear Algebra and its Applications

JF - Linear Algebra and its Applications

ER -

Optimal assignments with supervisions

Abstract

Keywords

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Projects

Tropical Optimisation

Cite this