Optimal assignments with supervisions
| Autor: | Sergei Sergeev, Marie Maccaig, Adi Niv |
|---|---|
| Přispěvatelé: | Kibbutzim College, Centre de Mathématiques Appliquées - Ecole Polytechnique (CMAP), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS), TROPICAL (TROPICAL), École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)-Centre National de la Recherche Scientifique (CNRS)-Inria Saclay - Ile de France, Institut National de Recherche en Informatique et en Automatique (Inria)-Institut National de Recherche en Informatique et en Automatique (Inria), School of Mathematics, University of Birmingham |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Jacobi identity
Tropical algebra Theoretical computer science 05C17 05C22 05C38 05C50 05E15 15A15 15A24 15A80 90B80 010103 numerical & computational mathematics Commutative Algebra (math.AC) 01 natural sciences Task (project management) symbols.namesake FOS: Mathematics Discrete Mathematics and Combinatorics Mathematics - Combinatorics 0101 mathematics ComputingMilieux_MISCELLANEOUS Mathematics Numerical Analysis Algebra and Number Theory Supervisor Graph theoretic 010102 general mathematics Mathematics - Commutative Algebra ComputingMethodologies_PATTERNRECOGNITION symbols Geometry and Topology Combinatorics (math.CO) [MATH.MATH-OC]Mathematics [math]/Optimization and Control [math.OC] |
| Zdroj: | Linear Algebra and its Applications Linear Algebra and its Applications, Elsevier, 2020, 595, pp.72-100. ⟨10.1016/j.laa.2020.02.032⟩ Linear Algebra and its Applications, 2020, 595, pp.72-100. ⟨10.1016/j.laa.2020.02.032⟩ |
| ISSN: | 0024-3795 |
| DOI: | 10.1016/j.laa.2020.02.032⟩ |
| Popis: | 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. The first author was supported by INRIA postdoctoral fellowship and SCE Young research grant. The second author was supported by a public grant as part of the Investissement d'avenir project, reference ANR-11-LABX-0056-LMH, LabEx LHM. The third author was supported by EPSRC Grant EP/P019676/1 |
| Databáze: | OpenAIRE |
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