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Keywords = Sperner’s Lemma

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12 pages, 874 KiB  
Article
Envy-Free Allocation by Sperner’s Lemma Adapted to Rotation Shifts in a Company
by Sagrario Lantarón, Mariló López, Susana Merchán, Javier Rodrigo and José Samuel Rodríguez
Mathematics 2021, 9(9), 1015; https://doi.org/10.3390/math9091015 - 30 Apr 2021
Viewed by 1993
Abstract
This article discusses a theoretical construction based on the graph theory to rework the space of potential partitions in envy-free distribution. This work has the objective of applying Sperner’s lemma to the distribution of three rotating shifts for three workers who are to [...] Read more.
This article discusses a theoretical construction based on the graph theory to rework the space of potential partitions in envy-free distribution. This work has the objective of applying Sperner’s lemma to the distribution of three rotating shifts for three workers who are to cover a 24 h job position in a company. As a novel feature, worker’s preferences have been modeled as functions of probability for the three shifts, according to salary offers for said shifts. Envy-free allocation was achieved, since each worker received their preferred shift without the need for negotiation between agents in conflict. Adaptation to the type of dynamic situations that arise with rotating shifts, as well as the consideration of probabilistic preferences by workers are some of the main novelties of this work. Full article
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8 pages, 165 KiB  
Article
Stable Multicommodity Flows
by Tamás Király and Júlia Pap
Algorithms 2013, 6(1), 161-168; https://doi.org/10.3390/a6010161 - 18 Mar 2013
Cited by 8 | Viewed by 7389
Abstract
We extend the stable flow model of Fleiner to multicommodity flows. In addition to the preference lists of agents on trading partners for each commodity, every trading pair has a preference list on the commodities that the seller can sell to the buyer. [...] Read more.
We extend the stable flow model of Fleiner to multicommodity flows. In addition to the preference lists of agents on trading partners for each commodity, every trading pair has a preference list on the commodities that the seller can sell to the buyer. A blocking walk (with respect to a certain commodity) may include saturated arcs, provided that a positive amount of less preferred commodity is traded along the arc. We prove that a stable multicommodity flow always exists, although it is PPAD-hard to find one. Full article
(This article belongs to the Special Issue Special Issue on Matching under Preferences)
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