A review of some fair allocation algorithms for indivisible items

This work reviews some fair and efficient algorithms in the allocation problem of indivisible items in the general additive and g-binary additive instances for the cases of goods, chores, and mixtures of goods and chores. Firstly, the state of the art is studied to comprehend the fundamental concepts, advancements, and limitations of the problem. Subsequently, notions of fairness and efficiency, as well as some weaker versions, are examined. Then, in the general additive instance, the behavior of the Round Robin, Double Round Robin, MUW solution, and MNW solution algorithms is analyzed to identify the properties that hold in the cases of goods, chores, and combinations of both. After this, the algorithms' behavior in the g-binary additive instance is scrutinized to identify if the algorithms achieve any additional properties. Finally, a classification of the properties fulfilled by the Round Robin, Double Round Robin, MUW solution, and MNW solution algorithms is obtained in the cases of goods, chores, and mixtures of goods and chores. Moreover, it is demonstrated that the MNW solution algorithm in g-binary additive instances maximizes both Nash and utilitarian social welfare.

• Autore principale: Chipantasig Chipantashi, Jefferson Javier (author)
• Natura: bachelorThesis
• Lingua: eng
• Pubblicazione: 2025
• Soggetti: Algoritmos; Elementos indivisibles; Bienestar social; Algorithms; Indivisible items; Social welfare
• Accesso online: http://repositorio.yachaytech.edu.ec/handle/123456789/971