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Fairness in Temporal Slot Assignment

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Part of the Lecture Notes in Computer Science book series (LNCS,volume 13584)

Abstract

We investigate settings where projects need to be assigned to time slots based on preferences of multiple agents. We consider a variety of objectives, including utilitarian social welfare, egalitarian social welfare, Nash social welfare, Pareto optimality, equitability, and proportionality. We introduce a general-purpose randomized algorithm, which, for each of these objectives, can decide whether it is achievable for a given instance; the running time of this algorithm is in the complexity class XP with respect to the number of agents. We also provide complexity results for the case where the number of agents is large, and identify special cases that admit efficient algorithms.

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Notes

  1. 1.

    We omit a discussion of utilitarian social welfare, since an outcome maximizing this measure of welfare can be computed in polynomial time for arbitrary n, m and \(\ell \) (Theorem 1).

  2. 2.

    It is important to note that this does not mean that when \(\lambda = 1\), Egal under FP is always NP-complete. We cannot use the \(\gamma = m\) argument here, even if \(m \ge 3\).

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Correspondence to Edith Elkind .

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Elkind, E., Kraiczy, S., Teh, N. (2022). Fairness in Temporal Slot Assignment. In: Kanellopoulos, P., Kyropoulou, M., Voudouris, A. (eds) Algorithmic Game Theory. SAGT 2022. Lecture Notes in Computer Science, vol 13584. Springer, Cham. https://doi.org/10.1007/978-3-031-15714-1_28

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