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- W4226203987 abstract "We study an online version of the max-min fair allocation problem for indivisible items. In this problem, items arrive one by one, and each item must be allocated irrevocably on arrival to one of n agents, who have additive valuations for the items. Our goal is to maximize the egalitarian social welfare, which is the minimum happiness among the agents. In research on the topic of online allocation, this is a fundamental and natural problem. Our main result is to reveal the asymptotic competitive ratios of the problem for both the adversarial and i.i.d. input models. For the adversarial case, we design a polynomial-time deterministic algorithm that is asymptotically 1/n-competitive, and we show that this guarantee is optimal. Moreover, the algorithm satisfies proportionality in an asymptotic sense, that is, each agent receives a bundle of value at least nearly 1/n of the whole. For the case when the items are drawn from an unknown identical and independent distribution, we construct a simple polynomial-time deterministic algorithm that outputs a nearly optimal allocation. We analyze the strict competitive ratio and show almost tight bounds for the solution. We further mention some implications of our results on variants of the problem." @default.
- W4226203987 created "2022-05-05" @default.
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- W4226203987 date "2022-01-01" @default.
- W4226203987 modified "2023-10-03" @default.
- W4226203987 title "Online Max-min Fair Allocation" @default.
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- W4226203987 doi "https://doi.org/10.1007/978-3-031-15714-1_30" @default.
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