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DOI: 10.4230/LIPIcs.APPROX/RANDOM.2024.13

The Average-Value Allocation Problem

Authors: Kshipra Bhawalkar, Zhe Feng, Anupam Gupta, Aranyak Mehta, David Wajc, and Di Wang

Published in: LIPIcs, Volume 317, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)

Abstract

We initiate the study of centralized algorithms for welfare-maximizing allocation of goods to buyers subject to average-value constraints. We show that this problem is NP-hard to approximate beyond a factor of e/(e-1), and provide a 4e/(e-1)-approximate offline algorithm. For the online setting, we show that no non-trivial approximations are achievable under adversarial arrivals. Under i.i.d. arrivals, we present a polytime online algorithm that provides a constant approximation of the optimal (computationally-unbounded) online algorithm. In contrast, we show that no constant approximation of the ex-post optimum is achievable by an online algorithm.

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Kshipra Bhawalkar, Zhe Feng, Anupam Gupta, Aranyak Mehta, David Wajc, and Di Wang. The Average-Value Allocation Problem. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 317, pp. 13:1-13:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{bhawalkar_et_al:LIPIcs.APPROX/RANDOM.2024.13,
  author =	{Bhawalkar, Kshipra and Feng, Zhe and Gupta, Anupam and Mehta, Aranyak and Wajc, David and Wang, Di},
  title =	{{The Average-Value Allocation Problem}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2024)},
  pages =	{13:1--13:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-348-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{317},
  editor =	{Kumar, Amit and Ron-Zewi, Noga},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2024.13},
  URN =		{urn:nbn:de:0030-drops-210062},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2024.13},
  annote =	{Keywords: Resource allocation, return-on-spend constraint, approximation algorithm, online algorithm}
}

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The Average-Value Allocation Problem

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