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The Average-Value Allocation Problem

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

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Subject Classification

ACM Subject Classification
  • Theory of computation → Approximation algorithms analysis
  • Theory of computation → Online algorithms
Keywords
  • Resource allocation
  • return-on-spend constraint
  • approximation algorithm
  • online algorithm

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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) https://doi.org/10.4230/LIPIcs.APPROX/RANDOM.2024.13

Author Details

Kshipra Bhawalkar
  • Google Research, Mountain View, USA
Zhe Feng
  • Google Research, Mountain View, USA
Anupam Gupta
  • NYU & Google Research, New York City & Mountain View, USA
Aranyak Mehta
  • Google Research, Mountain View, USA
David Wajc
  • Technion, Haifa, Israel
Di Wang
  • Google Research, Mountain View, USA

Funding

  • Gupta, Anupam: Supported in part by NSF awards CCF-1955785 and CCF-2006953.
  • Wajc, David: Supported in part by a Taub Family Foundation "Leader in Science and Technology" fellowship. Work done while the author was visiting Google Research.

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