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Computer Science > Data Structures and Algorithms

arXiv:2407.10401 (cs)
[Submitted on 15 Jul 2024]

Title:The Average-Value Allocation Problem

Authors:Kshipra Bhawalkar, Zhe Feng, Anupam Gupta, Aranyak Mehta, David Wajc, Di Wang
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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 $\frac{e}{e-1}$, and provide a $\frac{4e}{e-1}$-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.
Subjects: Data Structures and Algorithms (cs.DS); Computer Science and Game Theory (cs.GT)
Cite as: arXiv:2407.10401 [cs.DS]
  (or arXiv:2407.10401v1 [cs.DS] for this version)
  https://doi.org/10.48550/arXiv.2407.10401

Submission history

From: Di Wang [view email]
[v1] Mon, 15 Jul 2024 02:41:51 UTC (60 KB)
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