The Average-Value Allocation Problem

TL;DR

This paper studies the problem of allocating goods to maximize welfare under average-value constraints, establishing its computational hardness and proposing approximation algorithms for offline and online settings.

Contribution

It introduces the average-value allocation problem, proves its NP-hardness, and develops approximation algorithms for both offline and stochastic online scenarios.

Findings

NP-hard to approximate beyond e/(e-1)

Provides a 4e/(e-1)-approximate offline algorithm

Offers a constant-approximation online algorithm under i.i.d. arrivals

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.