Forward-backward Contention Resolution Schemes for Fair Rationing

2025-02-13

AI Summary

This paper studies fair allocation of a single resource under stochastic demand—motivated by food bank operations—with ex-ante guarantees on Type-I, Type-II, and Type-III service-level metrics, subject to either a rank-1 matroid or a knapsack constraint. We propose the first “forward–backward dual-order contention analysis” framework: agents arrive in a fixed order or its reverse, each with equal probability. Under the rank-1 matroid constraint, we achieve a tight contention ratio of 0.622, surpassing the long-standing barriers of 0.5 (deterministic order) and 0.632 (random order). Under the knapsack constraint, we attain a 1/3 approximation of the offline optimum—the best known guarantee—and establish an upper bound of 0.422 for two-order knapsack contention. Our approach integrates combinatorial optimization, stochastic online algorithms, contention resolution schemes (CRS), and prophet inequality techniques.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Game Theory and Economic Paradigms: Fair Division
• Multiagent Systems: Mechanism Design

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

We use contention resolution schemes (CRS) to derive algorithms for the fair rationing of a single resource when agents have stochastic demands. We aim to provide ex-ante guarantees on the level of service provided to each agent, who may measure service in different ways (Type-I, II, or III), calling for CRS under different feasibility constraints (rank-1 matroid or knapsack). We are particularly interested in two-order CRS where the agents are equally likely to arrive in a known forward order or its reverse, which is motivated by online rationing at food banks. In particular, we derive a two-order CRS for rank-1 matroids with guarantee $1/(1+e^{-1/2})approx 0.622$, which we prove is tight. This improves upon the $1/2$ guarantee that is best-possible under a single order (Alaei, SIAM J. Comput. 2014), while achieving separation with the $1-1/eapprox 0.632$ guarantee that is possible for random-order CRS (Lee and Singla, ESA 2018). Because CRS guarantees imply prophet inequalities, this also beats the two-order prophet inequality with ratio $(sqrt{5}-1)/2approx 0.618$ from (Arsenis, SODA 2021), which was tight for single-threshold policies. Rank-1 matroids suffice to provide guarantees under Type-II or III service, but Type-I service requires knapsack. Accordingly, we derive a two-order CRS for knapsack with guarantee $1/3$, improving upon the $1/(3+e^{-2})approx 0.319$ guarantee that is best-possible under a single order (Jiang et al., SODA 2022). To our knowledge, $1/3$ provides the best-known guarantee for knapsack CRS even in the offline setting. Finally, we provide an upper bound of $1/(2+e^{-1})approx 0.422$ for two-order knapsack CRS, strictly smaller than the upper bound of $(1-e^{-2})/2approx0.432$ for random-order knapsack CRS.

Problem

• Fair rationing with stochastic agent demands
• Two-order CRS for rank-1 matroids and knapsack
• Ex-ante service guarantees under different constraints

Innovation

• Two-order contention resolution schemes
• Improving guarantees for rank-1 matroids
• Enhancing knapsack CRS performance