Forward-backward Contention Resolution Schemes for Fair Rationing
Will Ma, Calum MacRury, Cliff Stein

TL;DR
This paper develops contention resolution schemes (CRS) for fair resource allocation with stochastic demands, providing new guarantees for rank-1 matroids and knapsack constraints, especially under two-order arrival models.
Contribution
It introduces the first two-order CRS guarantees for rank-1 matroids and knapsack, improving existing bounds and establishing tightness and upper bounds for these models.
Findings
Two-order CRS for rank-1 matroids with guarantee ~0.622, tight bound.
Two-order CRS for knapsack with guarantee 1/3, best-known offline guarantee.
Upper bound of ~0.422 for two-order knapsack CRS, below random-order bound.
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 , which we prove is tight. This improves upon the guarantee that is best-possible under a single order (Alaei, SIAM J. Comput. 2014), while achieving separation with the guarantee that is possible…
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Taxonomy
TopicsCorporate Governance and Law · Credit Risk and Financial Regulations
