Inspired by the recent COVID-19 pandemic, we study a generalization of the multi-resource allocation problem with heterogeneous demands and Leontief utilities. Unlike existing settings, we allow each agent to specify requirements to only accept allocations from a subset of the total supply for each resource. These requirements can take form in location constraints (e.g. A hospital can only accept volunteers who live nearby due to commute limitations). This can also model a type of substitution effect where some agents need 1 unit of resource A \emph{or} B, both belonging to the same meta-type. But some agents specifically want A, and others specifically want B. We propose a new mechanism called Dominant Resource Fairness with Meta Types which determines the allocations by solving a small number of linear programs. The proposed method satisfies Pareto optimality, envy-freeness, strategy-proofness, and a notion of sharing incentive for our setting. To the best of our knowledge, we are the first to study this problem formulation, which improved upon existing work by capturing more constraints that often arise in real life situations. Finally, we show numerically that our method scales better to large problems than alternative approaches.

Inspired by the recent COVID-19 pandemic, we study a generalization of the multi-resource allocation problem with heterogeneous demands and Leontief utilities. Specifically, we assume each agent can only receive allocations from a subset of the total supply for each resource. Such constraints often arise from location constraints (e.g. among all of the volunteer nurses, only a subset of them can work at hospital A due to commute constraints. So hospital A can only receive allocations of volunteers from a subset of the total supply). We propose a new mechanism called Group Dominant Resource Fairness which determines the allocations by solving a small number of linear programs. The proposed method satisfies Pareto optimality, envy-freeness, strategy-proofness, and under an additional mild assumption, also proportionality. We show numerically that our method scales better to large problems than alternative approaches. Finally, although motivated by the problem of medical resource allocation in a pandemic, our mechanism can be applied more broadly to resource allocation under Leontief utilities with external constraints.

We study the problem of learning a hypergraph via edge detecting queries. In this problem, a learner queries subsets of vertices of a hidden hypergraph and observes whether these subsets contain an edge or not. In general, learning a hypergraph with m edges of maximum size d requires Ω((2m/d) d/2 ) queries [7]. In this paper, we aim to identify families of hypergraphs that can be learned without suffering from a query complexity that grows exponentially in the size of the edges.We show that hypermatchings and low-degree near-uniform hypergraphs with n vertices are learnable with poly(n) queries. For learning hypermatchings (hypergraphs of maximum degree 1), we give an O(log 3 n)-round algorithm with O(n log 5 n) queries. We complement this upper bound by showing that there are no algorithms with poly(n) queries that learn hypermatchings in o(log log n) adaptive rounds. For hypergraphs with maximum degree ∆ and edge size ratio ρ, we give a non-adaptive algorithm with O((2n) ρ∆+1 log 2 n) queries. To the best of our knowledge, these are the first algorithms with poly(n, m) query complexity for learning non-trivial families of hypergraphs that have a super-constant number of edges of super-constant size.