We study in this paper an online matching problem where a central platform needs to match a number of limited resources to different groups of users that arrive sequentially over time. The reward of each matching option depends both on the type of resource and the time period the user arrives....

Given an input graph Gin =(V,E_in), we consider the problem of designing a sparse subgraph G = (V, E) with E ⊆ E_in that supports a large matching after some nodes in V are randomly deleted. We study three families of sparse graph designs (namely, Clusters, Rings, and Erdős-Rényi graphs) and...