Monitoring and management operations that query nodes based on their availability can be extremely useful in a variety of largescale distributed systems containing hundreds to thousands of hosts, e.g., p2p systems, Grids, and PlanetLab. This paper presents decentralized and scalable solutions to a subset of such availability-based management tasks. Specifically, we propose AVMEM, which is the first availabilityaware overlay to date. AVMEM is intended for generic non-cooperative scenarios where nodes may be selfish and may wish to route messages to a large set of other nodes, especially if the selfish node has low availability. Under this setting, our concrete contributions are the following: (1) AVMEM allows arbitrary classes of application-specified predicates to create the membership relationships in the overlay. In order to avoid selfish nodes from exploiting the system, we focus on predicates that are random and consistent. In other words, whether a given node y is a neighbor...