Uniform and Ergodic Sampling in Unstructured Peer-to-Peer Systems with Malicious Nodes

We consider the problem of uniform sampling in large scale open systems. Uniform sampling is a fundamental primitive that guarantees that any individual in a population has the same probability to be selected as sample. An important issue that seriously hampers the feasibility of uniform sampling in open and large scale systems is the unavoidable presence of malicious nodes. In this paper we show that restricting the number of requests that malicious nodes can issue and allowing for a full knowledge of the composition of the system is a necessary and sufficient condition to guarantee uniform and ergodic sampling. In a nutshell, a uniform and ergodic sampling guarantees that any node in the system is equally likely to appear as a sample at any non malicious node in the system and that infinitely often any node has a non-null probability to appear as a sample of honest nodes.