Abstract : In this paper, we describe a fully decentralized algorithm, called "dating service" to organize communications into a fully heterogeneous network, that ensures that communication capabilities of the nodes are not exceeded. We prove that with high probability, this service ensures that a constant fraction of all possible communications is organized. Interestingly enough, this property holds true even if a node is not able to choose another node uniformly at random. We also present, as an application of the dating service, an algorithm for rumor spreading that enables to broadcast a unit-size message to all the nodes of a P2P system in logarithmic number of steps with high probability.
