A Fully Distributed Lagrangean Metaheuristic for a P2P Overlay Network Design Problem

In peer-to-peer (P2P) networks it is a central problem to maintain a so called overlay network with certain desired properties. An overlay network is defined by logical connections (i.e., the ”who knows whom” relation) between peers over an underlying physical network. If node i is connected to node j in an overlay network, it means that node i knows the address of j and so it can send messages to j. An overlay network must fulfill certain requirements to allow for optimal cost and efficiency of the application of the overlay. Besides, a typical P2P network is large, heterogeneous and very dynamic, which makes the overlay network construction problem even harder. In this work we address the Membership Overlay Problem (MOP) [8], a special case of the general overlay network construction problem. In this problem, we are interested in constructing an overlay network which is unstructured, that is, used to define the membership of a dynamic set of peers. Unstructured overlay networks have many important applications such as information dissemination and data aggregation (datamining) [3, 7]. In this case, each node sends gossip messages periodically to its neighbors. It is important that load is distributed in a fair manner so that the throughput of the network is maximized without any nodes being overloaded.