Local Access to Sparse and Large Global Information in P2P Networks: a Case for Compressive Sensing

In this paper we face the following problem: how to provide each peer local access to the full information (not just a summary) that is distributed over all edges of an overlay network? How can this be done if local access is performed at a given rate? We focus on large and sparse information and we propose to exploit the compressive sensing (CS) theory to efficiently collect and pro-actively disseminate this information across a large overlay network. We devise an approach based on random walks (RW) to spread CS random combinations to participants in a random peer-to-peer (P2P) overlay network. CS allows the peer to compress the RW payload in a distributed fashion: given a constraint on the RW size, e.g., the maximum UDP packet payload size, this amounts to being able to distribute larger information and to guarantee that a large fraction of the global information is obtained by each peer. We analyze the performance of the proposed method by means of a simple (yet accurate) analytical model describing the structure of the so called CS sensing matrix in presence of peer dynamics and communication link failures. We validate our model predictions against a simulator of the system at the peer and network level on different models of random overlay networks. The model we developed can be exploited to select the parameters of the RW and the criteria to build the sensing matrix in order to achieve successful information recovery. Finally, a prototype has been developed and deployed over the PlanetLab network to prove the feasibility of the proposed approach in a realistic environment. Our analysis reveals that the method we propose is feasible, accurate and robust to peer and information dynamics. We also argue that centralized and other distributed approaches, i.e., flooding and gossiping, are unfit in the context we consider.