text: Peer-to-peer (P2P) overlay networks such as BitTorrent and Avalanche are increasingly used for disseminating potentially large files from a server to many end users via the Internet. The key idea is to divide the file into many equally-sized parts and then let users download each part (or, for network coding based systems such as Avalanche, linear combinations of the parts) either from the server or from another user who has already downloaded it. However, their performance evaluation has typically been limited to comparing one system relative to another and typically been realized by means of simulation and measurements. In contrast, we provide an analytic performance analysis that is based on a new uplink-sharing version of the well-known broadcasting problem. Assuming equal upload capacities, we show that the minimal time to disseminate the file is the same as for the simultaneous send receive version of the broadcasting problem. For general upload capacities, we provide a mixed integer linear program (MILP) solution and a complementary fluid limit solution. We thus provide a lower bound which can be used as a performance benchmark for any P2P file dissemination system. We also investigate the performance of a decentralized strategy, providing evidence that the performance of necessarily decentralized P2P file dissemination systems should be close to this bound and therefore that it is useful in practice.
  @cite_4: We consider the problem of broadcasting multiple messages from one processor to many processors in telephone-like communication systems. In such systems, processors communicate in rounds, where in every round, each processor can communicate with exactly one other processor by exchanging messages with it. Finding an optimal solution for this problem was open for over a decade. In this paper, we present an optimal algorithm for this problem when the number of processors is even. For an odd number of processors, we provide an algorithm which is within an additive term of 3 of the optimum. A by-product of our solution is an optimal algorithm for the problem of broadcasting multiple messages for any number of processors in the simultaneous send receive model. In this latter model, in every round, each processor can send a message to one processor and receive a message from another processor.
summary: In @cite_4 , the authors considered the bidirectional telephone model in which nodes can both send one message and receive one message simultaneously, but they must be matched pairwise. That is, in each given round, a node can only receive a message from the same node to which it sends a message. They provide an optimal algorithm for odd @math , which takes @math rounds. For even @math their algorithm is optimal up to an additive term of @math , taking @math rounds.