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.
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.
@cite_4
2054243578
We consider the problem of topology recognition in wireless (radio) networks modeled as undirected graphs. Topology recognition is a fundamental task in which every node of the network has to output a map of the underlying graph i.e., an isomorphic copy of it, and situate itself in this map. In wireless networks, nodes communicate in synchronous rounds. In each round a node can either transmit a message to all its neighbors, or stay silent and listen. At the receiving end, a node @math hears a message from a neighbor @math in a given round, if @math listens in this round, and if @math is its only neighbor that transmits in this round. Nodes have labels which are (not necessarily different) binary strings. The length of a labeling scheme is the largest length of a label. We concentrate on wireless networks modeled by trees, and we investigate two problems. What is the shortest labeling scheme that permits topology recognition in all wireless tree networks of diameter @math and maximum degree @math ? What is the fastest topology recognition algorithm working for all wireless tree networks of diameter @math and maximum degree @math , using such a short labeling scheme? We are interested in deterministic topology recognition algorithms. For the first problem, we show that the minimum length of a labeling scheme allowing topology recognition in all trees of maximum degree @math is @math . For such short schemes, used by an algorithm working for the class of trees of diameter @math and maximum degree @math , we show almost matching bounds on the time of topology recognition: an upper bound @math , and a lower bound @math , for any constant @math .