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.
The simultaneous send receive model @cite_3 supposes that during each round every user may receive one message and send one message. Unlike the telephone model, it is not required that a user can send a message only to the same user from which it receives a message. The optimal number of rounds turns out to be @math and we will return to this result in Section .
@cite_3
2138489200
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. We study the communication complexity of rumor spreading in the random phone-call model. Suppose nplayers communicate in parallel rounds, where in each round every player calls a randomly selected communication partner. A player u is allowed to exchange messages during a round only with the player that u called, and with all the players that @math received calls from, in that round. In every round, a (possibly empty) set of rumors to be distributed among all players is generated, and each of the rumors is initially placed in a subset of the players. Karp et. al Karp2000 showed that no rumor-spreading algorithm that spreads a rumor to all players with constant probability can be both time-optimal, taking O(lg n) rounds, and message-optimal, using O(n) messages per rumor. For address-oblivious algorithms, in particular, they showed that Ω(n lg lg n) messages per rumor are required, and they described an algorithm that matches this bound and takes O(lg n) rounds. We investigate the number of communication bits required for rumor spreading. On the lower-bound side, we establish that any address-oblivious algorithm taking O(lg n) rounds requires Ω(n (b+ lg lg n)) communication bits to distribute a rumor of size b bits. On the upper-bound side, we propose an address-oblivious algorithm that takes O(lg n) rounds and uses O(n(b+ lg lg n lg b)) bits. These results show that, unlike the case for the message complexity, optimality in terms of both the running time and the bit communication complexity is attainable, except for very small rumor sizes b In a secure message transmission (SMT) scenario, a sender wants to send a message in a private and reliable way to a receiver. Sender and receiver are connected by n wires, t of which can be controlled by an adaptive adversary with unlimited computational resources. In Eurocrypt 2008, Garay and Ostrovsky considered an SMT scenario where sender and receiver have access to a public discussion channel and showed that secure and reliable communication is possible when n ≥ t + 1. In this paper, we will show that a secure protocol requires at least three rounds of communication and two rounds invocation of the public channel and hence give a complete answer to the open question raised by Garay and Ostrovsky. We also describe a round optimal protocol that has constant transmission rate over the public channel. In the problem of secure message transmission in the public discussion model (SMT-PD), a sender wants to send a message MS ∈ 0,1 l to a receiver privately and reliably. Sender and receiver are connected by n channels, also known as simple wires, up to of which may be maliciously controlled by a computationally unbounded adversary, as well as one public channel, which is reliable but not private. The SMT-PD abstraction has been shown instrumental in achieving secure multiparty computation on sparse networks, where a subset of the nodes are able to realize a broadcast functionality, which plays the role of the public channel. In this paper, we present the first SMT-PD protocol with sublinear (i.e., logarithmic in l, the message length) communication on the public channel. In addition, the protocol incurs a simple-wire communication complexity of O(ln n-t), which, as we also show, is optimal. By contrast, the best known bounds in both public and simple channels were linear. Furthermore, our protocol has an optimal round complexity of (3, 2), meaning three rounds, two of which must invoke the public channel. Finally, we ask the question whether some of the lower bounds on resource use for a single execution of SMT-PD can be beaten on average through amortization. In other words, if sender and receiver must send several messages back and forth (where later messages depend on earlier ones), can they do better than the naive solution of repeating an SMT-PD protocol each time? We show that amortization can indeed drastically reduce the use of the public channel; it is possible to limit the total number of uses of the public channel to two, no matter how many messages are ultimately sent between two nodes. (Since two uses of the public channel are required to send any reliable communication whatsoever, this is the best possible.).