We consider the problem of broadcasting a live stream of data in an unstructured network. The broadcasting problem has been studied extensively for edge-capacitated networks. We give the first proof that whenever demand λ + ε is feasible for ε > 0, a simple local-control algorithm is stable under demand λ, and as a corollary a famous theorem of Edmonds. We then study the node-capacitated case and show a similar optimality result for the complete graph. We study through simulation the delay that users must wait in order to playback a video stream with a small number of skipped packets, and discuss the suitability of our algorithms for live video streaming. I. INTRODUCTIONWe consider the problem of broadcasting a live stream of data, such as a movie, to all nodes in an unstructured network. When edges have capacities, this problem has been well-studied since the 1970s -Edmonds, Lovasz and Gabow and others have given centralized schemes based on packing spanning trees [1]- [5].The broadcast problem is at the core of every content distribution system; in particular, current live streaming distribution systems such as CoolStreaming [6], PPLive [7], SplitStream [8]. These systems either construct the overlay topology in such a way to easy packet scheduling, and in doing so reduce the network efficiency by not optimally using all the available resources, or use heuristic algorithms for packet distribution with unknown performance properties.We present a completely distributed and suprisingly simple algorithm for broadcasting in arbitrary networks, which does not require coding yet provably achieves the optimal broadcast rate. This is the first known result of this kind. Our analysis is based on fluid models and Lyapunov functions applied to a novel powerset representation of the network. As a corollary we retrieve a famous theorem of Edmonds [1].In the second part of the paper, we introduce a new model for broadcasting a live stream of data in a peer-to-peer network based on the node-capacitated broadcast problem -each node has a specified upload capacity (we assume that download capacity is infinite), modeling the user's connection to the network, and the user must choose how this capacity is allocated among peers. This introduces an allocation problem in addition to the problem of scheduling packet transmissions. We present a completely distributed algorithm for the nodecapacitated broadcast problem, and show that it achieves the optimal rate in certain classes of network.

PERVASIVE computing 53Trust is situation-specific; trust in one environment doesn't directly transfer to another environment. So a notion of context is necessary.Authorized licensed use limited to: TRINITY COLLEGE DUBLIN. Downloaded on January 21, 2009 at 05:54 from IEEE Xplore. Restrictions apply.them in a particular way-for example, to update old address book entries with accurate information. However, the principal could deviate from this expected behavior, and the combined likelihood and severity of this is the risk of granting them a privilege. Risk analysisIn SECURE, the risks of a trust-mediated action are decomposed by possible outcomes. Each outcome's risk depends on the other principal's trustworthiness (the likelihood) and the outcome's intrinsic cost. For example, an address update might itself be out-of-date or maliciously misleading. These two outcomes' costs would reflect the user's wasted time, and the likelihoods would depend on trust in the other party.An outcome's costs could span a range of values. For example, a user might have received a correct phone book entry. This third outcome's cost could show a net benefit to the user, as the user might successfully use it later. However, if the number became out-ofdate by the time it was used, that would be a net loss. To reflect this uncertainty, you might represent the distribution of costs as a cost-PDF (probability density function). Figure 1 illustrates a user contemplating a parameterized interaction with principal p. For each possible outcome, the user has a parameterized cost-PDF (a family of cost-PDFs) that represents the range of possible costs and benefits the user might incur should each outcome occur.While the risk evaluator assesses the possible cost-PDFs, the trust calculator provides information t that determines the risk's likelihood based on the principal's identity p and other parameters of the action. The risk evaluator then uses this trust information to select the appropriate cost-PDF.Finally, the request analyzer combines all the outcomes' cost-PDFs to decide if the action should be taken or to arrange further interaction. Because any uncertainty is preserved right up to the decision point, this allows more complex decision making than simple thresholding, allowing responses such as "not sure" if there isn't enough information.In our continuing example, if Liz's PDA received a phone number from Vinny's PDA, she might not think it was maliciously misleading based on her trust in Vinny's honesty. She might think it could be out-of-date, however, if Vinny had given her stale information before, attributing a higher risk to this outcome. Finally, she'd consider the potential benefit of having a correct number, again moderated by Vinny's trustworthiness. Liz's PDA would do all these calculations on her behalf using its model of her trust beliefs, as Figure 2 illustrates. If the benefits outweighed the other outcomes' costs, the PDA would then accept the information.On the other hand, if John-a colleague from a competing research gr...

We study labelling schemes for X-constrained path problems. Given a graph (V, E) and X ⊆ V , a path is X-constrained if all intermediate vertices avoid X. We study the problem of assigning labels J(x) to vertices so that given {J(x) : x ∈ X} for any X ⊆ V , we can route on the shortest X-constrained path between x, y ∈ X. This problem is motivated by Internet routing, where the presence of routing policies means that shortest-path routing is not appropriate. For graphs of tree width k, we give a routing scheme using routing tables of size O(k 2 log 2 n). We introduce m-clique width, generalizing clique width, to show that graphs of m-clique width k also have a routing scheme using size O(k 2 log 2 n) tables.

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