Andrew Twigg

Using trust for secure collaboration in uncertain environments

The SECURE project investigates the design of security mechanisms for pervasive computing based on trust. It addresses how entities in unfamiliar pervasive computing environments can overcome initial suspicion to provide secure collaboration.

Epidemic live streaming: optimal performance trade-offs

Several peer-to-peer systems for live streaming have been recently deployed (e.g. CoolStreaming, PPLive, SopCast). These all rely on distributed, epidemic-style dissemination mechanisms. Despite their popularity, the fundamental performance trade-offs of such mechanisms are still poorly understood. In this paper we propose several results that contribute to the understanding of such trade-offs. Specifically, we prove that the so-called random peer, latest useful chunk mechanism can achieve dissemination at an optimal rate and within an optimal delay, up to an additive constant term. This qualitative result suggests that epidemic live streaming algorithms can achieve near-unbeatable rates and delays. Using mean-field approximations, we also derive recursive formulas for the diffusion function of two schemes referred to as latest blind chunk, random peer and latest blind chunk, random useful peer. Finally, we provide simulation results that validate the above theoretical results and allow us to compare the performance of various practically interesting diffusion schemes terms of delay, rate, and control overhead. In particular, we identify several peer/chunk selection algorithms that achieve near-optimal performance trade-offs. Moreover, we show that the control overhead needed to implement these algorithms may be reduced by restricting the neighborhood of each peer without substantial performance degradation.

Randomized Decentralized Broadcasting Algorithms

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 lambda + epsiv is feasible for epsiv > 0, a simple local-control algorithm is stable under demand lambda, 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.

Compact forbidden-set routing

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(k2 log2 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(k2 log2 n) tables.

Attack-resistance of computational trust models

The World Wide Web encourages widely-distributed, open, decentralized systems that span multiple administrative domains. Recent research has turned to trust management according to M. Blaze et al. (1996) as a framework for decentralizing security decisions in such systems. However, while traditional security measures such as cryptography and encryption are well-understood (theoretically and empirically), the same cannot be said for computational trust models. This paper describes the attack-resistance of several well-referenced trust models, in a move toward a possible framework and terminology for such analyses. We present a number of open questions, and consider possible future directions in the area.

Peer-to-Peer Technologies

Publisher Summary This chapter discusses the working of scalable, self-organizing distributed systems that are often referred to as peer-to-peer (P2P) systems. P2P systems push the limits of scalability and robustness, but tend to focus on more homogeneous resources and slower network connections than do contemporary Grids. P2P systems are a potential source of resources for Grid applications; a peer-to-peer research can be a source of scalable and robust algorithms that can be applied to Grid services. P2P systems are Internet applications that harness the resources of a large number of autonomous participants. P2P and Grid computing are both concerned with enabling resource sharing within distributed communities. However, different base assumptions have led to distinct requirements and technical directions. P2P systems have focused on resource sharing in environments characterized by potentially millions of users, most with homogenous desktop systems and low bandwidth, intermittent connections to the Internet. P2P computing has had a dramatic effect on mainstream computing, even blurring the distinctions among computer science, engineering, and politics. An unfortunate side effect is that due consideration often has not been given to the classic research in distributed systems.

Connectivity check in 3-connected planar graphs with obstacles

Abstract We define a vertex labelling for every planar 3-connected graph with n vertices from which one can answer connectivity queries. A connectivity query asks whether there exists in the given graph a path linking u and v that avoids a set F of edges and a set X of vertices. The vertices u,v and those of X are given by their labels. The edges of F are given by the labels of their ends. Each label has a size of O ( log ( n ) ) bits. Our construction makes an essential use of straight-line embeddings on n × n grids of simple loop-free planar graphs. Such embeddings can be constructed in linear time by Schnyders algorithm [W. Schnyder. Embedding Planar Graphs in the Grid. SODA, First ACM-SIAM Symposium on Discrete Algorithms, San Francisco, pages 138–148, 1990] (see also [H. de Fraysseix, J. Pach, and R. Pollack. Small Sets Supporting Fary Embeddings of Planar Graphs. In Twentieth Annual ACM Symposium on Theory of Computing, pages 426–433. ACM, 1988; H. de Fraysseix, J. Pach, and R. Pollack. How to Draw a Planar Graph on a Grid. Combinatorica, 10:41–51, 1990]).

Locality-preserving allocations problems and coloured bin packing

We study the following problem, introduced by Chung et al. in 2006. We are given, online or offline, a set of coloured items of different sizes, and wish to pack them into bins of equal size so that we use few bins in total (at most α times optimal), and that the items of each colour span few bins (at most β times optimal). We call such allocations ( α , β ) -approximate. As usual in bin packing problems, we allow additive constants and consider ( α , β ) as the asymptotic performance ratios. We prove that for e 0 , if we desire small α, no scheme can beat ( 1 + e , ? ( 1 / e ) ) -approximate allocations and similarly as we desire small β, no scheme can beat ( 1.69103 , 1 + e ) -approximate allocations. We give offline schemes that come very close to achieving these lower bounds. For the online case, we prove that no scheme can even achieve ( O ( 1 ) , O ( 1 ) ) -approximate allocations. However, a small restriction on item sizes permits a simple online scheme that computes ( 2 + e , 1.7 ) -approximate allocations.