Proximal Byzantine Consensus

Distributed control systems require high reliability and availability guarantees despite often being deployed at the edge of network infrastructure. Edge computing resources are less secure and less reliable than centralized resources in data centers. Replication and consensus protocols improve robustness to network faults and crashed or corrupted nodes, but these volatile environments can cause non-faulty nodes to temporarily diverge, increasing the time needed for replicas to converge on a consensus value, and give Byzantine attackers too much influence over the convergence process. This paper proposes proximal Byzantine consensus, a new approximate consensus protocol where clients use statistical models of streaming computations to decide a consensus value. In addition, it provides an interval around the decision value and the probability that the true (non-faulty, noise-free) value falls within this interval. Proximal consensus (PC) tolerates unreliable network conditions, Byzantine behavior, and other sources of noise that cause honest replica states to diverge. We evaluate our approach for scalar values, and compare PC simulations against a vector consensus (VC) protocol simulation. Our simulations demonstrate that consensus values selected by PC have lower error and are more robust against Byzantine attacks. We formally characterize the security guarantees against Byzantine attacks and demonstrate attacker influence is bound with high probability. Additionally, an informal complexity analysis suggests PC scales better to higher dimensions than convex hull-based protocols such as VC

An architecture for an ATM network continuous media server exploiting temporal locality of access

With the continuing drop in the price of memory, Video-on-Demand (VoD) solutions that have so far focused on maximising the throughput of disk units with a minimal use of physical memory may now employ significant amounts of cache memory. The subject of this thesis is the study of a technique to best utilise a memory buffer within such a VoD solution. In particular, knowledge of the streams active on the server is used to allocate cache memory. Stream optimised caching exploits reuse of data among streams that are temporally close to each other within the same clip; the data fetched on behalf of the leading stream may be cached and reused by the following streams. Therefore, only the leading stream requires access to the physical disk and the potential level of service provision allowed by the server may be increased. The use of stream optimised caching may consequently be limited to environments where reuse of data is significant. As such, the technique examined within this thesis focuses on a classroom environment where user progress is generally linear and all users progress at approximately the same rate for such an environment, reuse of data is guaranteed. The analysis of stream optimised caching begins with a detailed theoretical discussion of the technique and suggests possible implementations. Later chapters describe both the design and construction of a prototype server that employs the caching technique, and experiments that use of the prototype to assess the effectiveness of the technique for the chosen environment using `emulated' users. The conclusions of these experiments indicate that stream optimised caching may be applicable to larger scale VoD systems than small scale teaching environments. Future development of stream optimised caching is considered

Algorithms for Tolerated Tverberg Partitions

Abstract. Let P be a d-dimensional n-point set. A partition T of P is called a Tverberg partition if the convex hulls of all sets in T intersect in at least one point. We say T is t-tolerated if it remains a Tverberg partition after deleting any t points from P. Soberón and Strausz proved that there is always a t-tolerated Tverberg partition with ⌈n/(d + 1)(t + 1)⌉ sets. However, so far no nontrivial algorithms for computing or approximating such partitions have been presented. For d ≤ 2, we show that the Soberón-Strausz bound can be improved, and we show how the corresponding partitions can be found in polynomial time. For d ≥ 3, we give the rst polynomial-time approximation algorithm by presenting a reduction to the (untolerated) Tverberg problem. Finally, we show that it is coNP-complete to determine whether a given Tverberg partition is t-tolerated.