Towards Scalable Network Delay Minimization

Reduction of end-to-end network delays is an optimization task with applications in multiple domains. Low delays enable improved information flow in social networks, quick spread of ideas in collaboration networks, low travel times for vehicles on road networks and increased rate of packets in the case of communication networks. Delay reduction can be achieved by both improving the propagation capabilities of individual nodes and adding additional edges in the network. One of the main challenges in such design problems is that the effects of local changes are not independent, and as a consequence, there is a combinatorial search-space of possible improvements. Thus, minimizing the cumulative propagation delay requires novel scalable and data-driven approaches. In this paper, we consider the problem of network delay minimization via node upgrades. Although the problem is NP-hard, we show that probabilistic approximation for a restricted version can be obtained. We design scalable and high-quality techniques for the general setting based on sampling and targeted to different models of delay distribution. Our methods scale almost linearly with the graph size and consistently outperform competitors in quality

A Scalable Asynchronous Distributed Algorithm for Topic Modeling

Learning meaningful topic models with massive document collections which contain millions of documents and billions of tokens is challenging because of two reasons: First, one needs to deal with a large number of topics (typically in the order of thousands). Second, one needs a scalable and efficient way of distributing the computation across multiple machines. In this paper we present a novel algorithm F+Nomad LDA which simultaneously tackles both these problems. In order to handle large number of topics we use an appropriately modified Fenwick tree. This data structure allows us to sample from a multinomial distribution over $T$ items in $O(\log T)$ time. Moreover, when topic counts change the data structure can be updated in $O(\log T)$ time. In order to distribute the computation across multiple processor we present a novel asynchronous framework inspired by the Nomad algorithm of \cite{YunYuHsietal13}. We show that F+Nomad LDA significantly outperform state-of-the-art on massive problems which involve millions of documents, billions of words, and thousands of topics

Scalable Approach to Uncertainty Quantification and Robust Design of Interconnected Dynamical Systems

Development of robust dynamical systems and networks such as autonomous aircraft systems capable of accomplishing complex missions faces challenges due to the dynamically evolving uncertainties coming from model uncertainties, necessity to operate in a hostile cluttered urban environment, and the distributed and dynamic nature of the communication and computation resources. Model-based robust design is difficult because of the complexity of the hybrid dynamic models including continuous vehicle dynamics, the discrete models of computations and communications, and the size of the problem. We will overview recent advances in methodology and tools to model, analyze, and design robust autonomous aerospace systems operating in uncertain environment, with stress on efficient uncertainty quantification and robust design using the case studies of the mission including model-based target tracking and search, and trajectory planning in uncertain urban environment. To show that the methodology is generally applicable to uncertain dynamical systems, we will also show examples of application of the new methods to efficient uncertainty quantification of energy usage in buildings, and stability assessment of interconnected power networks

Scalable Byzantine Reliable Broadcast

Byzantine reliable broadcast is a powerful primitive that allows a set of processes to agree on a message from a designated sender, even if some processes (including the sender) are Byzantine. Existing broadcast protocols for this setting scale poorly, as they typically build on quorum systems with strong intersection guarantees, which results in linear per-process communication and computation complexity. We generalize the Byzantine reliable broadcast abstraction to the probabilistic setting, allowing each of its properties to be violated with a fixed, arbitrarily small probability. We leverage these relaxed guarantees in a protocol where we replace quorums with stochastic samples. Compared to quorums, samples are significantly smaller in size, leading to a more scalable design. We obtain the first Byzantine reliable broadcast protocol with logarithmic per-process communication and computation complexity. We conduct a complete and thorough analysis of our protocol, deriving bounds on the probability of each of its properties being compromised. During our analysis, we introduce a novel general technique that we call adversary decorators. Adversary decorators allow us to make claims about the optimal strategy of the Byzantine adversary without imposing any additional assumptions. We also introduce Threshold Contagion, a model of message propagation through a system with Byzantine processes. To the best of our knowledge, this is the first formal analysis of a probabilistic broadcast protocol in the Byzantine fault model. We show numerically that practically negligible failure probabilities can be achieved with realistic security parameters