Navigable Graphs for High-Dimensional Nearest Neighbor Search: Constructions and Limits

There has been significant recent interest in graph-based nearest neighbor search methods, many of which are centered on the construction of navigable graphs over high-dimensional point sets. A graph is navigable if we can successfully move from any starting node to any target node using a greedy routing strategy where we always move to the neighbor that is closest to the destination according to a given distance function. The complete graph is navigable for any point set, but the important question for applications is if sparser graphs can be constructed. While this question is fairly well understood in low-dimensions, we establish some of the first upper and lower bounds for high-dimensional point sets. First, we give a simple and efficient way to construct a navigable graph with average degree $O(\sqrt{n \log n })$ for any set of $n$ points, in any dimension, for any distance function. We compliment this result with a nearly matching lower bound: even under the Euclidean metric in $O(\log n)$ dimensions, a random point set has no navigable graph with average degree $O(n^{\alpha})$ for any $\alpha < 1/2$. Our lower bound relies on sharp anti-concentration bounds for binomial random variables, which we use to show that the near-neighborhoods of a set of random points do not overlap significantly, forcing any navigable graph to have many edges.

Realtime Mobile Bandwidth and Handoff Predictions in 4G/5G Networks

Mobile apps are increasingly relying on high-throughput and low-latency content delivery, while the available bandwidth on wireless access links is inherently time-varying. The handoffs between base stations and access modes due to user mobility present additional challenges to deliver a high level of user Quality-of-Experience (QoE). The ability to predict the available bandwidth and the upcoming handoffs will give applications valuable leeway to make proactive adjustments to avoid significant QoE degradation. In this paper, we explore the possibility and accuracy of realtime mobile bandwidth and handoff predictions in 4G/LTE and 5G networks. Towards this goal, we collect long consecutive traces with rich bandwidth, channel, and context information from public transportation systems. We develop Recurrent Neural Network models to mine the temporal patterns of bandwidth evolution in fixed-route mobility scenarios. Our models consistently outperform the conventional univariate and multivariate bandwidth prediction models. For 4G \& 5G co-existing networks, we propose a new problem of handoff prediction between 4G and 5G, which is important for low-latency applications like self-driving strategy in realistic 5G scenarios. We develop classification and regression based prediction models, which achieve more than 80\% accuracy in predicting 4G and 5G handoffs in a recent 5G dataset.