Survivability in Time-varying Networks

Time-varying graphs are a useful model for networks with dynamic connectivity such as vehicular networks, yet, despite their great modeling power, many important features of time-varying graphs are still poorly understood. In this paper, we study the survivability properties of time-varying networks against unpredictable interruptions. We first show that the traditional definition of survivability is not effective in time-varying networks, and propose a new survivability framework. To evaluate the survivability of time-varying networks under the new framework, we propose two metrics that are analogous to MaxFlow and MinCut in static networks. We show that some fundamental survivability-related results such as Menger's Theorem only conditionally hold in time-varying networks. Then we analyze the complexity of computing the proposed metrics and develop several approximation algorithms. Finally, we conduct trace-driven simulations to demonstrate the application of our survivability framework to the robust design of a real-world bus communication network

Hierarchical Composition of Memristive Networks for Real-Time Computing

Advances in materials science have led to physical instantiations of self-assembled networks of memristive devices and demonstrations of their computational capability through reservoir computing. Reservoir computing is an approach that takes advantage of collective system dynamics for real-time computing. A dynamical system, called a reservoir, is excited with a time-varying signal and observations of its states are used to reconstruct a desired output signal. However, such a monolithic assembly limits the computational power due to signal interdependency and the resulting correlated readouts. Here, we introduce an approach that hierarchically composes a set of interconnected memristive networks into a larger reservoir. We use signal amplification and restoration to reduce reservoir state correlation, which improves the feature extraction from the input signals. Using the same number of output signals, such a hierarchical composition of heterogeneous small networks outperforms monolithic memristive networks by at least 20% on waveform generation tasks. On the NARMA-10 task, we reduce the error by up to a factor of 2 compared to homogeneous reservoirs with sigmoidal neurons, whereas single memristive networks are unable to produce the correct result. Hierarchical composition is key for solving more complex tasks with such novel nano-scale hardware

Random graph models for dynamic networks

We propose generalizations of a number of standard network models, including the classic random graph, the configuration model, and the stochastic block model, to the case of time-varying networks. We assume that the presence and absence of edges are governed by continuous-time Markov processes with rate parameters that can depend on properties of the nodes. In addition to computing equilibrium properties of these models, we demonstrate their use in data analysis and statistical inference, giving efficient algorithms for fitting them to observed network data. This allows us, for instance, to estimate the time constants of network evolution or infer community structure from temporal network data using cues embedded both in the probabilities over time that node pairs are connected by edges and in the characteristic dynamics of edge appearance and disappearance. We illustrate our methods with a selection of applications, both to computer-generated test networks and real-world examples.Comment: 15 pages, four figure

A Distributed Tracking Algorithm for Reconstruction of Graph Signals

The rapid development of signal processing on graphs provides a new perspective for processing large-scale data associated with irregular domains. In many practical applications, it is necessary to handle massive data sets through complex networks, in which most nodes have limited computing power. Designing efficient distributed algorithms is critical for this task. This paper focuses on the distributed reconstruction of a time-varying bandlimited graph signal based on observations sampled at a subset of selected nodes. A distributed least square reconstruction (DLSR) algorithm is proposed to recover the unknown signal iteratively, by allowing neighboring nodes to communicate with one another and make fast updates. DLSR uses a decay scheme to annihilate the out-of-band energy occurring in the reconstruction process, which is inevitably caused by the transmission delay in distributed systems. Proof of convergence and error bounds for DLSR are provided in this paper, suggesting that the algorithm is able to track time-varying graph signals and perfectly reconstruct time-invariant signals. The DLSR algorithm is numerically experimented with synthetic data and real-world sensor network data, which verifies its ability in tracking slowly time-varying graph signals.Comment: 30 pages, 9 figures, 2 tables, journal pape

Scheduling with Rate Adaptation under Incomplete Knowledge of Channel/Estimator Statistics

In time-varying wireless networks, the states of the communication channels are subject to random variations, and hence need to be estimated for efficient rate adaptation and scheduling. The estimation mechanism possesses inaccuracies that need to be tackled in a probabilistic framework. In this work, we study scheduling with rate adaptation in single-hop queueing networks under two levels of channel uncertainty: when the channel estimates are inaccurate but complete knowledge of the channel/estimator joint statistics is available at the scheduler; and when the knowledge of the joint statistics is incomplete. In the former case, we characterize the network stability region and show that a maximum-weight type scheduling policy is throughput-optimal. In the latter case, we propose a joint channel statistics learning - scheduling policy. With an associated trade-off in average packet delay and convergence time, the proposed policy has a stability region arbitrarily close to the stability region of the network under full knowledge of channel/estimator joint statistics.Comment: 48th Allerton Conference on Communication, Control, and Computing, Monticello, IL, Sept. 201