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Given its status as a classic problem and its importance to both theoreticians and practitioners, edit distance provides an excellent lens through which to understand how the theoretical analysis of algorithms impacts practical implementations. From an applied perspective, the goals of theoretical analysis are to predict the empirical performance of an algorithm and to serve as a yardstick to design novel algorithms that perform well in practice. In this paper, we systematically survey the types of theoretical analysis techniques that have been applied to edit distance and evaluate the extent to which each one has achieved these two goals. These techniques include traditional worst-case analysis, worst-case analysis parametrized by edit distance or entropy or compressibility, average-case analysis, semi-random models, and advice-based models. We find that the track record is mixed. On one hand, two algorithms widely used in practice have been born out of theoretical analysis and their empirical performance is captured well by theoretical predictions. On the other hand, all the algorithms developed using theoretical analysis as a yardstick since then have not had any practical relevance. We conclude by discussing the remaining open problems and how they can be tackled.

Minimum cut/maximum flow (min-cut/max-flow) algorithms solve a variety of problems in computer vision and thus significant effort has been put into developing fast min-cut/max-flow algorithms. As a result, it is difficult to choose an ideal algorithm for a given problem. Furthermore, parallel algorithms have not been thoroughly compared. In this paper, we evaluate the state-of-the-art serial and parallel min-cut/max-flow algorithms on the largest set of computer vision problems yet. We focus on generic algorithms, i.e., for unstructured graphs, but also compare with the specialized GridCut implementation. When applicable, GridCut performs best. Otherwise, the two pseudoflow algorithms, Hochbaum pseudoflow and excesses incremental breadth first search, achieves the overall best performance. The most memory efficient implementation tested is the Boykov-Kolmogorov algorithm. Amongst generic parallel algorithms, we find the bottom-up merging approach by Liu and Sun to be best, but no method is dominant. Of the generic parallel methods, only the parallel preflow push-relabel algorithm is able to efficiently scale with many processors across problem sizes, and no generic parallel method consistently outperforms serial algorithms. Finally, we provide and evaluate strategies for algorithm selection to obtain good expected performance. We make our dataset and implementations publicly available for further research.

The majority of internet traffic is video content. This drives the demand for video compression in order to deliver high quality video at low target bitrates. This paper investigates the impact of adjusting the rate distortion equation on compression performance. An constant of proportionality, k, is used to modify the Lagrange multiplier used in H.265 (HEVC). Direct optimisation methods are deployed to maximise BD-Rate improvement for a particular clip. This leads to up to 21% BD-Rate improvement for an individual clip. Furthermore we use a more realistic corpus of material provided by YouTube. The results show that direct optimisation using BD-rate as the objective function can lead to further gains in bitrate savings that are not available with previous approaches.

Given a set $P$ of $n$ points in the plane, the $k$-center problem is to find $k$ congruent disks of minimum possible radius such that their union covers all the points in $P$. The $2$-center problem is a special case of the $k$-center problem that has been extensively studied in the recent past \cite{CAHN,HT,SH}. In this paper, we consider a generalized version of the $2$-center problem called \textit{proximity connected} $2$-center (PCTC) problem. In this problem, we are also given a parameter $\delta\geq 0$ and we have the additional constraint that the distance between the centers of the disks should be at most $\delta$. Note that when $\delta=0$, the PCTC problem is reduced to the $1$-center(minimum enclosing disk) problem and when $\delta$ tends to infinity, it is reduced to the $2$-center problem. The PCTC problem first appeared in the context of wireless networks in 1992 \cite{ACN0}, but obtaining a nontrivial deterministic algorithm for the problem remained open. In this paper, we resolve this open problem by providing a deterministic $O(n^2\log n)$ time algorithm for the problem.

Most deep learning models for computational imaging regress a single reconstructed image. In practice, however, ill-posedness, nonlinearity, model mismatch, and noise often conspire to make such point estimates misleading or insufficient. The Bayesian approach models images and (noisy) measurements as jointly distributed random vectors and aims to approximate the posterior distribution of unknowns. Recent variational inference methods based on conditional normalizing flows are a promising alternative to traditional MCMC methods, but they come with drawbacks: excessive memory and compute demands for moderate to high resolution images and underwhelming performance on hard nonlinear problems. In this work, we propose C-Trumpets -- conditional injective flows specifically designed for imaging problems, which greatly diminish these challenges. Injectivity reduces memory footprint and training time while low-dimensional latent space together with architectural innovations like fixed-volume-change layers and skip-connection revnet layers, C-Trumpets outperform regular conditional flow models on a variety of imaging and image restoration tasks, including limited-view CT and nonlinear inverse scattering, with a lower compute and memory budget. C-Trumpets enable fast approximation of point estimates like MMSE or MAP as well as physically-meaningful uncertainty quantification.

Hybrid precoding is a cost-efficient technique for millimeter wave (mmWave) massive multiple-input multiple-output (MIMO) communications. This paper proposes a deep learning approach by using a distributed neural network for hybrid analog-and-digital precoding design with limited feedback. The proposed distributed neural precoding network, called DNet, is committed to achieving two objectives. First, the DNet realizes channel state information (CSI) compression with a distributed architecture of neural networks, which enables practical deployment on multiple users. Specifically, this neural network is composed of multiple independent sub-networks with the same structure and parameters, which reduces both the number of training parameters and network complexity. Secondly, DNet learns the calculation of hybrid precoding from reconstructed CSI from limited feedback. Different from existing black-box neural network design, the DNet is specifically designed according to the data form of the matrix calculation of hybrid precoding. Simulation results show that the proposed DNet significantly improves the performance up to nearly 50% compared to traditional limited feedback precoding methods under the tests with various CSI compression ratios.

In this work, we focus on the high-dimensional trace regression model with a low-rank coefficient matrix. We establish a nearly optimal in-sample prediction risk bound for the rank-constrained least-squares estimator under no assumptions on the design matrix. Lying at the heart of the proof is a covering number bound for the family of projection operators corresponding to the subspaces spanned by the design. By leveraging this complexity result, we perform a power analysis for a permutation test on the existence of a low-rank signal under the high-dimensional trace regression model. We show that the permutation test based on the rank-constrained least-squares estimator achieves non-trivial power with no assumptions on the minimum (restricted) eigenvalue of the covariance matrix of the design. Finally, we use alternating minimization to approximately solve the rank-constrained least-squares problem to evaluate its empirical in-sample prediction risk and power of the resulting permutation test in our numerical study.

Federated learning (FL) has been recognized as a viable distributed learning paradigm which trains a machine learning model collaboratively with massive mobile devices in the wireless edge while protecting user privacy. Although various communication schemes have been proposed to expedite the FL process, most of them have assumed ideal wireless channels which provide reliable and lossless communication links between the server and mobile clients. Unfortunately, in practical systems with limited radio resources such as constraint on the training latency and constraints on the transmission power and bandwidth, transmission of a large number of model parameters inevitably suffers from quantization errors (QE) and transmission outage (TO). In this paper, we consider such non-ideal wireless channels, and carry out the first analysis showing that the FL convergence can be severely jeopardized by TO and QE, but intriguingly can be alleviated if the clients have uniform outage probabilities. These insightful results motivate us to propose a robust FL scheme, named FedTOE, which performs joint allocation of wireless resources and quantization bits across the clients to minimize the QE while making the clients have the same TO probability. Extensive experimental results are presented to show the superior performance of FedTOE for deep learning-based classification tasks with transmission latency constraints.

In large scale dynamic wireless networks, the amount of overhead caused by channel estimation (CE) is becoming one of the main performance bottlenecks. This is due to the large number users whose channels should be estimated, the user mobility, and the rapid channel change caused by the usage of the high-frequency spectrum (e.g. millimeter wave). In this work, we propose a new hybrid channel estimation/prediction (CEP) scheme to reduce overhead in time-division duplex (TDD) wireless cell-free massive multiple-input-multiple-output (mMIMO) systems. The scheme proposes sending a pilot signal from each user only once in a given number (window) of coherence intervals (CIs). Then minimum mean-square error (MMSE) estimation is used to estimate the channel of this CI, while a deep neural network (DNN) is used to predict the channels of the remaining CIs in the window. The DNN exploits the temporal correlation between the consecutive CIs and the received pilot signals to improve the channel prediction accuracy. By doing so, CE overhead is reduced by at least 50 percent at the expense of negligible CE error for practical user mobility settings. Consequently, the proposed CEP scheme improves the spectral efficiency compared to the conventional MMSE CE approach, especially when the number of users is large, which is demonstrated numerically.

Vector Perturbation Precoding (VPP) can speed up downlink data transmissions in Large and Massive Multi-User MIMO systems but is known to be NP-hard. While there are several algorithms in the literature for VPP under total power constraint, they are not applicable for VPP under per-antenna power constraint. This paper proposes a novel, parallel tree search algorithm for VPP under per-antenna power constraint, called \emph{\textbf{TreeStep}}, to find good quality solutions to the VPP problem with practical computational complexity. We show that our method can provide huge performance gain over simple linear precoding like Regularised Zero Forcing. We evaluate TreeStep for several large MIMO~($16\times16$ and $24\times24$) and massive MIMO~($16\times32$ and $24\times 48$) and demonstrate that TreeStep outperforms the popular polynomial-time VPP algorithm, the Fixed Complexity Sphere Encoder, by achieving the extremely low BER of $10^{-6}$ at a much lower SNR.