Network Utility Maximization under Maximum Delay Constraints and Throughput Requirements

We consider the problem of maximizing aggregate user utilities over a multi-hop network, subject to link capacity constraints, maximum end-to-end delay constraints, and user throughput requirements. A user's utility is a concave function of the achieved throughput or the experienced maximum delay. The problem is important for supporting real-time multimedia traffic, and is uniquely challenging due to the need of simultaneously considering maximum delay constraints and throughput requirements. We first show that it is NP-complete either (i) to construct a feasible solution strictly meeting all constraints, or (ii) to obtain an optimal solution after we relax maximum delay constraints or throughput requirements up to constant ratios. We then develop a polynomial-time approximation algorithm named PASS. The design of PASS leverages a novel understanding between non-convex maximum-delay-aware problems and their convex average-delay-aware counterparts, which can be of independent interest and suggest a new avenue for solving maximum-delay-aware network optimization problems. Under realistic conditions, PASS achieves constant or problem-dependent approximation ratios, at the cost of violating maximum delay constraints or throughput requirements by up to constant or problem-dependent ratios. PASS is practically useful since the conditions for PASS are satisfied in many popular application scenarios. We empirically evaluate PASS using extensive simulations of supporting video-conferencing traffic across Amazon EC2 datacenters. Compared to existing algorithms and a conceivable baseline, PASS obtains up to $100\%$ improvement of utilities, by meeting the throughput requirements but relaxing the maximum delay constraints that are acceptable for practical video conferencing applications

On the Min-Max-Delay Problem: NP-completeness, Algorithm, and Integrality Gap

We study a delay-sensitive information flow problem where a source streams information to a sink over a directed graph G(V,E) at a fixed rate R possibly using multiple paths to minimize the maximum end-to-end delay, denoted as the Min-Max-Delay problem. Transmission over an edge incurs a constant delay within the capacity. We prove that Min-Max-Delay is weakly NP-complete, and demonstrate that it becomes strongly NP-complete if we require integer flow solution. We propose an optimal pseudo-polynomial time algorithm for Min-Max-Delay, with time complexity O(\log (Nd_{\max}) (N^5d_{\max}^{2.5})(\log R+N^2d_{\max}\log(N^2d_{\max}))), where N = \max\{|V|,|E|\} and d_{\max} is the maximum edge delay. Besides, we show that the integrality gap, which is defined as the ratio of the maximum delay of an optimal integer flow to the maximum delay of an optimal fractional flow, could be arbitrarily large

Color Image Enhancement Based on Ant Colony Optimization Algorithm

In the collection, transmission, decoding process, the images are likely to produce noise. Noise makes the image color distorted and the articulation dropped, and also affects the image quality. Due to different causes, there are different types of noise, and the impulse noise is most common among them which exert great influence on the image quality. This paper, according to the characteristics of the color image, combines the ant colony algorithm and weighted vector median filter method to put forward an algorithm for the impulse noise removal and the color image enhancement. This method finds the optimal filter bank parameter by ant colony optimization (ACO) and processes image points polluted by the noise to achieve the purpose of image enhancement and protect the image details and edge information. Simulation experiment proves the correctness and validity of this method

Minimizing Age-of-Information with Throughput Requirements in Multi-Path Network Communication

We consider the scenario where a sender periodically sends a batch of data to a receiver over a multi-hop network, possibly using multiple paths. Our objective is to minimize peak/average Age-of-Information (AoI) subject to throughput requirements. The consideration of batch generation and multi-path communication differentiates our AoI study from existing ones. We first show that our AoI minimization problems are NP-hard, but only in the weak sense, as we develop an optimal algorithm with a pseudo-polynomial time complexity. We then prove that minimizing AoI and minimizing maximum delay are "roughly" equivalent, in the sense that any optimal solution of the latter is an approximate solution of the former with bounded optimality loss. We leverage this understanding to design a general approximation framework for our problems. It can build upon any $\alpha$-approximation algorithm of the maximum delay minimization problem, to construct an $(\alpha+c)$-approximate solution for minimizing AoI. Here $c$ is a constant depending on the throughput requirements. Simulations over various network topologies validate the effectiveness of our approach.Comment: Accepted by the ACM Twentieth International Symposium on Mobile Ad Hoc Networking and Computing (ACM MobiHoc 2019

Association Between Premorbid Body Mass Index and Amyotrophic Lateral Sclerosis: Causal Inference Through Genetic Approaches

Purpose: Inverse association between premorbid body mass index (BMI) and amyotrophic lateral sclerosis (ALS) was implied in observational studies; however, whether this association is causal remains largely unknown.Materials and Methods: We first conducted a meta-analysis to investigate whether there exits an association between premorbid BMI and ALS. We then employed a two-sample Mendelian randomization approach to evaluate the causal relationship of genetically increased BMI with the risk of ALS. The Mendelian randomization analysis was implemented using summary statistics for independent instruments obtained from large-scale genome-wide association studies of BMI (up to ~770,000 individuals) and ALS (up to ~81,000 individuals). The causal effect of BMI on ALS was estimated using inverse-variance weighted methods and was further validated through extensive complementary and sensitivity analyses.Results: The meta-analysis showed that a unit increase of premorbid BMI can result in about 3.0% (95% CI 2.1–4.5%) risk reduction of ALS. Using 1,031 instruments that were strongly related to BMI, the causal effect of per one standard deviation increase of BMI was estimated to be 1.04 (95% CI 0.97–1.11, p = 0.275) in the European population. This null association between BMI and ALS also held in the East Asian population and was robust against various modeling assumptions and outlier biases. Additionally, the Egger-regression and MR-PRESSO ruled out the possibility of horizontal pleiotropic effects of instruments.Conclusion: Our results do not support the causal role of genetically increased or decreased BMI on the risk of ALS