In this paper, we present new randomized algorithms that improve the complexity of the classic (∆+1)-coloring problem, and its generalization (∆+1)-list-coloring, in three well-studied models of distributed, parallel, and centralized computation:Congested Clique: We present an O(1)-round randomized algorithm for (∆ + 1)-list coloring in the congested clique model of distributed computing. This settles the asymptotic complexity of this problem. It moreover improves upon the O(log * ∆)-round randomized algorithms of Parter and Su [DISC'18] and O((log log ∆) · log * ∆)-round randomized algorithm of Parter [ICALP'18]. Massively Parallel Computation: We present a (∆ + 1)-list coloring algorithm with round complexity O( √ log log n) in the Massively Parallel Computation (MPC) model with strongly sublinear memory per machine. This algorithm uses a memory of O(n α ) per machine, for any desirable constant α > 0, and a total memory of O(m), where m is the size of the graph. Notably, this is the first coloring algorithm with sublogarithmic round complexity, in the sublinear memory regime of MPC. For the quasilinear memory regime of MPC, an O(1)-round algorithm was given very recently by Assadi et al. [SODA'19]. Centralized Local Computation: We show that (∆ + 1)-list coloring can be solved with ∆ O(1) ·O(log n) query complexity, in the centralized local computation model. The previous state-of-the-art for (∆ + 1)-list coloring in the centralized local computation model are based on simulation of known LOCAL algorithms. The deterministic O( √ ∆poly log ∆ + log * n)-round LOCAL algorithm of Fraigniaud et al. [FOCS'16] can be implemented in the centralized local computation model with query complexity ∆ O( √ ∆poly log ∆) ·O(log * n); the randomized O(log * ∆) + 2 O( √ log log n) -round LOCAL algorithm of Chang et al. [STOC'18] can be implemented in the centralized local computation model with query complexity ∆ O(log * ∆) · O(log n). a significantly more relaxed problem in comparison to ∆ + 1 coloring. For instance, we have long known a very simple O(∆)-coloring algorithm in LOCAL-model algorithm with round complexity 2 O( √ log log n) [BEPS16], but only recently such a round complexity was achieved for ∆ + 1 coloring [CLP18, HSS18]. Our focus is on the much more stringent ∆ + 1 coloring problem. For this problem, the LOCAL model algorithms of [CLP18, HSS18] need messages of O(∆ 2 log n) bits, and thus do not extend to CONGEST or CONGESTED-CLIQUE. For CONGESTED-CLIQUE model, the main challenge is when ∆ > √ n, as otherwise, one can simulate the algorithm of [CLP18] by leveraging the all-toall communication in CONGESTED-CLIQUE which means each vertex in each round is capable of communicating O(n log n) bits of information. Parter [Par18] designed the first sublogarithmic-time (∆+1) coloring algorithm for CONGESTED-CLIQUE, which runs in O(log log ∆ log * ∆) rounds. The algorithm of [Par18] is able to reduce the maximum degree to O( √ n) in O(log log ∆) iterations, and each iteration invokes the algorithm of [CLP18] on instances...

Multi-material additive manufacturing of polymers has experienced a remarkable increase in interest over the last 20 years. This technology can rapidly design and directly fabricate three-dimensional (3D) parts with multiple materials without complicating manufacturing processes. This research aims to obtain a comprehensive and in-depth understanding of the current state of research and reveal challenges and opportunities for future research in the area. To achieve the goal, this study conducts a scientometric analysis and a systematic review of the global research published from 2000 to 2021 on multi-material additive manufacturing of polymers. In the scientometric analysis, a total of 2512 journal papers from the Scopus database were analyzed by evaluating the number of publications, literature coupling, keyword co-occurrence, authorship, and countries/regions activities. By doing so, the main research frame, articles, and topics of this research field were quantitatively determined. Subsequently, an in-depth systematic review is proposed to provide insight into recent advances in multi-material additive manufacturing of polymers in the aspect of technologies and applications, respectively. From the scientometric analysis, a heavy bias was found towards studying materials in this field but also a lack of focus on developing technologies. The future trend is proposed by the systematic review and is discussed in the directions of interfacial bonding strength, printing efficiency, and microscale/nanoscale multi-material 3D printing. This study contributes by providing knowledge for practitioners and researchers to understand the state of the art of multi-material additive manufacturing of polymers and expose its research needs, which can serve both academia and industry.

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The rapid geographic spread of COVID-19, to which various factors may have contributed, has caused a global health crisis. Recently, the analysis and forecast of the COVID-19 pandemic have attracted worldwide attention. In this work, a large COVID-19 dataset consisting of COVID-19 pandemic, COVID-19 testing capacity, economic level, demographic information, and geographic location data in 184 countries and 1,241 areas from Dec 18, 2019, to Sep 30, 2020, were developed from public reports released by national health authorities and bureau of statistics. We proposed a machine learning model for COVID-19 prediction based on the Broad Learning System (BLS). Here, we leveraged Random Forest to screen out the key features. Then, we combine the bagging strategy and Broad Learning System to develop a Random-forest-Bagging Broad Learning System (RF-Bagging-BLS) approach to forecast the trend of the COVID-19 pandemic. In addition, we compared the forecasting results with Linear Regression (LR) model, K-Nearest Neighbors (KNN), Decision Tree (DT), Adaptive Boosting (Ada), Random Forest (RF), Gradient Boosting Decision Tree (GBDT), Support Vector Regression (SVR), Extra Trees (ET) regressor, CatBoost (CAT), LightGBM (LGB), XGBoost (XGB), and Broad Learning System (BLS).The RF-Bagging BLS model showed better forecasting performance in terms of relative mean square error (RMSE), coefficient of determination (R 2 ), adjusted coefficient of determination (R 2 adj ), median absolute error (MAD), and mean absolute percentage error (MAPE) than other models. Hence, the proposed model demonstrates superior predictive power over other benchmark models.

At the end of 2019, a new coronavirus (COVID-19) epidemic has triggered global public health concern. Here, a model integrating the daily intercity migration network, which constructed from real-world migration records and the Susceptible–Exposed–Infected–Removed model, is utilized to predict the epidemic spreading of the COVID-19 in more than 300 cities in China. However, the model has more than 1800 unknown parameters, which is a challenging task to estimate all unknown parameters from historical data within a reasonable computation time. In this article, we proposed a pseudocoevolutionary simulated annealing (SA) algorithm for identifying these unknown parameters. The large volume of unknown parameters of this model is optimized through three procedures co-adapted SA-based optimization processes, respectively. Our results confirm that the proposed method is both efficient and robust. Then, we use the identified model to predict the trends of the epidemic spreading of the COVID-19 in these cities. We find that the number of infections in most cities in China has reached their peak from February 29, 2020, to March 15, 2020. For most cities outside Hubei province, the total number of infected individuals would be less than 100, while for most cities in Hubei province (exclude Wuhan), the total number of infected individuals would be less than 3000.