Complex Problems Research Articles

Exploiting travel sequences to optimise facility layouts with multiple input/output points

The facility layout problem (FLP) involves arranging departments on a shop floor to optimise specific objectives, traditionally focussing on pairwise flows between departments. However, these methods often underestimate total travel distances, especially when flows involve multiple input/output points and visits to more than two departments. To address this, connected movements – actual routes taken by transporters – must be considered. This study uses data captured from an Internet of Things (IoT) network and stored on cloud servers to analyze worker movements and accurately calculate travel distances. A mixed-integer programming model is proposed to minimise total travel distance using connected movements as input. Due to the problem's complexity, a biased random key genetic algorithm is employed to find optimal layouts. A case study at a fertiliser production company demonstrates the effectiveness of the approach, achieving a 15% reduction in travel distance compared to layouts generated by traditional methods. The IoT-enabled method also minimises productivity losses by optimising worker movements. While the study focuses on fertiliser manufacturing, the findings are applicable to other settings, such as warehousing, where complex movement sequences and multiple IO points are common in processes like picking, packing, and shipping.

A Better Wound Care Assessment on Burn Patients

Backgrounds: Burn, a damage and tissue loss caused by heat with a high morbidity and mortality, have a many variation and complex problem that require special management. After a period of shock, there were infections that threaten the burn patients. These hazards aggravate the wound to become wider, and it affects the mortality and the length of stay. That is why to reduce mortality rate and length of stay, we need a proper wound care.Methods:A retrospective descriptive studies was perform on 2b degree burn patients (20-25%) that treated with tangential excision and mebo or tangential excision and stsg. Data was taken from burns unit Cipto Mangunkusumo hospital in period of January to December 2011.Results: There were 30 patients (73.2%) that have been treat with tangential excision and mebo, and 11 patients (26.8%) that have been treat with tangential excision and stsg. The average length of stay for the tangential excision and mebo is 22.47 ? 23 days(SD 4.361), whereas patients with tangential excision and stsg is 15.82 ?16 days (SD 2.089). There were 8 patients (26.7%) with tangential excision and mebo that die, whereas patients with tangential excision and stsg were 2 patients (18.2%) that die. There were significant difference in the average length of stay (p = 0.018), but there was no difference in the proportion of patients dying status (P = 0.611).Conclusion:Wound care by tangential excision and stsg on 2b degree burn patient (20-25%), have a better outcome than patients treated by tangential excision and mebo.

Single-qubit gate teleportation provides a quantum advantage

Gate-teleportation circuits are arguably among the most basic examples of computations believed to provide a quantum computational advantage: In seminal work \cite{TerhalDiVincenzo04}, Terhal and DiVincenzo have shown that these circuits elude simulation by efficient classical algorithms under plausible complexity-theoretic assumptions. Here we consider possibilistic simulation \cite{wang2021possibilistic}, a particularly weak form of this task where the goal is to output any string appearing with non-zero probability in the output distribution of the circuit. We show that even for single-qubit Clifford-gate-teleportation circuits this simulation problem cannot be solved by constant-depth classical circuits with bounded fan-in gates. Our results are unconditional and are obtained by a reduction to the problem of computing the parity, a well-studied problem in classical circuit complexity.

Enhancing offshore parcel delivery efficiency through vessel-unmanned aerial vehicle collaborative routing

Offshore oil and gas production is vital for global energy supply, but it faces logistical challenges due to the high costs and inefficiencies of traditional supply methods. This paper introduces the vessel-unmanned aerial vehicle (UAV) routing problem with multiple visits in a single flight (VURP-M), a novel logistical model that addresses aimed at enhancing the replenishment of offshore platforms with small, essential items. The VURP-M allows the UAV to perform multiple visits during a single flight, optimising the delivery process. To tackle the VURP-M, we propose two mixed-integer second-order cone programs that capture the problem's complexities. Given its NP-hard nature, we employ an adaptive large neighbourhood search (ALNS) method, featuring a segmented initialisation process and problem-specific operators guided by a rule-based mechanism to improve solution efficiency. The ALNS formulates an initial solution by solving a travelling salesman problem to create a giant tour, which is then used to group sequential targets into multiple UAV flights. The subsequent optimal resolution of a SOCP determines the take-off and landing points for each flight. Subsequently, the ALNS refines the initial solution through destroy and repair operators, enhancing the search for superior sequences and allocation schemes. The effectiveness of our approach is demonstrated through a real-world case study and numerical experiments on random instances featuring up to 100 platforms. The results offer implications of the collaborative vessel-UAV model for the offshore logistics industry.

Challenges and Opportunities in Deep Reinforcement Learning With Graph Neural Networks: A Comprehensive Review of Algorithms and Applications.

Deep reinforcement learning (DRL) has empowered a variety of artificial intelligence fields, including pattern recognition, robotics, recommendation systems, and gaming. Similarly, graph neural networks (GNNs) have also demonstrated their superior performance in supervised learning for graph-structured data. In recent times, the fusion of GNN with DRL for graph-structured environments has attracted a lot of attention. This article provides a comprehensive review of these hybrid works. These works can be classified into two categories: 1) algorithmic contributions, where DRL and GNN complement each other with an objective of addressing each other's shortcomings and 2) application-specific contributions that leverage a combined GNN-DRL formulation to address problems specific to different applications. This fusion effectively addresses various complex problems in engineering and life sciences. Based on the review, we further analyze the applicability and benefits of fusing these two domains, especially in terms of increasing generalizability and reducing computational complexity. Finally, the key challenges in integrating DRL and GNN, and potential future research directions are highlighted, which will be of interest to the broader machine learning community.

GABoost: Graph Alignment Boosting via Local Optimum Escape

Heterogeneous graphs provide a universal data structure for representing various kinds of structured data in numerous domains. The graph alignment problem aims to find the correspondences of vertices in different graphs, playing a fundamental role in many downstream tasks of heterogeneous graph mining. In recent years, many graph alignment methods have been proposed, ranging from classical optimization methods , spectral methods , to embedding learning based-methods . Due to the problem's complexity, the result found by most existing methods is either a heuristic solution or a critical point in the solution space. In this paper, we propose GABoost, a graph alignment boosting algorithm that takes as input an initial alignment between two heterogeneous graphs and outputs a boosted alignment via an iterative local-optimum-escape process. One of the distinctive features of GABoost is that it can be sequentially composed with any graph alignment methods to improve the output of upstream methods. To examine the effectiveness of GABoost, we select 7 upstream methods of graph alignment as well as 6 real-world datasets, and quantitatively investigate the degree to which GABoost boosts these methods. The results show that GABoost improves the alignment accuracy of the 7 upstream methods by 25.25% on average with acceptable time overhead.

A dynamic yard space reservation algorithm based on reward-penalty mechanism

Increasing throughput at container terminals leads to higher yard occupancy rates, reduced yard service capacity, and inefficient use of space. These issues result in longer waiting times for trucks, underutilized yard slots, and longer distances between berth positions and the yard, particularly under high occupancy conditions. Traditional methods for allocating yard space fail to adequately consider dynamic container arrival patterns, conflict between container operations, and efficient use of yard resources. This paper introduces an innovative approach to improve yard efficiency by dividing yard container retrieval into time intervals and dynamically reserving yard slots within each interval. This method aims to minimize operational conflicts, reduce distances between blocks and berths, and avoid excessive reservations. We propose a dynamic reservation algorithm based on a reward-penalty mechanism to handle the problem's complexity and real-time demands. Furthermore, a time-series reward-penalty mechanism, which considers past reservation feedback and future reservation potential, ensures the concentration and continuity of container groups in the yard. Our evaluation metrics and multiple experimental scenarios demonstrate that this method significantly enhances yard efficiency and overall port productivity compared to static and other dynamic algorithms.

Reinforced Labels: Multi-Agent Deep Reinforcement Learning for Point-Feature Label Placement.

Over the recent years, Reinforcement Learning combined with Deep Learning techniques has successfully proven to solve complex problems in various domains, including robotics, self-driving cars, and finance. In this article, we are introducing Reinforcement Learning (RL) to label placement, a complex task in data visualization that seeks optimal positioning for labels to avoid overlap and ensure legibility. Our novel point-feature label placement method utilizes Multi-Agent Deep Reinforcement Learning to learn the label placement strategy, the first machine-learning-driven labeling method, in contrast to the existing hand-crafted algorithms designed by human experts. To facilitate RL learning, we developed an environment where an agent acts as a proxy for a label, a short textual annotation that augments visualization. Our results show that the strategy trained by our method significantly outperforms the random strategy of an untrained agent and the compared methods designed by human experts in terms of completeness (i.e., the number of placed labels). The trade-off is increased computation time, making the proposed method slower than the compared methods. Nevertheless, our method is ideal for scenarios where the labeling can be computed in advance, and completeness is essential, such as cartographic maps, technical drawings, and medical atlases. Additionally, we conducted a user study to assess the perceived performance. The outcomes revealed that the participants considered the proposed method to be significantly better than the other examined methods. This indicates that the improved completeness is not just reflected in the quantitative metrics but also in the subjective evaluation by the participants.

Quantum Speed-Ups for String Synchronizing Sets, Longest Common Substring, and k -mismatch Matching

Longest common substring (LCS) is an important text processing problem, which has recently been investigated in the quantum query model. The decision version of this problem, LCS with threshold \(d\) , asks whether two length- \(n\) input strings have a common substring of length \(d\) . The two extreme cases, \(d=1\) and \(d=n\) , correspond, respectively to Element Distinctness and Unstructured Search, two fundamental problems in quantum query complexity. However, the intermediate case \(1\ll d\ll n\) was not fully understood. We show that the complexity of LCS with threshold \(d\) smoothly interpolates between the two extreme cases up to \(n^{o(1)}\) factors: — LCS with threshold \(d\) has a quantum algorithm in \(n^{2/3+o(1)}/d^{1/6}\) query complexity and time complexity, and requires at least \(\Omega(n^{2/3}/d^{1/6})\) quantum query complexity. Our result improves upon previous upper bounds \(\widetilde{O}(\min\{n/d^{1/2},n^{2/3}\})\) (Le Gall and Seddighin ITCS 2022, Akmal and Jin SODA 2022), and answers an open question of Akmal and Jin. Our main technical contribution is a quantum speed-up of the powerful String Synchronizing Set technique introduced by Kempa and Kociumaka (STOC 2019). It consistently samples \(n/\tau^{1-o(1)}\) synchronizing positions in the string depending on their length- \(\Theta(\tau)\) contexts, and each synchronizing position can be reported by a quantum algorithm in \(\widetilde{O}(\tau^{1/2+o(1)})\) time. Our quantum string synchronizing set also yields a near-optimal LCE data structure in the quantum setting. As another application of our quantum string synchronizing set, we study the \(k\) -mismatch Matching problem, which asks if the pattern has an occurrence in the text with at most \(k\) Hamming mismatches. Using a structural result of Charalampopoulos et al. (FOCS 2020), we obtain: — \(k\) -mismatch matching has a quantum algorithm with \(k^{3/4}n^{1/2+o(1)}\) query complexity and \(\widetilde{O}(kn^{1/2})\) time complexity. We also observe a non-matching quantum query lower bound of \(\Omega(\sqrt{kn})\) .

Hybrid Filtering and Probabilistic Techniques for Privacy-Preserving Community Detection in OSNs

Online Social Networks (OSNs) face the major challenge of protecting participant's privacy, due to the high dimensionality and volume of the data. In real-time social networks, where hundreds of personal details of people are shared every day, there remains a significant threat to privacy. Privacy preservation is challenging for a community detection problem due to the high computational complexity and memory requirements, especially in larger real-world OSN graphs. Although weighted nodes provide better results, as they allow capturing the frequencies of the values, the privacy preservation of sensitive attributes such as specific profiles becomes harder compared to these models. This problem can result in queries and subsequent learnings from social network profiles of specific individuals, which may be of personal, political or otherwise concern. Online social networks (OSNs) grapple with significant privacy challenges due to the extensive dimensions and vast quantities of data involved. This research fills the void in current privacy-preserving community detection methodologies, which face problems in computational complexity and memory usage in large-scale OSNs. The proposed framework seeks to bolster privacy preservation through a comprehensive multi-step process. Data filtering uses a blended data filter system to remove outliers and irrelevant data, thus enhancing the quality of the input data. Density-Oriented Clustering phase employs a density-oriented clustering model to identify communities, with each cluster representing a distinct community. Privacy Preservation component introduces a new privacy preservation technique for sensitive OSN attributes, surpassing existing k-anonymization methods. The developed density-based social network community detection model and its novel privacy-preserving scheme are evaluated using the datasets Yelp, Football, Zachary and Dolphin from the SNAP dataset. Experimental results on these datasets embed a comprehensive evaluation based on the order of each node and the graph-based networks, where each node is laden with weights as proximity values, indicating the semantic proximity between communities and individuals. The proposed framework employs the normalized mutual information (NMI), modularity (Q), Rand index and runtime measurements to demonstrate widespread advantages in the multi-dimensional functional space, including greater accuracy, cluster compatibility, and computational tractability over the existing prominent traditional models for OSNs.

Construction of Practical Teaching Mode of Law Course Based on Multi-Mode and Low-Resource Language Learning

China's legal profession is a new profession emerging in the process of China's rule of law. Its development and refinement are increasing in accordance with the rapid social, economic and political development. However, as a lawyer, people need to learn real kung fu. For complex and changeable legal practice problems, people should use the simplest and most effective way to solve them. Therefore, it is necessary to study the curriculum of law specialty to achieve its purpose. It is also necessary to reform the traditional education methods, introduce modern scientific and technological means, and improve their effectiveness, so as to construct a practical teaching mode of Professional Courses in Law (PCL). For practical legal courses, it can be conducted through multi-mode low-resource language learning method. This paper aimed to study how to study the ability of students to obtain information, process information and analyze and process information based on intelligent multi-image feature fusion. Based on the investigation of teaching objectives and teachers' teaching requirements, and the analysis and arrangement of the investigation results, a multi-task learning system model based on image intelligent features was established. In this experiment, 494 valid questionnaires were used to analyze the current situation of PCL practical teaching. Among them, 10.32% and 65.59% of the students were very satisfied with the results of PCL practical teaching, and 18.02% and 59.31% of the students liked PCL practical teaching very much. In the survey on the influencing factors of PCL practical teaching activities, 61.34% of the students thought that the students did not know enough and were not enthusiastic enough. On the whole, the students are satisfied with the practical teaching arrangement of PCL, but from the actual situation, the effect of practical teaching is not very good, and the expected goal has not been achieved.

Continuous Query-based Data Trading

In the era of big data, traditional data trading methods designed for one-time queries on static databases fail to meet the demands of continuous query-based trading on streaming data, often resulting in repeated and inaccurate charges due to neglecting computation sharing in continuous query execution. To address this, we introduce CQTrade, the first trading framework tailored for continuous queries, which incorporates computation sharing across different time windows and queries, enhancing integration with existing trading systems. Our contributions include a theoretical analysis of computation-sharing techniques, the development of a general optimization problem to maximize seller revenue adaptable to various techniques, and the proposal of a branch-and-price algorithm to handle the problem's complexity. Our evaluation shows that the proposed framework improves the success rate of data trading by 12.8% and boosts the seller's revenue by an average of 28.7%, compared to the one-time query-based data trading methods used in the current data market.

Sum‐rate maximization for downlink multiuser MISO URLLC system aided by IRS with discrete phase shifters

AbstractIntelligent reflecting surface (IRS) has recently been considered as a potential technology for realizing ultra‐reliable and low‐latency (URLLC) in wireless networks. This paper proposes a resource optimization scheme to maximize the sum‐rate for an IRS‐assisted downlink multiuser multi‐input single‐output (MISO) URLLC system. For the perfect CSI scenario, we jointly optimize each user's block‐length and packet‐error probability, the precoding vectors at the base station (BS), and the passive beamforming with discrete phase shifts at the IRS. Given the problem's complexity, we design a computationally efficient iterative algorithm using successive convex approximation (SCA) and semidefinite relaxation (SDR) techniques to obtain a locally optimal solution. Specifically, for the imperfect CSI scenario, we construct a robust resource optimization problem model and incorporate the S‐procedure to address the impact of channel uncertainty, proposing an iterative algorithm based on the alternating optimization (AO) method to achieve a locally optimal solution. Simulation results demonstrate that: 1) An IRS equipped with a 2‐bit quantized resolution phase shifter is sufficient to achieve a system sum‐rate comparable to that of an ideal phase shifter; 2) Compared to other Baseline schemes, Algorithm 2 exhibits better robustness and superior performance gains under imperfect CSI.

Coupled Memristor Oscillators for Neuromorphic Locomotion Control: Modeling and Analysis.

The recent surge of interest in brain-inspired architectures along with the development of nonlinear dynamical electronic devices and circuits has enabled energy-efficient hardware realizations of several important neurobiological systems and features. Central pattern generator (CPG) is one such neural system underlying the control of various rhythmic motor behaviors in animals. A CPG can produce spontaneous coordinated rhythmic output signals without any feedback mechanism, ideally realizable by a system of coupled oscillators. Bio-inspired robotics aims to use this approach to control the limb movement for synchronized locomotion. Hence, devising a compact and energy-efficient hardware platform to implement neuromorphic CPGs would be of great benefit for bio-inspired robotics. In this work, we demonstrate that four capacitively coupled vanadium dioxide (VO2) memristor-based oscillators can produce spatiotemporal patterns corresponding to the primary quadruped gaits. The phase relationships underlying the gait patterns are governed by four tunable bias voltages (or four coupling strengths) making the network programmable, reducing the complex problem of gait selection and dynamic interleg coordination to the choice of four control parameters. To this end, we first introduce a dynamical model for the VO2 memristive nanodevice, then perform analytical and bifurcation analysis of a single oscillator, and finally demonstrate the dynamics of coupled oscillators through extensive numerical simulations. We also show that adopting the presented model for a VO2 memristor reveals a striking resemblance between VO2 memristor oscillators and conductance-based biological neuron models such as the Morris-Lecar (ML) model. This can inspire and guide further research on implementation of neuromorphic memristor circuits that emulate neurobiological phenomena.

Generate custom travel magazine layouts

Among the problems of specifying the style and number of elements of a travel magazine, the problem of generating magazine layout by constraining text, and constraining graph layout remains a complex and unsolved problem. In this paper, we generate layouts of text satisfying constraints via GAN. Due to the complexity and variety of graph designs, we enhance the performance of the discriminator and the generator so that the layouts generated by the generator are more constrained. Add non-corresponding constraint text and real layout pairs to the discriminator to enhance the performance of the discriminator; then add a spatial attention mechanism to the layout encoder to extract the features of the layout and generate high-quality layouts. We demonstrate that the proposed method can generate high-quality layouts of text satisfying the constraints, and we validate the effectiveness of this method through user ratings.

Performance of high-order Godunov-type methods in simulations of astrophysical low Mach number flows

High-order Godunov methods for gas dynamics have become a standard tool for simulating different classes of astrophysical flows. Their accuracy is mostly determined by the spatial interpolant used to reconstruct the pair of Riemann states at cell interfaces and by the Riemann solver that computes the interface fluxes. In most Godunov-type methods, these two steps can be treated independently, so that many different schemes can in principle be built from the same numerical framework. Because astrophysical simulations often test out the limits of what is feasible with the computational resources available, it is essential to find the scheme that produces the numerical solution with the desired accuracy at the lowest computational cost. However, establishing the best combination of numerical options in a Godunov-type method to be used for simulating a complex hydrodynamic problem is a nontrivial task. In fact, formally more accurate schemes do not always outperform simpler and more diffusive methods, especially if sharp gradients are present in the flow. For this work, we used our fully compressible Seven-League Hydro (SLH) code to test the accuracy of six reconstruction methods and three approximate Riemann solvers on two- and three-dimensional (2D and 3D) problems involving subsonic flows only. We considered Mach numbers in the range from 10−3 to 10−1, which are characteristic of many stellar and geophysical flows. In particular, we considered a well-posed, 2D, Kelvin–Helmholtz instability problem and a 3D turbulent convection zone that excites internal gravity waves in an overlying stable layer. Although the different combinations of numerical methods converge to the same solution with increasing grid resolution for most of the quantities analyzed here, we find that (i) there is a spread of almost four orders of magnitude in computational cost per fixed accuracy between the methods tested in this study, with the most performant method being a combination of a low-dissipation Riemann solver and a sextic reconstruction scheme; (ii) the low-dissipation solver always outperforms conventional Riemann solvers on a fixed grid when the reconstruction scheme is kept the same; (iii) in simulations of turbulent flows, increasing the order of spatial reconstruction reduces the characteristic dissipation length scale achieved on a given grid even if the overall scheme is only second order accurate; (iv) reconstruction methods based on slope-limiting techniques tend to generate artificial, high-frequency acoustic waves during the evolution of the flow; and (v) unlimited reconstruction methods introduce oscillations in the thermal stratification near the convective boundary, where the entropy gradient is steep.

Round-trip hub location problem

In this paper, we introduce a novel network design for the Hub Location Problem, inspired by the round-trip structure commonly used by transport service providers. Our design integrates spoke nodes assigned to a central hub node, creating round-trips where the hub node serves as the starting point, visits all assigned spoke nodes, and returns to the hub. To enhance transportation services and provide additional redundancy, we introduce a new type of nodes called runaway nodes to the network. The motivation for this research arises from two real-life cases encountered during consultancy projects, underscoring the necessity for an optimized network design in transportation services. To address the proposed problem, we introduce a mixed-integer linear programming (MIP) mathematical model. However, due to the problem's complexity, the feasibility of the MIP model is limited to small-scale instances. To tackle medium and large-scale instances, we introduce two hyper-heuristic approaches based on reinforcement learning. These hyper-heuristic approaches harness the power of reinforcement learning to guide the selection of low-level heuristics and improve solution quality. We conduct extensive computational experiments to evaluate the efficiency and effectiveness of the proposed approaches. The results of our experiments affirm the efficiency of the proposed hyper-heuristic approaches, showcasing their ability to discover high-quality solutions for the Hub Location Problem.

A mathematical model and solution algorithms for optimising system-level configurations of reconfigurable single part flow lines

This study addresses a system-level configuration selection problem for reconfigurable single part flow lines (R-SPFLs) with parallel identical flexible machines at each stage. The problem is to determine the number of stages, the number of machines of a certain type at each stage and the assignment of operations to each stage in order to satisfy the demand of a part type. Precedence relations among the operations and space limitations are also considered. For the objective of minimising the sum of machine purchase and operation processing costs, a nonlinear integer programming model is developed that gives the optimal solutions. Then, due to the problem's complexity, a basic variable neighbourhood search algorithm is proposed that constructs an initial solution using a greedy-type heuristic and improves it using a shaking and a local search improvement methods. Moreover, the basic algorithm is extended to a general one that uses a variable neighbourhood descent method. Computational results show that the two algorithms outperform the previous one significantly in both solution quality and computation times, and the general algorithm improves the basic one significantly. Finally, the applicability of the variable neighbourhood search algorithms is shown by reporting a brief case study.

WaRENet: A Novel Urban Waterlogging Risk Evaluation Network

In this article, we propose a novel urban waterlogging risk evaluation network (WaRENet) to evaluate the risk of waterlogging. The WaRENet distinguishes whether an urban image involves waterlogging by classification module, and estimates the waterlogging risk levels by multi-class reference objects detection module (MCROD). First, in the waterlogging scene classification, ResNet combined with Se-block is used to identify the waterlogging scene, and lightweight gradient-weighted class activation mapping (Grad-CAM) is also integrated to roughly locate overall waterlogging areas with low computational burden. Second, in the MCROD module, we detect reference objects, e.g., cars and persons in waterlogging scenes. The positional relationship between water depths and reference objects serves as risk indicators for accurately evaluating waterlogging risk. Specifically, we incorporate switchable atrous convolution (SAC) into YOLOv5 to solve occlusions and varying scales problems in complex waterlogging scenes. Moreover, we construct a large-scale urban waterlogging dataset called UrbanWaterloggingRiskDataset (UWRDataset) with 6,351 images for waterlogging scene classification and 3,217 images for reference objects detection. Experimental results on the dataset show that our WaRENet outperforms all comparison methods. The waterlogging scene classification module achieves accuracy of 95.99%. The MCROD module obtains mAP of 54.9%, while maintaining a high processing speed of 70.04 fps.

Parallel and Distributed Graph Neural Networks: An In-Depth Concurrency Analysis.

Graph neural networks (GNNs) are among the most powerful tools in deep learning. They routinely solve complex problems on unstructured networks, such as node classification, graph classification, or link prediction, with high accuracy. However, both inference and training of GNNs are complex, and they uniquely combine the features of irregular graph processing with dense and regular computations. This complexity makes it very challenging to execute GNNs efficiently on modern massively parallel architectures. To alleviate this, we first design a taxonomy of parallelism in GNNs, considering data and model parallelism, and different forms of pipelining. Then, we use this taxonomy to investigate the amount of parallelism in numerous GNN models, GNN-driven machine learning tasks, software frameworks, or hardware accelerators. We use the work-depth model, and we also assess communication volume and synchronization. We specifically focus on the sparsity/density of the associated tensors, in order to understand how to effectively apply techniques such as vectorization. We also formally analyze GNN pipelining, and we generalize the established Message-Passing class of GNN models to cover arbitrary pipeline depths, facilitating future optimizations. Finally, we investigate different forms of asynchronicity, navigating the path for future asynchronous parallel GNN pipelines. The outcomes of our analysis are synthesized in a set of insights that help to maximize GNN performance, and a comprehensive list of challenges and opportunities for further research into efficient GNN computations. Our work will help to advance the design of future GNNs.