Dijkstra Algorithm Research Articles

Refining Dijkstra's Algorithm: Employing Smart Solutions for Efficient Waste Management and Pollution Mitigation

This study explores the application of Dijkstra's algorithm to enhance waste disposal management systems, focusing on optimizing routing for efficient waste disposal. By modeling waste disposal pathways, the research aims to identify the shortest and most cost-effective routes, thereby reducing both pollution and operational costs. The analysis demonstrates that Dijkstra's algorithm can effectively streamline waste collection processes in Abakaliki, Ebonyi State, Nigeria, enabling the waste management board to minimize distance, time, and expenses associated with waste transportation. The developed model is both scalable and adaptable, promoting the integration of Geographic Information Systems (GIS) and real-time data for dynamic route optimization. The findings suggest significant potential for this approach not only in waste management but also in other domains such as traffic management and urban planning. This paper advocates for further exploration of user-friendly interfaces and alert systems to enhance operational efficiency. This research highlights the overall transformative potential of Dijkstra's algorithm in improving the sustainability and effectiveness of municipal services.

Numerical Data Processing by The Implementation of Trees and Graphs

Trees and Graphs play a vital role in transport and logistics. In tree, decision tree is one of the important, not only implemented for data processing, but also considered for Numerical data analysis. The decision tree is a flow chart-like structure, in which each internal node represents a ‘test’ on an attribute, which has a node known as root being at the top, which further divides the given data into branches depending upon the conditions. Every branch consists of a rule, and each leaf node is its outcome. A support tool with a tree-like structure that models probable outcomes, cost of resources, utilities, and possible consequences. Decision trees are also used in operations research along with planning logistics. They can help in determining appropriate plans that will help a company achieve its target. In Graph, Dijkstra's algorithm is an admired algorithm used to find the shortest paths between nodes in a graph, which may represent road networks for example. Dijkstra's algorithm finds the shortest path from a given source node to every other node. It can also be used to find the shortest path to a specific destination node, by concluding the algorithm once the shortest path to the destination node is found. It is also commonly used on graphs where the edge weights are in real numbers. A common application of shortest path algorithms is network routing protocols and also support in route optimization for delivery services, ensuring timely and cost-effective deliveries by finding the best paths for transportation.

Latency Reduction in Immersive Systems through Request Scheduling with Digital Twin Networks in Collaborative Edge Computing

Immersive systems, which offer immersive interactive experiences by tightly coupling the real and virtual worlds, encompassing Augmented Reality (AR) and Virtual Reality (VR), have undergone rapid development in recent years. The inherent latency issue of immersive systems poses considerable challenges for AR/VR applications that are highly sensitive to delay. To address this challenge, we propose utilizing edge collaboration as an efficient means to schedule AR/VR requests, owing to the inherent ability of edge nodes to seamlessly coordinate within the same geographical region and optimally allocate request resources to minimize latency. However, when it comes to edge nodes across different regions, a significant hurdle emerges. These nodes often lack real-time knowledge about cached resources across other regions, making cross-regional edge collaboration for AR/VR request scheduling an extremely challenging problem. We formally define and prove the NP-hardness of this problem. To tackle this complexity, we introduce a Federated Digital Twin Model Construction (FedDT), which establishes a global digital twin network connecting different edge nodes. This network simulates and reflects the resource status and availability of each edge node in real time. Subsequently, we devise an extended Dijkstra algorithm to determine the shortest path between AR/VR requests and edge nodes, taking into account current network conditions to optimize service delay. Both theoretical analysis and experimental results confirm that compared with baseline methods, our proposed solution consistently achieves an average delay reduction of 36.78% across various scenarios, effectively demonstrating its superior performance.

On the Energy Behaviors of the Bellman–Ford and Dijkstra Algorithms: A Detailed Empirical Study

The Single-Source Shortest Paths (SSSP) graph problem is a fundamental computation. This study attempted to characterize concretely the energy behaviors of the two primary methods to solve it, the Bellman–Ford and Dijkstra algorithms. The very different interactions of the algorithms with the hardware may have significant implications for energy. The study was motivated by the multidisciplinary nature of the problem. Gaining better insights should help vital applications in many domains. The work used reliable embedded sensors in an HPC-class CPU to collect empirical data for a wide range of sizes for two graph cases: complete as an upper-bound case and moderately dense. The findings confirmed that Dijkstra’s algorithm is drastically more energy efficient, as expected from its decisive time complexity advantage. In terms of power draw, however, Bellman–Ford had an advantage for sizes that fit in the upper parts of the memory hierarchy (up to 2.36 W on average), with a region of near parity in both power draw and total energy budgets. This result correlated with the interaction of lighter logic and graph footprint in memory with the Level 2 cache. It should be significant for applications that rely on solving a lot of small instances since Bellman–Ford is more general and is easier to implement. It also suggests implications for the design and parallelization of the algorithms when efficiency in power draw is in mind.

Mathematical Techniques for Autonomous Vehicle Navigation Systems

Advanced mathematical methods are used a lot in autonomous car guidance systems to make sure they work correctly, reliably, and efficiently. This abstract talks about some of the most important mathematics methods used to create and improve these systems. One important method is probabilistic robots, which uses Bayesian filters, such as the Kalman filter and its nonlinear versions (Extended Kalman Filter and Unscented Kalman Filter), to estimate a vehicle's state and make sense of sensor data that isn't always clear or loud. Path planning algorithms, like A and Dijkstra's algorithm, are needed to find the best routes. Sampling-based methods, like Rapidly-exploring Random Trees (RRT), can help with problems in high-dimensional space. Control theory is a very important part of keeping a car stable and following the direction you want it to take. Model Predictive Control (MPC), for example, is used a lot because it can handle control jobs with multiple variables while considering the system's behavior. To model how a vehicle moves, differential equations and dynamical systems theory are used to show how control inputs affect how the vehicle acts over time. Also, methods that combine data from different sources like LiDAR, cameras, and GPS are very important for making an accurate and complete picture of the world. Optimization methods improve tracking even more by adjusting the path of the car, cutting down on energy use, and shortening trip times. Besides these methods, machine learning and deep learning are being added to guidance systems more and more to help them make better decisions and be more flexible in settings that are changing quickly and are very complicated. These models can learn from very large datasets by finding trends and making predictions that are important for tasks like finding objects, understanding scenes, and making decisions on their own. Autonomous car tracking systems are getting smarter, more capable, and more reliable by using both old-fashioned math methods and new, cutting-edge machine learning methods together. This makes it possible for them to be widely used in real life.

Unmanned vehicle off-road path-planning method with comprehensive constraints on multiple environmental factors

ABSTRACT In complex off-road environments, different slopes, slope directions, and land types differently affect unmanned vehicle trafficability. Thus, we propose an unmanned vehicle off-road path-planning method with comprehensive constraints on multiple environmental factors. First, the influence of slope, aspect, and surface-coverage type on unmanned vehicle drivability was quantitatively evaluated, and the slope and land type influence layers were formed. Concurrently, a goal guidance layer was formed using the artificial potential field method. Second, the slope influence, land type influence, and goal guidance layers were used to quantitatively evaluate each grid’s pass cost value. Finally, the traditional A* algorithm, A* algorithm considering the impassable area, A* algorithm with comprehensive constraints, and Dijkstra algorithm with comprehensive constraints were used for path planning. The results show that the path slopes planned by A* algorithm with comprehensive constraints and Dijkstra algorithm with comprehensive constraints were smaller than those planned by A* algorithm and A* algorithm considering the impassable area; particularly, the length of the uphill path was shorter and the stability was better. The relevant research results provide methods and technical guidance for obtaining the shortest length, shortest time, and most stable and passable path in off-road environments.

Real-time quantitative risk analysis and routing optimization of gaseous hydrogen tube trailer transport: A Bayesian network and Dijkstra algorithm combining approach

Real-time quantitative risk analysis and routing optimization of gaseous hydrogen tube trailer transport: A Bayesian network and Dijkstra algorithm combining approach

A Dijkstra's Algorithm: Theory and Application to Asia Map

A Dijkstra's Algorithm: Theory and Application to Asia Map

Research on Indoor Automatic Path Planning Algorithm for Robots

The field of robotics has significantly advanced, especially in indoor autonomous navigation, with applications in households, offices, factories, and tourism. This research focuses on developing and optimizing algorithms for indoor autonomous path planning, aiming to enhance robots' ability to navigate efficiently and safely in various indoor environments. The research adopts a comprehensive methodological approach, beginning with a literature review to understand current state-of-the-art techniques in path planning and obstacle avoidance. Novel algorithms were designed and implemented, focusing on efficiency and real-time performance. These algorithms were tested in simulation environments and validated on actual robotic platforms. Performance metrics such as path efficiency, computational time, and obstacle avoidance success rates were used to assess the algorithms. The study evaluated global path planning algorithms like A* and Dijkstra’s, and local path planning algorithms such as Rapidly-exploring Random Trees (RRT) and Dynamic Window Approach (DWA). A* and Dijkstra's algorithms proved effective for global planning but required optimization for real-time applications. RRT excelled in complex environments but needed improvements for path optimality. DWA provided robust real-time obstacle avoidance. Hybrid approaches combining these algorithms showed enhanced performance, balancing global and local planning strengths. Machine learning techniques further improved adaptability and efficiency. The integration of advanced sensor technologies and accurate map construction methods is crucial for effective indoor navigation. LIDAR, ultrasonic sensors, and depth cameras were key in providing precise environmental perception. Hybrid maps combining grid and topological approaches offered detailed local information and efficient long-distance planning. Optimization techniques like parameter tuning and algorithm fusion, along with machine learning, significantly enhanced algorithm performance. Future research should explore intelligent algorithms, multi-robot collaboration, and human-robot interaction to further advance the field.

Fuzzy Traveling Salesman Problem of Fuzzy Hexagonal Numbers using Ranking Method and Dijkstra's Algorithms

Fuzzy Traveling Salesman Problem of Fuzzy Hexagonal Numbers using Ranking Method and Dijkstra's Algorithms

Solving the Robust Shortest Path Problem with Multimodal Transportation

This paper explores the challenges of finding robust shortest paths in multimodal transportation networks. With the increasing complexity and uncertainties in modern transportation systems, developing efficient and reliable routing strategies that can adapt to various disruptions and modal changes is essential. By incorporating practical constraints in parameter uncertainty, this paper establishes a robust shortest path mixed-integer programming model based on a multimodal transportation network under transportation time uncertainty. To solve robust shortest path problems with multimodal transportation, we propose a modified Dijkstra algorithm that integrates parameter uncertainty with multimodal transportation. The effectiveness of the proposed multimodal transportation shortest path algorithm is verified using empirical experiments on test sets of different scales and a comparison of the runtime using a commercial solver. The experimental results on the multimodal transportation networks demonstrate the effectiveness of our approach in providing robust and efficient routing solutions. The results demonstrate that the proposed method can generate optimal solutions to the robust shortest path problem in multimodal transportation under time uncertainty and has practical significance.

Shortest Path Problem under Pythagorean Fuzzy Network Using Dijkstra’s Algorithm

In this article investigates the Shortest Path Problem (SPP) in uncertain settings using Pythagorean fuzzy numbers (PFNs). A heuristic methodology using modified Dijkstra's algorithm is developed to exploit error, uncertainty, and partial truth for a low-cost solution. The method calculates minimum distance between starting and destination nodes and evaluates its effectiveness. Pythagorean fuzzy graphs can handle ambiguous situations.

New Dynamic Programming algorithm for the Multiobjective Minimum Spanning Tree problem

The Multiobjective Minimum Spanning Tree (MO-MST) problem generalizes the Minimum Spanning Tree problem by weighting the edges of the input graph using vectors instead of scalars. In this paper, we design a new Dynamic Programming MO-MST algorithm. Dynamic Programming for a MO-MST instance requests solving a One-to-One Multiobjective Shortest Path (MOSP) instance and both instances have equivalent solution sets. The MOSP instance is defined on a so called transition graph. We study the original size of this graph in detail and reduce its size using cost-dependent arc pruning criteria. To solve the MOSP instance on the reduced transition graph, we design the Implicit Graph Multiobjective Dijkstra Algorithm (IG-MDA), exploiting recent improvements on MOSP algorithms from the literature. All in all, the new IG-MDA outperforms the current state of the art on a big set of instances from the literature. Our code and results are publicly available.

Comparison of Djikstra, Hybrid-PSO algorithms for optimizing the distribution route of papaya seeds and honey products (Case Study: PT. Agro Apiari Mandiri)

Dynamic global competencies in the industrial sector drive fierce competition in capturing markets and increasing customer satisfaction, which requires efficiency in various aspects of business including distribution. PT. Agro Apiari Mandiri faces challenges in optimizing delivery routes to avoid delays. This study aims to compare the Dijkstra and Hybrid-PSO algorithms to determine the optimal distribution route in the Bogor, West Java, and Lebak, Banten regions, in order to reduce the distance and delivery time. The research methods include literature study, data collection, and route optimization model creation. The results show that PSO is more efficient in optimizing delivery routes than other methods, with variations in PSO parameters affecting total travel time, number of vehicles, and computing time. Implementation uses hardware and software such as MSI Laptops and Matlab. In conclusion, the use of PSO in distribution route optimization makes a significant contribution to the company's cost and distribution efficiency and can be a reference for further research in distribution route optimization.

Reservoir Irrigation Operation Design Based on Dijkstra Algorithm Combined with ACO Algorithm

Reservoir Irrigation Operation Design Based on Dijkstra Algorithm Combined with ACO Algorithm

An improved 3D Dijkstra algorithm of evacuation route considering tailings dam failure

An improved 3D Dijkstra algorithm of evacuation route considering tailings dam failure

Multi-Objective Route Planning Model for Ocean-Going Ships Based on Bidirectional A-Star Algorithm Considering Meteorological Risk and IMO Guidelines

In this study, a new route planning model is proposed to help ocean-going ships avoid dangerous weather conditions and ensure safe ship navigation. First, we integrate ocean-going ship vulnerability into the study of the influence of meteorological and oceanic factors on navigational risk. A multi-layer fuzzy comprehensive evaluation model for weather risk assessment is established. A multi-objective nonlinear route planning model is then constructed by comprehensively considering the challenges of fuel consumption, risk, and time during ship navigation. The International Maritime Organization (IMO) guidelines are highlighted as constraints in the calculations, and wind, wave, and calm water resistance to ships in the latest ITTC method is added to the fuel consumption and sailing time in the objective function. Finally, considering the large amount of data required for ocean voyages, the bidirectional A* algorithm is applied to solve the model and reduce the planning time. Furthermore, our model is applied to the case of an accident reported in the Singapore Maritime Investigation Report, and the results show that the model-planned route is very close to the original planned route using the Towing Manual, with an average fit of 98.22%, and the overall meteorological risk of the model-planned route is 11.19% smaller than the original route; our model can therefore be used to plan a safer route for the vessel. In addition, the importance of risk assessments and the IMO guidelines as well as the efficiency of the bidirectional A* algorithm were analyzed and discussed. The results show that the model effectively lowers the meteorological risk, is more efficient than the traditional route planning algorithm, and is 86.82% faster than the Dijkstra algorithm and 49.16% faster than the A* algorithm.

TourMapQA: using deep learning to develop a vietnam map-based tourism question answering system

<p>A question answering system is an important task in information retrieval. In recent years, this system has been interested in research and achieved outstanding results. In general, the output of the question answering is text. However, few studies have used a map as an answer to the question answering in Vietnam tourism. This paper introduces a question answering system integrating long short-term memory (LSTM) on the Vietnam map. Specifically, our model received an input question about any road in Vietnam. Then, the model used LSTM to indicate the coordinate of that road and called the Dijkstra algorithm to find the shortest path from the current location to the input road. Next, from the coordinate of the input road, we leveraged the LSTM model to identify sightseeing places that were on the shortest path. Finally, our system showed all the sightseeing places on the Vietnam map. Technically, the experimental results showed that our model’s performance was improved than previous models such as recurrent neural network, recurrent neural network with embedding, bidirectional recurrent neural network, and encoder-decoder recurrent neural network. Practically in terms, we applied our method to build a real application and compared it with Google Maps, and Bing Map.</p>

Optimizing Energy Efficiency in Wireless Sensor Networks Using Dijkstra's Algorithm

Optimizing Energy Efficiency in Wireless Sensor Networks Using Dijkstra's Algorithm

The Multi-Objective Shortest Path Problem with Multimodal Transportation for Emergency Logistics

The optimization of emergency logistical transportation is crucial for the timely dispatch of aid and support to affected areas. By incorporating practical constraints into emergency logistics, this study establishes a multi-objective shortest path mixed-integer programming model based on a multimodal transportation network. To solve multi-objective shortest path problems with multimodal transportation, we design an ideal point method and propose a procedure for constructing the complete Pareto frontier based on the k-shortest path multi-objective algorithm. We use modified Dijkstra and Floyd multimodal transportation shortest path algorithms to build a k-shortest path multi-objective algorithm. The effectiveness of the proposed multimodal transportation shortest path algorithm is verified using empirical experiments carried out on test sets of different scales and a comparison of the runtime using a commercial solver. The results show that the modified Dijkstra algorithm has a runtime that is 100 times faster on average than the modified Floyd algorithm, which highlights its greater applicability in large-scale multimodal transportation networks, demonstrating that the proposed method both has practical significance and can generate satisfactory solutions to the multi-objective shortest path problem with multimodal transportation in the context of emergency logistics.