Floyd-Warshall Research Articles

Floyd-Warshall Algorithm Based on Picture Fuzzy Information

The Floyd-Warshall algorithm is frequently used to determine the shortest path between any pair of nodes. It works well for crisp weights, but the problem arises when weights are vague and uncertain. Let us take an example of computer networks, where the chosen path might no longer be appropriate due to rapid changes in network conditions. The optimal path from among all possible courses is chosen in computer networks based on a variety of parameters. In this paper, we design a new variant of the Floyd-Warshall algorithm that identifies an All-Pair Shortest Path (APSP) in an uncertain situation of a network. In the proposed methodology, multiple criteria and their mutual association may involve the selection of any suitable path between any two node points, and the values of these criteria may change due to an uncertain environment. We use trapezoidal picture fuzzy addition, score, and accuracy functions to find APSP. We compute the time complexity of this algorithm and contrast it with the traditional Floyd-Warshall algorithm and fuzzy Floyd-Warshall algorithm.

Implementation of the Floyd-Warshall Algorithm and Bellman-Ford Algorithm to Determine the Shortest Path in the Distribution of LPG Gas

In this article, the method use to determine the shortest path in the distribution of LPG is the Floyd-Warshall algorithm and the Bellman-Ford algorithm. These two methods will be compared to find out methods that can provide the best result. The best result is the path that has the minimum distance of distribution of LPG. Both of these algorithms are focused on simulating calculations that begin by representing the map in the form of a graph. Finally, the results obtained from this study are that using the Floyd-Warshall algorithm produces a path with a total distance of 111.05 KM while the Bellman-Ford algorithm produces 332.3 KM.

On the practical applica tion of the Floyd-Warshall algorithm and its modifications

The paper considers variants of the Floyd – Warshall algorithm, i.e. algorithms for finding shortest paths in a weighted graph with given edge weights; in one execution of the algorithm, the lengths of shortest paths between all pairs of vertices are found. Although the standard versions of the algorithm do not return the paths found, these paths can be reconstructed using simple modifications of the algorithm. Variants of this algorithm can also be used to find the transitive closure of some binary relation, as well as the widest paths between all pairs of vertices of a weighted graph. At the same time, according to the authors, the study of the topic is far from complete; it is confirmed, in particular, by many publications on the Internet on “algorithmic” sites. Despite the fact that the cubic complexity of the algorithm for solving this problem is not improved (at least for standard input data representation options), one can strive to improve the specific running time of the algorithms. Moreover, we deliberately worsen the complexity of the algorithm implementations we are considering (actually multiplying it by the logarithm of the number of vertices); however, due to the possibility of a successful iteration of the edges, conducted in order of increasing their cost, we achieve a reduction in the average running time of the implemented programs.

A novel traceback model for DDoS attacks using modified Floyd-Warshall algorithm

Distributed denial of service, DDoS, attacks are drastically increasing, therefore, they cause serious threats for information networks. This paper proposes, for the first time, the use of a graph theoretic approach to exploit the entropy techniques for detecting and tracing back DDoS attackers. It presents a novel approach to traceback DDoS attacks using modified Floyd-Warshall algorithm, TDA/MFWA. Such model starts by feeding the network adjacency matrix in which the link weights are changed to comply with the network traffic entropy, accordingly the reachability from node to node can be examined. Then we borrowed the idea of enumerating all the intermediate points between every pair of network nodes from Floyd-Warshall algorithm and modified it to find out the victim node(s). The fact that entropy at network nodes is systematically accounted using a modified Floyd-Warshall algorithm contributes to the smartness and dependability of TDA/MFWA.

Strategic Evaluation and Optimization of Clan Sides Based on Floyd Algorithm

Strategic Evaluation and Optimization of Clan Sides Based on Floyd Algorithm

A novel traceback model for DDoS attacks using modified Floyd-Warshall algorithm

A novel traceback model for DDoS attacks using modified Floyd-Warshall algorithm

Tuning block-parallel all-pairs shortest path algorithm for efficient multi-core implementa- tion.

Finding shortest paths in a weighted graph is one of the key problems in computer-science, which has numerous practical applications in multiple domains. This paper analyzes the parallel blocked all-pairs shortest path algorithm at the aim of evaluating the influence of the multi-core system and its hierarchical cache memory on the parameters of algorithm implementation depending on the size of the graph and the size of distance matrix’s block. It proposes a technique of tuning the block-size to the given multi-core system. The technique involves profiling tools in the tuning process and allows the increase of the parallel algorithm throughput. Computational experiments carried out on a rack server equipped with two Intel Xeon E5-2620 v4 processors of 8 cores and 16 hardware threads each have convincingly shown for various graph sizes that the behavior and parameters of the hierarchical cache memory operation don’t depend on the graph size and are determined only by the distance matrix’s block size. To tune the algorithm to the target multi-core system, the preferable block size can be found once for the graph size whose in-memory matrix representation is larger than the size of cache shared among all processor’s cores. Then this blocksize can be reused on graphs of bigger size for efficient solving the all-pairs shortest path problem

Autonomous UAV object Avoidance with Floyd-warshall differential evolution approach

Unmanned Aerial Vehicles (UAVs) are recently focused with significant research attention from commercial to military industries. Due to its wide range of applications such as traffic monitoring, surveillance, aerial photograph and rescue mission, many research studies were conducted related to UAV development. UAV are commonly called as ‘drones’ used to suit dull, dangerous and dirty missions that can be suited by manned aircraft. UAV can be controlled either remotely or using automation approaches so that it can be travelled into predefined path. To make the autonomous UAV, the most complex issue that is faced by UAV is obstacle / object avoidance. Obstacle detection and avoidance are important for UAV and it is the complex problem to solve due to the payload restriction. This will limit the sensor count mounted on the vehicle. Radar was used to find the distance between the object and vehicle. This can help to detect and track the moving objects speed and direction towards the vehicle. This paper considered the object avoidance problem as path planning problem. There were many path planning methods related to UAV which formulates the path planning as an optimization problem to avoid the obstacles. With the consideration, this paper proposed an efficient and optimal approach called Floyd Warshall- Differential evolution (FWDE) approach to detect the frontal obstacles of UAV. Finally, statistical analysis of the simulated environment reveals that the proposed evolutionary method can efficiently avoid both static and dynamic objects for UAVs. This efficient avoidance algorithm for UAV can be experimented with simulation environment with three kinds of scenarios having different number of cells. The obtained accuracy and recall value of the proposed system is 95.21% and 91.56%.

The time characteristics’ analysis of deterministic information processing models in automated control systems

The article presents the formation of the approach for evaluating and analyzing the time characteristics of deterministic information processing models in automated control systems. The approach of operational routes formalization within the technological management cycle and its time characteristic assessment is proposed as an optimization procedure. The Floyd algorithm’s realization to determining the shortest time path of the technological control cycle’s graph is shown.

A Standalone Graph-Theory Based Tool for Full-Chip ESD Verification

In this article, a novel flow of the automatic electrostatic discharge (ESD) verification is presented. A basic overview of the most important methodology steps is shown, with more detailed explanation of breaking voltage (BV) model generation. Based on transmission line pulsing measurements, the BV models are used for modeling devices under ESD stress conditions. The principle behind the custom-made tool ESDh is disclosed. Being based on graph-theory algorithm, specifically the Floyd-Warshall algorithm, the tool detects and reconstructs current paths between any node-to-node pair of the integrated circuit (IC). In addition, ESDh can calculate the full current-voltage (IV curve) of any current path. Consequently, this approach is able to find failing paths, failing devices, and failing levels of tested IC. As the method in this work uses the full netlist, without dismissing the core circuitry, ESDh can be used for verifying the self-protection levels of the IC.

Associated Fault Diagnosis of Power Supply Systems Based on Graph Matching: A Knowledge and Data Fusion Approach

With the rapid development of more-electric and all-electric aircraft, the role of power supply systems in aircraft is becoming increasingly prominent. However, due to the complex coupling within the power supply system, a fault in one component often leads to parameter abnormalities in multiple components within the system, which are termed associated faults. Compared with conventional faults, the diagnosis of associated faults is difficult because the fault source is hard to trace and the fault mode is difficult to identify accurately. To this end, this paper proposes a graph-matching approach for the associated fault diagnosis of power supply systems based on a deep residual shrinkage network. The core of the proposed approach involves supplementing the incomplete prior fault knowledge with monitoring data to obtain a complete cluster of associated fault graphs. The association graph model of the power supply system is first constructed based on a topology with characteristic signal propagation and the associated measurements of typical components. Furthermore, fault propagation paths are backtracked based on the Warshall algorithm, and abnormal components are set to update and enhance the association relationship, establishing a complete cluster of typical associated fault mode graphs and realizing the organic combination and structured storage of knowledge and data. Finally, a deep residual shrinkage network is used to diagnose the associated faults via graph matching between the current state graph and the historical graph cluster. The comparative experiments conducted on the simulation model of an aircraft power supply system demonstrate that the proposed method can achieve high-precision associated fault diagnosis, even under circumstances where there are an insufficient number of samples and missing parameters.

Planning of electric vehicle fast-charging station based on POI interest point division, functional area, and multiple temporal and spatial characteristics

There are some problems with the fast-charging station of urban electric vehicles (EV), including blind construction, unreasonable planning location, and neglect of user requirements. This paper presents a planning method considering functional zoning and traffic influencing factors. Firstly, the planning area’s POI points and road network information are processed based on the geographic information software ArcGIS, and the urban functional zoning is divided. Then, two factors that affect the user’s time-consuming cost are studied, such as regional traffic congestion and signal waiting time. Secondly, according to the initial location of the user, the road network adjacency matrix, and the probability function of the user selecting the fast-charging station, the Floyd algorithm is used to calculate the time-consuming cost of the user to the fast-charging station. In order to reflect the profitability of the fast-charging station, the payback period function is also introduced. Finally, the MOSAPSO algorithm is used to solve the multi-objective function composed of the investment cost, operation, and maintenance cost, payback period, and user time-consuming cost of the fast-charging station. The optimized site selection and management layout of fast charging stations provide a certain reference for urban EV fast charging stations.

Measuring urban ecological network resilience: A disturbance scenario simulation method

Human disturbance of urban ecosystems is intensifying, as is ecological fragmentation. As such, effective connections between green spaces must be established and restored to form structurally resilient urban ecological networks. In this study, we focused on indicators of city-scale ecological network resilience. We constructed a network model, analyzed the disturbance simulation results, and identified key nodes. Shenzhen, a megacity in China was selected for empirical research. First, we used Floyd algorithm to extract least-cost paths and then generate the corridor network, constructing an ecological network model with 386 nodes and 4910 edges. Second, focusing on the nodes of the constructed ecological network, we adopted a selected attack strategy to conduct dynamic simulations, using two parameters, network efficiency and maximum connectivity, to evaluate the resilience of the ecological network to changes under various disturbance scenarios. The results showed that the ecological network structure in the study area was relatively stable, and the first 30 % of nodes substantially impacted network resilience. The outcomes reflect the state of urban ecosystems that have been disturbed by socio-economic systems and are practically important for formulating adaptive spatial planning and management policies.

Path Planning of Electric VTOL UAV Considering Minimum Energy Consumption in Urban Areas

As a new mode of transportation in the future, electric vertical take-off and landing unmanned aerial vehicles (eVTOL UAV) can undertake the task of logistics distribution and carry people in urban areas. It is challenging to carry out research designed to plan the path of eVTOL UAVs which can have a safe and sustainable operation mode in urban areas. Therefore, this work proposes a method for planning an obstacle-free path for eVTOL UAVs in urban areas with the goal of minimizing energy consumption. It aims to improve the safety and sustainability of eVTOL UAV operations. Based on variations of air density with height, a more accurate formula for calculating battery energy consumption of eVTOL UAV is derived. It is used in the vertical takeoff and landing phase and horizontal flight phase, respectively. Considering the influence of buildings on eVTOL UAV operation, a path planning method applicable to complex urban environments is proposed. The safe nodes of eVTOL UAV flight are obtained by using Voronoi diagrams based on building locations. Then, the complete shortest and obstacle-free path is obtained by using a Dubins geometric path and Floyd algorithm. After obtaining the obstacle-free paths for all flight height zones, the battery energy consumption of the eVTOL UAV in each flight height zone is calculated. Then, the flight height with the minimum energy consumption is obtained. The simulation results show that the path length obtained by the proposed path planning method is shorter than that obtained by particle swarm optimization; the total battery energy consumption changes in the same pattern in the low-altitude areas and high-altitude areas; the difference between the maximum and minimum energy consumption in the small area enables the eVTOL UAV to cover about 350 m more, and about 420 m more in the large area. Therefore, in future high-frequency UAV mission flights, choosing the altitude with the lowest energy consumption can reduce UAV operator costs. It can also significantly increase UAV transport range and make UAVs operate more sustainably.

Ndist2vec: Node with Landmark and New Distance to Vector Method for Predicting Shortest Path Distance along Road Networks

The ability to quickly calculate or query the shortest path distance between nodes on a road network is essential for many real-world applications. However, the traditional graph traversal shortest path algorithm methods, such as Dijkstra and Floyd–Warshall, cannot be extended to large-scale road networks, or the traversal speed on large-scale networks is very slow, which is computational and memory intensive. Therefore, researchers have developed many approximate methods, such as the landmark method and the embedding method, to speed up the processing time of graphs and the shortest path query. This study proposes a new method based on landmarks and embedding technology, and it proposes a multilayer neural network model to solve this problem. On the one hand, we generate distance-preserving embedding for each node, and on the other hand, we predict the shortest path distance between two nodes of a given embedment. Our approach significantly reduces training time costs and is able to approximate the real distance with a relatively low Mean Absolute Error (MAE). The experimental results on a real road network confirm these advantages.

A multi-path traffic-covering pollution routing model with simultaneous pickup and delivery

Urban traffic in many developing countries has affected travel time and fuel costs, causing disturbances in the transportation schedule of companies dealing with logistic issues. The resulting environmental impact is another driver forcing these companies to reconsider their transportation schedule. Conventional pollution routing problems (PRPs) try to achieve a balance among greenhouse gas (GHG) emissions, fuel consumption, travel time, and distance. These models are not developed to cover traffic congestion and optimize speed on each route, while such factors affect the routing costs. To fill this gap, we propose a multi-path traffic-covering PRP with simultaneous pickup and delivery, which finds alternative paths in case of traffic congestion and determines the lowest-cost routes. Accordingly, we contribute to the multi-path vehicle routing models, which have mainly considered predetermined alternative routes between the nodes instead of providing algorithms for finding alternative low-traffic routes. We apply a four-phase metaheuristic algorithm to solve the model, containing a Clustering-based Floyd-Warshall (CFW) algorithm developed through the K-means method to create a network graph around the high-traffic path and find the alternative paths. The results of analyzing the model indicated that the total costs decreased by about 25% compared to the model without alternative paths. This improved level of much more than the typical range of 2–5% improvement showed the model contributions to the prior research using the same initial conditions but different solution methods.

Analyzing green view index and green view index best path using Google street view and deep learning

Abstract As an important part of urban landscape research, analyzing and studying street-level greenery can increase the understanding of a city’s greenery, contributing to better urban living environment planning and design. Planning the best path of urban greenery is a means to effectively maximize the use of urban greenery, which plays a positive role in the physical and mental health of urban residents and the path planning of visitors. In this paper, we used Google street view to obtain street view images of Osaka City. The semantic segmentation model is adopted to segment the street view images and analyze the green view index (GVI) of Osaka City. Based on the GVI, we take advantage of the adjacency matrix and Floyd–Warshall algorithm to calculate GVI best path, solving the limitations of ArcGIS software. Our analysis not only allows the calculation of specific routes for the GVI best paths but also realizes the visualization and integration of neighborhood urban greenery. By summarizing all the data, we can conduct an intuitive feeling and objective analysis of the street-level greenery in the research area. Based on this, such as urban residents and visitors can maximize the available natural resources for a better life. The dataset and code are available at https://github.com/Jackieam/GVI-Best-Path.

Graph Application in Finding the fastest Path From Subang City To Cirebon City

This paper discusses the application of one of the Discrete Mathematics materials, namely Graph Theory, in determining the fastest route from Subang City, more precisely from Subang Pusakanagara, Subang to Cirebon City. The fastest path is the route taken by considering the minimum travel time from one place to another. There are various ways to determine the minimum travel path, but the goal is the same, namely to find a travel path with the minimum travel time. The research process begins with formulating a problem using Graph Theory with the help of the Google Maps application and the experiences of the researchers. This Google Maps application is very useful when traveling long distances but want to use the path with minimal travel time. After formulating the problem, it is continued with the implementation of the Weighted Average Method and ends with the Floyd Warshall Algorithm. The result of this study is to find the fastest path from the starting point, namely Subang Pusakanagara to the end point, namely Cirebon City.

Research on emergency supplies distribution in 5G network environment based on TSP model

Along with the improvement of technology and the gradual popularization of 5G network, the application of UAVs is becoming more and more widespread, and the delivery mode of "delivery vehicle + UAV" has gradually become a new and effective delivery method. In order to solve the real problem of emergency supplies to be delivered to the disaster area after the disaster and to improve the efficiency of emergency supplies delivery, this new and effective delivery mode is used to solve the delivery problem. In this paper, a TSP model based on Floyd algorithm and genetic algorithm is established and the optimal distribution scheme is given. In the delivery mode of "delivery vehicle + UAV", the individual evaluation function is improved, and the flight conditions of UAV are introduced, and the optimal delivery scheme is given by simulation selection, crossover and variation. In the mode of "delivery vehicle + UAV" and the delivery vehicle has a single weight limit of 500 kg, The optimal solution is given for single "delivery vehicle + UAV" and the optimal solution is given for a single "delivery vehicle + UAV" and a double "delivery vehicle + UAV".

Research on smooth path planning method based on improved ant colony algorithm optimized by Floyd algorithm.

Aiming at the problems of slow convergence and easy fall into local optimal solution of the classic ant colony algorithm in path planning, an improved ant colony algorithm is proposed. Firstly, the Floyd algorithm is introduced to generate the guiding path, and increase the pheromone content on the guiding path. Through the difference in initial pheromone, the ant colony is guided to quickly find the target node. Secondly, the fallback strategy is applied to reduce the number of ants who die due to falling into the trap to increase the probability of ants finding the target node. Thirdly, the gravity concept in the artificial potential field method and the concept of distance from the optional node to the target node are introduced to improve the heuristic function to make up for the fallback strategy on the convergence speed of the algorithm. Fourthly, a multi-objective optimization function is proposed, which comprehensively considers the three indexes of path length, security, and energy consumption and combines the dynamic optimization idea to optimize the pheromone update method, to avoid the algorithm falling into the local optimal solution and improve the comprehensive quality of the path. Finally, according to the connectivity principle and quadratic B-spline curve optimization method, the path nodes are optimized to shorten the path length effectively.