Floyd-Warshall Research Articles

Competing all-pairs shortest paths algorithms for sparse / dense graphs: implementation and comparison

In this paper we consider two families of competing algorithms for finding the shortest paths between all pairs of vertices (APSP) in directed weighted large graphs with different edge densities: Dijkstra and Floyd-Warshall. For comparison, we have taken Dijkstra's algorithm with dynamically varying binary heap, which solves the APSP prob-lem purely in parallel by repeatedly executing on all vertices of the graph considered as source vertices, and we have taken blocked Floyd-Warshall algorithm, which is also well-parallelizable. It is known that in terms of computational complexity, the first algorithm is preferable on sparse graphs and the second algorithm is preferable on dense graphs. At the same time, it is not clear what are the ranges of graph densities at which the first algorithm will consume less CPU time than the second algorithm. This paper describes multithreaded implementations of parallel algorithms on multicore processors that make different usage of synchronization primitives such as mutex, conditional variable, lock-ing, and atomic operation. By conducting computational experiments on an 8-core Intel(R) Core(TM) i7-10700 CPU @ 2.90GHz, we found that each algorithm has a preferred graph density. In the case of multi-threaded parallel imple-mentation, the blocked Floyd-Warshall algorithm has lower running time than Dijkstra's algorithm if the graph densi-ty is greater than 0.5. Otherwise, Dijkstra's algorithm runs faster. In the case of single-threaded implementation, the split point is 0.43.

A balancing system for liquid metal batteries using the Floyd-Warshall algorithm

A balancing system for liquid metal batteries using the Floyd-Warshall algorithm

Path planning strategies for logistics robots: Integrating enhanced A‐star algorithm and DWA

AbstractPath planning is the key part in the process of transportation conducted by logistics robots, and there often exist some problems with it. The path designed is not always smooth enough and its search efficiency is low, for example. As a common global path planning algorithm, A‐star is based on the traditional algorithm, which is unable to solve the problem of uneven path in the movement of logistics robots. Through improving the heuristic function of the traditional A‐star algorithm, weighing the heuristic function dynamically, removing the redundant points of the traditional star algorithm path with Floyd algorithm, and setting a safe distance to prevent the logistics robot from collision at the same time, the path is finally curved to be more appropriate to the movement path of the logistics robot. The MATLAB simulation of A‐star algorithm before and after the improvement shows that the turning points of the advanced A‐star algorithm reduced 61.5% on average compared to the traditional algorithm. The path length decreased 2.4% and the traversing points reduced 58.5%. At the same time, the DWA algorithm introduces dynamic weight coefficients, which can dynamically adjust the weight coefficients when encountering obstacles, so as to safely reach the target point.

Improved Floyd-Warshall Algorithm for Solving Travelling Salesman Problem

The shortest path problem is a fundamental challenge in graph theory, focused on identifying the most efficient routes between nodes in a network. It stands as one of the extensively researched combinatorial optimization problems. In this paper, we explained the fundamental concepts of shortest path algorithms, with a particular emphasis on Floyd Warshall algorithm. We apply the algorithm and showed how this algorithm can be effectively employed to determine the shortest path in various scenarios. Furthermore, this paper addresses real-life applications, particularly focusing on the traveling salesman problem. Individuals often have the option to travel along different routes to reach their destination. However, selecting suboptimal routes can result in time-consuming journeys. To tackle this issue, we apply the Floyd Warshall algorithm to solve the traveling salesman problem (TSP). Additionally, we demonstrate the enhancement of the Floyd Warshall algorithm's efficiency for TSP using the rectangular algorithm. This paper concludes with a comparative analysis between the original and improved Floyd Warshall algorithms, emphasizing the computational reduction achieved through the proposed enhancements. Jagannath University Journal of Science, Volume 11, Number 1, June 2024, pp. 45−52

Research on AGV Path Planning Based on Improved Directed Weighted Graph Theory and ROS Fusion

This article addresses the common issues of insufficient computing power and path congestion for automated guided vehicles (AGVs) in real-world production environments, as well as the shortcomings of traditional path-planning algorithms that mainly consider the shortest path while ignoring vehicle turning time and stability. We propose a secondary path-planning method based on an improved directed weighted graph theory integrated with an ROS. Firstly, the production environment is modeled in detail to identify the initial position of the AGV. Secondly, the operational area is systematically divided, key nodes are selected and optimized, and a directed weighted graph is constructed with optimized weights. It is integrated with the ROS for path planning, using the Floyd algorithm to find the optimal path. The effectiveness and superiority of this method have been demonstrated through simulation verification and actual AGV operation testing. The path planning strategy and fusion algorithm proposed in this article that comprehensively considers distance and angle steering are simple and practical, effectively reducing production costs for enterprises. This method is suitable for logistics sorting and small transport AGVs with a shorter overall path-planning time, higher stability, and limited computing power, and it has reference significance and practical value.

Task allocation and path planning for multi-robot systems in intelligent warehousing

Faced with today's increasingly complex market demands, traditional manual warehouse systems are becoming inadequate, necessitating the urgent intelligent transformation and upgrading of warehouse systems. In this context, this paper aims to design a task allocation and path planning strategy for a multi-robot warehouse system to efficiently accomplish mixed single-robot and multi-robot types of warehouse tasks. The study proposes a warehouse task allocation strategy that incorporates traffic flow impact factors into the auction algorithm, optimizing task allocation by predicting robot density in various areas of the environment. For multi-robot formation tasks, a three-robot formation model based on the virtual structure method is designed. Additionally, a two-layer path planning strategy is proposed: the outer layer conducts global path planning based on the Floyd algorithm, while the inner layer resolves various collision issues through traffic rule constraints, achieving local optimal path planning. Simulation experiments conducted on the MATLAB platform show that the multi-robot system can flexibly handle mixed types of warehouse tasks, effectively reducing collision risks between robots and stagnation in dense areas, thereby improving the safety and efficiency of the multi-robot system. This study provides a reference for future research and practical applications of multi-robot systems.

Optimized dynamic service placement for enhanced scheduling in fog-edge computing environments

The traditional cloud computing model struggles to efficiently handle the vast number of Internet of Things (IoT) services due to its centralized nature and physical distance from end-users. In contrast, edge and fog computing have emerged as promising solutions for supporting latency-sensitive IoT applications by distributing computational resources closer to the data source. However, these technologies are limited by their size and computational capacities, making optimal service placement a critical challenge. This paper addresses this challenge by introducing a dynamic and distributed service placement policy tailored for edge and fog environments. By leveraging the inherent advantages of proximity in fog and edge nodes, the proposed policy seeks to enhance service delivery efficiency, reduce latency, and improve resource utilization. The proposed method focuses on optimizing the placement of high-demand services closer to the data generation sources to enhance scheduling efficiency in fog computing environments. Our method is divided into three interconnected modules. The first module is the service type estimator, which is responsible for distributing services to appropriate nodes. Here, we use the Political Optimizer (PO) as a new metaheuristic algorithm for deploying IoT services. The second module is service dependency estimator, which manages service dependencies. Here, we load dependent services near the data using a path matrix based on the Warshall algorithm. Finally, the third module is resource demand scheduling, which estimates resource demand to facilitate optimal scheduling. Here, we use a popularity-based policy to manage resource demand and service execution scheduling. Implementation results demonstrate significant improvements over existing state-of-the-art policies, highlighting the efficacy of the proposed policy in enhancing service delivery within fog-edge computing frameworks.

Electric Vehicle Charging Load Demand Forecasting in Different Functional Areas of Cities with Weighted Measurement Fusion UKF Algorithm

The forecasting of charging demand for electric vehicles (EVs) plays a vital role in maintaining grid stability and optimizing energy distribution. Therefore, an innovative method for the prediction of EV charging load demand is proposed in this study to address the downside of the existing techniques in capturing the spatial–temporal heterogeneity of electric vehicle (EV) charging loads and predicting the charging demand of electric vehicles. Additionally, an innovative method of electric vehicle charging load demand forecasting is proposed, which is based on the weighted measurement fusion unscented Kalman filter (UKF) algorithm, to improve the accuracy and efficiency of forecasting. First, the data collected from OpenStreetMap and Amap are used to analyze the distribution of urban point-of-interest (POI), to accurately classify the functional areas of the city, and to determine the distribution of the urban road network, laying a foundation for modeling. Second, the travel chain theory was applied to thoroughly analyze the travel characteristics of EV users. The Improved Floyd (IFloyd) algorithm is used to determine the optimal route. Also, a Monte Carlo simulation is performed to estimate the charging load for electric vehicle users in a specific region. Then, a weighted measurement fusion UKF (WMF–UKF) state estimator is introduced to enhance the accuracy of prediction, which effectively integrates multi-source data and enables a more detailed prediction of the spatial–temporal distribution of load demand. Finally, the proposed method is validated comparatively against traffic survey data and the existing methods by conducting a simulation experiment in an urban area. The results show that the method proposed in this paper is applicable to predict the peak hours more accurately compared to the reference method, with the accuracy of first peak prediction improved by 53.53% and that of second peak prediction improved by 23.23%. The results not only demonstrate the high performance of the WMF–UKF prediction model in forecasting peak periods but also underscore its potential in supporting grid operations and management, which provides a new solution to improving the accuracy of EV load demand forecasting.

GPU-accelerated parallel all-pair shortest path routing within stochastic road networks

All-pair shortest path routing within stochastic road networks is often more complicated and computationally challenging than routing in deterministic networks because uncertainties in travel time are introduced. We develop and test a GPU-enabled approach to resolve this computational challenge. This approach is based on a simulation framework that includes four steps: simulation of road networks impedances, computation of candidate paths using an all-pair shortest path algorithm, travel time estimation across candidate paths, and all-pair optimal path calculations. We developed GPU algorithms to accelerate the second and third steps, which are computationally demanding for large road networks. We used the road network of Wuhan, China as a case study. Our experiments indicate that the GPU approach leads to thousands of times in improvement of acceleration, which makes all-pair shortest path routing within stochastic road networks computationally feasible.

Modelling the Shortest Path for Inner Warehouse Travelling Using the Floyd–Warshall Algorithm

Modelling the Shortest Path for Inner Warehouse Travelling Using the Floyd–Warshall Algorithm

Solution to the problem of setting up medical points and road maintenance in mountainous areas based on optimization

Assume there are 100 villages in a mountainous area. To improve the medical standards of the local residents, three medical points need to be established in several villages, and the roads need to be repaired. This paper modifies the Floyd algorithm to derive all the shortest paths between nodes. Based on the Prim algorithm, a minimum spanning tree model is constructed to find the road maintenance method with the lowest cost; a nested greedy algorithm is used to construct an optimization model under multiple variables, effectively solving the problem of setting up medical points and road maintenance in mountainous areas.

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.

Railway alignment optimization in regions with densely-distributed obstacles based on semantic topological maps

Railway alignment development in a study area with densely-distributed obstacles, in which regions favorable for alignments are isolated (termed an isolated island effect, i.e., IIE), is a computation-intensive and time-consuming task. To enhance search efficiency and solution quality, an environmental suitability analysis is conducted to identify alignment-favorable regions (AFRs), focusing the subsequent alignment search on these areas. Firstly, a density-based clustering algorithm (DBSCAN) and a specific criterion are customized to distinguish AFR distribution patterns: continuously-distributed AFRs, obstructed effects, and IIEs. Secondly, a study area characterized by IIEs is represented with a semantic topological map (STM), integrating between-island and within-island paths. Specifically, between-island paths are derived through a multi-directional scanning strategy, while within-island paths are optimized using a Floyd-Warshall algorithm. To this end, the intricate alignment optimization problem is simplified into a shortest path problem, tackled with conventional shortest path algorithms (of which Dijkstra’s algorithm is adopted in this work). Lastly, the proposed method is applied to a real case in a mountainous region with karst landforms. Numerical results indicate its superior performance in both construction costs and environmental suitability compared to human designers and a prior alignment optimization method.

Rewc-GNN Algorithm for the Property Prediction of Large-Scale Crystals.

The space group of a crystal describes the symmetry and periodic arrangement of its structure. As the fundamental element in the structure, it plays a vital role in determining the physical and chemical properties of crystals. The investigation of crystal space group information allows for the prediction of material properties, thereby providing guidance for material design and synthesis to enhance their performance or functionality. Currently prevalent first-principles-based computational methods exhibit good accuracy, but they rely heavily on computing resources, greatly limiting the efficiency of material screening. In this paper, our study is oriented toward the prediction the spatial group of crystals, and an algorithm named Rewc, based on graph neural networks (GNNs) is proposed. This algorithm encodes all atoms and the interactions between atoms in the crystal as features by combining Floyd algorithm and k-hop message passing and employs multilayer convolutional networks to extract connections between k layers. This allows for the automatic learning of more representative atomic vector representations through iterations of feature information for each atom and its neighbors. Experimental results demonstrate that the Rewc framework exhibits reliable accuracy and good generalization capabilities in predicting the crystal structure compared to previous GNN methods.

Projection methods for finding the greatest element of the intersection of max-closed convex sets

We focus on the problem of finding the greatest element of the intersection of max-closed convex sets. For this purpose, we analyze the famous method of cyclic projections and show that, if this method is suitably initialized and applied to max-closed convex sets, it converges to the greatest element of their intersection. Moreover, we propose another projection method, called the decreasing projection, which turns out both theoretically and practically preferable to Euclidean projections in this particular case. Next, we argue that several known algorithms, such as Bellman-Ford and Floyd-Warshall algorithms for shortest paths or Gauss-Seidel variant of value iteration in Markov decision processes, can be interpreted as special cases of iteratively applying decreasing projections onto certain max-closed convex sets. Finally, we link decreasing projections (and thus also the aforementioned algorithms) to bounds consistency in constraint programming.

Scaled consensus of heterogeneous multi-agent systems under asynchronous DoS attacks

This paper addresses the issue of scaled consensus in heterogeneous multi-agent systems (HMASs) under asynchronous Denial-of-Service (DoS) attacks. In the system structure, our exploration centers on the challenge of achieving scaled consensus in HMASs. The aim is to guarantee that the states of both first-order and second-order agents within the system reach predetermined scalar values, aligning with diverse real-world scenarios. Subsequently, the security of the system in directed communication topology under asynchronous DoS attack is also taken into account. To achieve above research objectives, an impulsive control scheme based on topology switching is proposed and a corresponding algorithm for determining the pulse moments based on the Floyd algorithm is devised. This scheme utilizes the topology switching caused by asynchronous DoS attacks as the driving force for impulsive control. Furthermore, leveraging the correlation property of random matrices, we derive the sufficient conditions for the system to achieve secure control. Finally, a numerical simulation is provided to validate the effectiveness of the protocol and the accuracy of conclusions.

Predictive Model for EV Charging Load Incorporating Multimodal Travel Behavior and Microscopic Traffic Simulation

A predictive model for the spatiotemporal distribution of electric vehicle (EV) charging load is proposed in this paper, considering multimodal travel behavior and microscopic traffic simulation. Firstly, the characteristic variables of travel time are fitted using advanced techniques such as Gaussian mixture distribution. Simultaneously, the user’s multimodal travel behavior is delineated by introducing travel purpose transfer probabilities, thus establishing a comprehensive travel spatiotemporal model. Secondly, the improved Floyd algorithm is employed to select the optimal path, taking into account various factors including signal light status, vehicle speed, and the position of starting and ending sections. Moreover, the approach of multi-lane lane change following and the utilization of cellular automata theory are introduced. To establish a microscopic traffic simulation model, a real-time energy consumption model is integrated with the aforementioned techniques. Thirdly, the minimum regret value is leveraged in conjunction with various other factors, including driving purpose, charging station electricity price, parking cost, and more, to simulate the decision-making process of users regarding charging stations. Subsequently, an EV charging load predictive framework is proposed based on the approach driven by electricity prices and real-time interaction of coupled network information. Finally, this paper conducts large-scale simulations to analyze the spatiotemporal distribution characteristics of EV charging load using a regional transportation network in East China and a typical power distribution network as case studies, thereby validating the feasibility of the proposed method.

Rethinking LEO constellations routing

SummaryThis study investigates the unsplittable multicommodity flow (UMCF) as a routing algorithm for LEO constellations. Usually, LEO routing schemes enable the Floyd–Warshall algorithm (shortest path) to minimize the end‐to‐end latency of the flows crossing the constellation. We propose to solve the UMCF problem associated with the system as a solution for routing over LEO. We use a heuristic algorithm based on randomized rounding known in the optimization literature to efficiently solve the UMCF problem. Furthermore, we explore the impact of choosing the first/last hop before entering/exiting the constellation. Using network simulation over Telesat constellation, we show that UMCF maximizes the end‐to‐end links usage, providing better routing while minimizing the delay and the congestion level, which is an issue today over new megaconstellations.

Analysis of optimization waste transportation using saving matrix and floyd warshall methods in Binjai

Analysis of optimization waste transportation using saving matrix and floyd warshall methods in Binjai

Implementation of Shortest Path Algorithms

An important area of study that models the relationships between items is called graph theory. The shortest path between two objects is one of the most important concepts in graph theory. Many algorithms, such as Dijkstra's Algorithm, Prim’s Algorithm, Floyd Warshall Algorithm have been created for this purpose.