Classical Dijkstra Algorithm Research Articles

Fuzzy Dijkstra Algorithm to Find the Shortest Path

Shortest path for crisp numbers can be found efficiently using the Dijkstra’s algorithm. There are some uncertain conditions in the environment which introduces a fuzzy number for the distances between two nodes. A classical Dijkstra algorithm is modified to fuzzy Dijkstra algorithm to address the problem. Graded mean integration is used to enhance the algorithm by calculating and comparing the path length between two nodes when the arc length is fuzzy. A sample network is shown to understand the shortest path for fuzzy numbers. Key Words: dijkstra’s algorithm, fuzzy numbers, graded mean integration

Efficient fastest-path computations for road maps

In the age of real-time online traffic information and GPS-enabled devices, fastest-path computations between two points in a road network modeled as a directed graph, where each directed edge is weighted by a “travel time” value, are becoming a standard feature of many navigation-related applications. To support this, very efficient computation of these paths in very large road networks is critical. Fastest paths may be computed as minimal-cost paths in a weighted directed graph, but traditional minimal-cost path algorithms based on variants of the classical Dijkstra algorithm do not scale well, as in the worst case they may traverse the entire graph. A common improvement, which can dramatically reduce the number of graph vertices traversed, is the A* algorithm, which requires a good heuristic lower bound on the minimal cost. We introduce a simple, but very effective, heuristic function based on a small number of values assigned to each graph vertex. The values are based on graph separators and are computed efficiently in a preprocessing stage. We present experimental results demonstrating that our heuristic provides estimates of the minimal cost superior to those of other heuristics. Our experiments show that when used in the A* algorithm, this heuristic can reduce the number of vertices traversed by an order of magnitude compared to other heuristics.

Dijkstra and Bidirectional Dijkstra on Determining Evacuation Routes

Determination of the best path or often called the shortest path finding is a method that has many benefits and can be applied in various cases and fields of science. In previous studies, authors have developed the shortest path finding program using various algorithms, such as held-karp, iterative deepening search, bidirectional depth first search and depth limited search. In this research author implements shortest path finding on information system for determining fire disaster evacuation route using Dijkstra and bidirectional Dijkstra. The program was developed based on web using vuetify.js framework. Both algorithms were tested on several datasets and the results will be compared to find out the strengths and weaknesses. Based on the research, the algorithm was successfully developed based on the web using the vuetify.js framework and successfully tested on several datasets, it is known that 40% of the test results show that bidirectional Dijkstra is better than Dijkstra, 10% vice versa and 50% get the same results from both algorithms. From this comparison it can be concluded that the bidirectional Dijkstra algorithm is better than Dijkstra. This research succeeded in proving that the bidirectional Dijkstra algorithm can produce a better route than the standard or classic Dijkstra algorithm.

RETRACTED ARTICLE: Research on the construction and simulation of PO-Dijkstra algorithm model in parallel network of multicore platform

The development of multicore hardware has provided many new development opportunities for many application software algorithms. Especially, the algorithm with large calculation volume has gained a lot of room for improvement. Through the research and analysis, this paper has presented a parallel PO-Dijkstra algorithm for multicore platform which has split and parallelized the classical Dijkstra algorithm by the multi-threaded programming tool OpenMP. Experiments have shown that the speed of PO-Dijkstra algorithm has been significantly improved. According to the number of nodes, the completion time can be increased by 20–40%. Based on the improved heterogeneous dual-core simulator, the Dijkstra algorithm in Mi Bench is divided into tasks. For the G.72 encoding process, the number of running cycles using “by function” is 34% less than using “divided by data,” while the power consumption is only 83% of the latter in the same situation. Using “divide by data” will reduce the cost and management difficulty of real-time temperature. Using “divide by function” is a good choice for streaming media data. For the Dijkstra algorithm, the data is data without correlation, so using a simpler partitioning method according to the data partitioning can achieve good results. Through the simulation results and the analysis of the results of real-time power consumption, we conclude that for data such as strong data correlation of streaming media types, using “divide by function” will have better performance results; for data types where data correlation is not very strong, the effect of using “divide by data” is even better.

ANALYSIS OF UNICAST ROUTING IN COGNITIVE NETWORKS USING DDCR OVER TRADITIONAL NETWORKS

As there is rapid development of wireless and mobile communications, limited opening band is unable to meet the growing usage of mobile communication. In order to make better use of scarce spectrum resources, Cognitive Radio (CR) has been proposed to exploit underutilization portions of the spectrum, which is capable of interference sensing, environmental learning, and dynamic spectrum access. In this paper, a new routing algorithm for Cognitive Radio networks has been proposed. The algorithm is based on atomic time, known as DDCR (DillyDally Cognitive Routing). The DillyDally path is found by calculating the transmission delay of given packets on every link (weighted link). The transmission delays are found by using classic Dijkstra algorithm. Simulation results show the End-End delay of DDCR is less than that of the traditional routing algorithm. Thereby the network performance is improved.

Electric vehicle‐routing problem with charging demands and energy consumption

An electric vehicle-routing problem (EVRP) is developed to settle some operation distribution troubles such as battery energy limitations and difficulties in finding charging stations for electric vehicles (EVs). Meanwhile, in view of realistic traffic conditions and features of EVs, energy consumption with travel speed and cargo load is considered in the EVRP model. Moreover, to avoid the depletion of all battery power and ensure safe operation, EVs with insufficient battery power can be recharged at charging stations many times in transit. In conclusion, a large, realistic case study with the road network of Beijing urban, 100 customers and 30 charging stations is conducted to test the performance of the model and obtain an optimal operation scheme consisted of the routes, charging plan and driving paths. The EVRP model is solved based on the hybrid genetic algorithm to get the routes and charging plan. The dynamic Dijkstra algorithm with some improvements over the classical Dijkstra algorithm is applied to find the driving paths called the most energy efficient paths between any two adjacent visited nodes in the routes.

A new time-dependent shortest path algorithm for multimodal transportation network

Abstract: The shortest path problem is a classical combinatorial optimization problem with countless real-life applications. Numerous algorithms have been proposed to solve the SPP since the classical Dijkstra algorithm, as well as new approaches to improve the algorithms’ optimality. But according to the real-world transport conditions, researchers began to study variants of this problem which include the time-dependent SPP and the multimodal networks. In this paper, we introduce our new time-dependent shortest path algorithm for multimodal transportation network. The proposed algorithm is a goal-oriented single-source single-destination algorithm. It takes into account the concept of “closeness” to the target node as heuristic to drive the search towards its destination. The optimality of the algorithm is principally based on computing a virtual path which is basically an Euclidean distance from the source to the target aiming at a restriction of the search space.

Quadrotor Obstacle Avoidance Based on Integral Backstepping

This paper addressed obstacle avoidance problem of a quadrotor in outdoor environment. Path planning was finished by employing classical Dijkstra algorithm and the controller of the quadrotor adopted integral backstepping method. In order to get a smooth trajectory with time optimal and acceleration constraints properties, quantic polynomials were utilized to generate trajectory file. The scheme is particularly practical and useful because of its small computation burden and feasibility. Simulations have been done to verify the performance of the whole system. As a result, the quadrotor successfully tracked the path without any collision with obstacles except that there are some small error in the final part of position tracking performance (±1m) and some small delay in the attitude tracking about 0.3 ms. In conclusion, the proposed method showed acceptable performance for quadrotor obstacle avoidance.

An initial analysis of packet function-aware extension to Dijkstra algorithm for wireless networks

In this paper, we promote the packet function (e.g., packet size) -aware extension of the Dijkstra algorithm (i.e., PFA_SPF) as a base algorithm where any routing protocol can evolve it and integrate it with appropriate routing metrics. In particular, we propose a generic algorithm for packet function-aware path setup for multi-hop networks. The algorithm is based on a generic and novel extension of the classical Dijkstra algorithm in which the cost of each link is a non-negative-valued function of packet parameter(s) (e.g., packet size) rather than a scalar value. The algorithm minimizes the sum of the cost functions (e.g., total transmission delay or total energy consumption) experienced by each packet (e.g., maximizing the throughput) from the source to the destination node. We did initial analysis based on simulation of the algorithm for various random multi-hop wireless networks (e.g., 802.11), utilizing realistic link delay models. Finally, we demonstrate the initial significant potential performance improvements of our algorithm over the existing prior art.

The Shortest-Path Problem: Analysis and Comparison of Methods

Many applications in different domains need to calculate the shortest-path between two points in a graph. In this paper we describe this shortest path problem in detail, starting with the classic Dijkstra's algorithm and moving to more advanced solutions that are currently applied to road network routing, including the use of heuristics and precomputation techniques. Since several of these improvements involve subtle changes to the search space, it may be difficult to appreciate their benefits in terms of time or space requirements. To make methods more comprehensive and to facilitate their comparison, this book presents a single case study that serves as a common benchmark. The paper also compares the search spaces explored by the methods described, both from a quantitative and qualitative point of view, and including an analysis of the number of reached and settled nodes by different methods for a particular topology.

A flexible black-start network partitioning strategy considering subsystem recovery time balance

Summary When black out occurs, the whole power grid is divided into several subsystems to increase the efficiency and shorten the duration of power system restoration by using parallel restoration strategy. Therefore, reasonable network partitioning in black start phase after large-scale power failures is important in both theory and practice. In this paper, a flexible black start network partitioning strategy considering the subsystem recovery time balance is proposed. Based on the rules of zone division and analyzing initial black start partitioning model of subsystem shortest recovery path, subsystem recovery time balance index is defined to represent disparity of every subsystem's restoration process. Meanwhile, a flexible factor of total recovery time is introduced as part of objective function with the time balance index, aiming at reducing waiting time of the synchronization operation and strengthens efficiency of black start at the cost of the least total time increment. The classic Dijkstra algorithm and improved genetic algorithm are employed to obtain the optimal restoration plan in the paper. Case study on IEEE 118-bus test system shows the validity of the methodology proposed. Copyright © 2014 John Wiley & Sons, Ltd.

A REFINEMENT OF DIJKSTRA’S ALGORITHM FOR EXTRACTION OF SHORTEST PATHS IN GENERALIZED REAL TIME-MULTIGRAPHS

The networks of the present day communication systems, be it a public road transportation system or a MANET or an Adhoc Network, frequently face a lot of uncertainties in particular regarding traffic jam, flood or water logging or PWD maintenance work (in case of public road network), attack or damage from internal or external agents, sudden failure of one or few nodes. Consequently, at a real instant of time, the existing links/arcs of a given network (graph) are not always in their original/excellent condition physically or logically, rather in a weaker condition, or even sometimes disabled or blocked temporarily and waiting for maintenance/repair; and hence ultimately causing delay in communication or transportation. We do not take any special consideration if few of the links be in a better condition at the real time of communication, we consider only such cases where few links are in inferior condition (partially or fully damaged). The classical Dijkstra's algorithm to find the shortest path in graphs is applicable only if we assume that all the links of the concerned graph are available at their original (ideal) condition at that real time of communication, but at real time scenario it is not the case. Consequently, the mathematically calculated shortest path extracted by using Dijkstra's algorithm may become costlier (even in-feasible in some cases) in terms of time and/or in terms of other overhead costs; whereas some other path may be the most efficient or most optimal. Many real life situations of communication network or transportation network cannot be modeled into graphs, but can be well modeled into multigraphs because of the scope of dealing with multiple links (or arcs) connecting a pair of nodes. The classical Dijkstra's algorithm to find the shortest path in graphs is not applicable to multigraphs. In this study the authors make a refinement of the classical Dijkstra's algorithm to make it applicable to directed multigraphs having few links partially or fully damaged. We call such type of multigraphs by GRT-multigraphs and the modified algorithm is called by Dijkstra's Algorithm for GRT-Multigraphs (DA-GRTM, in short). The DA-GRTM outputs the shortest paths and the corresponding min cost in a GRT-multigraph at real time and thus the solution is a real time solution, not an absolute solution. It is claimed that DA-GRTM will play a major role in the present day communication systems which are in many cases giant networks, in particular in those networks which cannot be modeled into graphs but into multigraphs.

Research on Optimization of Distribution Routes for Fresh Agricultural Products Based on Dijkstra Algorithm

According to the specialty of fresh agricultural products, a delivery model was established. The model consists of single distribution center and multiple demand points. The integrated cost which consists of transport cost and time cost was taken as the optimization objective. It is used as weight in classic Dijkstra algorithm instead of distance. We also used a case study to illustrate saving method and classic Dijkstra algorithm with integrated cost. The comparison was conducted by calculating the integrated cost of optimal routes separately. Following the comparison, we draw a conclusion that in the field of fresh agricultural products distribution, classic Dijkstra algorithm which takes integrated cost as optimization objective is superior to the saving method in which distance is the optimization objective.

Dynamic lightpath provisioning in optical WDM mesh networks with asymmetric nodes

The wavelength selective switch-based reconfigurable optical add/drop multiplexers is a promising switching equipment for future reconfigurable wavelength-division multiplexing (WDM) mesh networks. However, its asymmetric switching property complicates the optimal routing and wavelength assignment problem. In an asymmetric switching scenario, using the classic Dijkstra's algorithm can lead to invalid paths traversing unconnected ports of an asymmetric node. To solve this problem, we propose both link-state (LS) and distance vector (DV) schemes for dynamic lightpath provisioning in optical WDM mesh networks with asymmetric nodes. The proposed LS schemes include the asymmetric switching-aware (ASA) Dijkstra's algorithm, the $$K$$ -shortest path-based algorithm, and the entire path searching (EPS) algorithm. Simulation results show that the ASA-Dijkstra's algorithm will bring notable improvement of the blocking performance with low computational complexity, while the EPS algorithm has much higher complexity and is not suitable to be employed in large-scale networks. On the other hand, our proposed DV solution, i.e., the information diffusion-based routing (IDBR), can achieve the lowest blocking probability with the lowest computational complexity. Moreover, IDBR does not require the distribution of local asymmetric switching information like the LS schemes, thus having a high level of topology confidentiality.

An Algorithm for Extracting Intuitionistic Fuzzy Shortest Path in a Graph

We consider an intuitionistic fuzzy shortest path problem (IFSPP) in a directed graph where the weights of the links are intuitionistic fuzzy numbers. We develop a method to search for an intuitionistic fuzzy shortest path from a source node to a destination node. We coin the concept of classical Dijkstra's algorithm which is applicable to graphs with crisp weights and then extend this concept to graphs where the weights of the arcs are intuitionistic fuzzy numbers. It is claimed that the method may play a major role in many application areas of computer science, communication network, transportation systems, and so forth. in particular to those networks for which the link weights (costs) are ill defined.

The Study of Diffraction Ray Tracing on the Surface of Airplane

This article makes the surface of airplane into quadrilateral gridding by using the method of discrete gridding generation, and calculates the data of gridding by using the classical Dijkstra algorithm (local algorithm) which can seek the shortest path from the start point and the end point. With that we can achieve diffraction ray tracing. This method can be used for any convex surface of the diffraction ray tracing.

A Fast Algorithm to Find All-Pairs Shortest Paths in Complex Networks

Finding shortest paths is a fundamental problem in graph theory, which has a large amount of applications in many areas like computer science, operations research, network routing and network analysis. Although many exact and approximate algorithms have been proposed, it is still a time-consuming task to calculate shortest paths for large-scale networks with tremendous volume of data available in recent years. In this paper, we find that the classic Dijkstra's algorithm can be improved by simple modification. We propose a fast algorithm which utilize the preiously-calculated results to accelerate the latter calculation. Simple optimization strategies are also proposed with consideration of characteristics of scale-free complex networks. Our experimental results show that the average running time of our algorithm is lower than the Dijkstra's algorithm by a factor relating to the connection probability in random networks of ER model. The performance of our algorithm is significantly better than the Dijkstra's algorithm in scale-free networks generated by the AB model. The results show that the time complexity is reduced to about O(n2.4) in scalefree complex networks. When the optimization strategies are applied, the algorithm performance is further improved slightly in scale-free networks.

An Efficient Constrained Shortest Path Algorithm for Traffic Navigation

FCD-based traffic navigation system is getting more and more attention from countries all over the world. Shortest path algorithm is one of the key techniques of a traffic navigation system. Since classical Dijkstra algorithm and heuristic A* algorithm cannot support some constrained conditions in practice, and existing algorithms supporting constraints require the road network to be modified ahead and have low efficiency. The paper studies the model of road network, and analyzes two types of constraints, one-way street and intersection turning prohibitions, then proposes the constrained A* algorithm and gives the Heuristic function. Finally, the paper tests and analyzes the algorithm, and evaluation performance of the prototype system which employs it. The result shows that the algorithm’s efficiency is fairly good.

Construction of Vehicle Dispatching Service System Based on GIS

Construction of nice vehicle dispatching service system is the key of urban intelligence modern transportation management. The three-tier architecture and the development platform of the system are introduced in the paper. The key technologies of implementation are discussed in detail. In key technologies, real-time signal is decoded by using control of serial communication in order to implement real-time position and optimization of classical Dijkstra algorithm is realized in the paper. System can obtain all kinds of information about vehicle rapidly and provide the effective service for the vehicle management and development.

Joint Routing and Spectrum Assignment Algorithm in Cognitive Radio Networks

Aiming to the shortcoming of traditional route protocols in cognitive radio networks, joint cognitive routing and spectrum assignment (JCRSA) algorithm was proposed. According to the characteristic of cognitive network, the most capacity channel is selected as communication channel on every link, and JCRSA calculates the transmission delay on every link for a given packet, and then uses classic Dijkstra algorithm to find the smallest transmission delay route. According to the route table, spectrum is assigned on every link. Simulation results show that the End-to-End delay of JCRSA is less than that of traditional routing algorithm.