Time-dependent Dijkstra’s algorithm under bipolar neutrosophic fuzzy environment

2021 ◽  
pp. 1-10
Author(s):  
Esra Çakır ◽  
Ziya Ulukan ◽  
Tankut Acarman
Keyword(s):  
Travel Time ◽  
Shortest Path ◽  
Real Life ◽  
Time Dependent ◽  
Dijkstra’S Algorithm ◽  
Fuzzy Environment ◽  
Dijkstra's Algorithm ◽  
Fuzzy Graphs ◽  
Negative Statements ◽  
Shortest Path Algorithms

Determining the shortest path and calculating the shortest travel time of a complex networks are important for transportation problems. Numerous approaches has been developed to search shortest path on graphs, and one of the well-known is the Dijkstra’s label correcting algorithm. Dijkstra’s approach is capable of determining shortest path of directed or undirected graph with non-negative weighted arcs. To handle with uncertainty in real-life, the Dijkstra’s algorithm should be adapted to fuzzy environment. The weight of arc -which is the vague travel time between two nodes- can be expressed in bipolar neutrosophic fuzzy sets containing positive and negative statements. In addition, the weights of arcs in bipolar neutrosophic fuzzy graphs can be affected by time. This study proposes the extended Dijkstra’s algorithm to search the shortest path and calculate the shortest travel time on a single source time-dependent network of bipolar neutrosophic fuzzy weighted arcs. The proposed approach is illustrated, and the results demonstrate the validity of the extended algorithm. This article is intended to guide future shortest path algorithms on time-dependent fuzzy graphs.

scholarly journals Shortest Path with Dynamic Weight Implementation using Dijkstra’s Algorithm

2016 ◽  
Vol 7 (3) ◽  
pp. 161 ◽  
Author(s):  
Elizabeth Nurmiyati Tamatjita ◽  
Aditya Wikan Mahastama
Keyword(s):  
Shortest Path ◽  
Real World ◽  
Minimum Cost ◽  
Dijkstra’S Algorithm ◽  
Traffic Condition ◽  
The Real ◽  
Dijkstra's Algorithm ◽  
Dynamic Weight ◽  
Shortest Path Algorithms

Shortest path algorithms have been long applied to solve daily problems by selecting the most feasible route with minimum cost or time. However, some of the problems are not simple. This study applied the case using Dijkstra's algorithm on a graph representing street routes with two possible digraphs: one-way and twoway. Each cost was able to be changed anytime, representing the change in traffic condition. Results show that the usage of one way digraph in mapping the route does make the goal possible to reach, while the usage of twoway digraph may cause confusion although it is probably the possible choice in the real world. Both experiments showed that there are no additional computation stresses in re-calculating the shortest path while going halfway to reach the goal.

scholarly journals Finding Your Way: Shortest Paths on Networks

2020 ◽  
Author(s):  
Teresa Rexin ◽  
Mason A. Porter
Keyword(s):  
Travel Time ◽  
Shortest Path ◽  
Real World ◽  
Shortest Paths ◽  
Travel Distance ◽  
Dijkstra’S Algorithm ◽  
Total Cost ◽  
The Real ◽  
Dijkstra's Algorithm ◽  
The Cost

Traveling to different destinations is a big part of our lives. How do we know the best way to navigate from one place to another? Perhaps we could test all of the different ways of traveling between two places, but another method is using mathematics and computation to find a shortest path. We discuss how to find a shortest path and introduce Dijkstra’s algorithm to minimize the total cost of a path, where the cost may be the travel distance or travel time. We also discuss how shortest paths can be used in the real world to save time and increase traveling efficiency.

scholarly journals Dijkstra Algorithm for Determining the Shortest Path in the Case of Seven Hotels in Manado City Towards Manado’s Sam Ratulangi Airport.

d'CARTESIAN ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 158
Author(s):  
Yohana Permata Hutapea ◽  
Chriestie E.J.C. Montolalu ◽  
Hanny A.H. Komalig
Keyword(s):  
Graph Theory ◽  
Travel Time ◽  
Shortest Path ◽  
Travel Distance ◽  
Dijkstra’S Algorithm ◽  
Dijkstra Algorithm ◽  
Google Maps ◽  
Transportation Mode ◽  
Dijkstra's Algorithm ◽  
The Difference

Manado city has many notable tourist sites, resulting in the increase of the number of tourists visiting every year. Tourists require hotels with adequate facilities for their stay, such as 4-star hotels. After visiting Manado, tourists go back to where they come from. One of the transportation mode being used is airplanes. They then need a path to go through and not the usual one; they need the shortest path to get to Sam Ratulangi airport. Based on previous research, the shortest path is modeled by Graph Theory. Hotels will be represented as vertices, and the path from each hotels and to the airport will be represented as edges. The shortest path are searched by using Dijkstra’s Algorithm then will see the difference to shortest path from google maps. Based on the analysis results, Dijkstra’s Algorithm selects the shortest path with the smallest weight. The difference between Dijkstra’s Algorithm and google maps can be concluded that, in determining the shortest path used for the trip from the 4-star hotel to the airport, Dijkstra’s Algorithm is emphasized towards short travel distance, whereas google maps is emphasized more in short travel time.

scholarly journals Journey to Crime Using Dijkstra’s Algorithm

2017 ◽  
Vol 1 (1) ◽  
pp. 1-14
Author(s):  
J. O. Olusina ◽  
J. B. Olaleye
Keyword(s):  
Information Systems ◽  
Geographic Information Systems ◽  
Shortest Path ◽  
Geographic Information ◽  
Service Area ◽  
Dijkstra’S Algorithm ◽  
Crime Mapping ◽  
Cost Matrix ◽  
Dijkstra's Algorithm ◽  
Journey To Crime

This paper describes some benefits of crime mapping in a Geographic Information Systems (G.I.S.) environment. The underlining principle of Journey to Crime was discussed. Crime Spots and Police Stations in the study area were mapped, Shortest-Path, Closest Facility, Service Area and OD (Origin – Destination) Cost Matrix were determined based on Dijkstra's Algorithm. Results show that the distribution of police stations does not correspond with the spread of crime spots.

A Different Approach for Solving the Shortest Path Problem Under Mixed Fuzzy Environment

2020 ◽  
Vol 9 (2) ◽  
pp. 132-161 ◽  
Author(s):  
Ranjan Kumar ◽  
Sripati Jha ◽  
Ramayan Singh
Keyword(s):  
Linear Programming ◽  
Shortest Path ◽  
Path Length ◽  
Real Life ◽  
Shortest Path Problem ◽  
Fuzzy Linear Programming ◽  
Fuzzy Membership ◽  
Fuzzy Membership Function ◽  
Membership Functions ◽  
Fuzzy Environment

The authors present a new algorithm for solving the shortest path problem (SPP) in a mixed fuzzy environment. With this algorithm, the authors can solve the problems with different sets of fuzzy numbers e.g., normal, trapezoidal, triangular, and LR-flat fuzzy membership functions. Moreover, the authors can solve the fuzzy shortest path problem (FSPP) with two different membership functions such as normal and a fuzzy membership function under real-life situations. The transformation of the fuzzy linear programming (FLP) model into a crisp linear programming model by using a score function is also investigated. Furthermore, the shortcomings of some existing methods are discussed and compared with the algorithm. The objective of the proposed method is to find the fuzzy shortest path (FSP) for the given network; however, this is also capable of predicting the fuzzy shortest path length (FSPL) and crisp shortest path length (CSPL). Finally, some numerical experiments are given to show the effectiveness and robustness of the new model. Numerical results show that this method is superior to the existing methods.

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