Finding the shortest path for a Hypergraph

2021 ◽  
pp. 2150120
Author(s):  
G. H. Shirdel ◽  
B. Vaez-Zadeh
Keyword(s):  
Graph Theory ◽  
Shortest Path ◽  
Complex Structure ◽  
Dijkstra Algorithm ◽  
Clique Graph ◽  
One To One

A hypergraph is given by [Formula: see text], where [Formula: see text] is a set of vertices and [Formula: see text] is a set of nonempty subsets of [Formula: see text], the member of [Formula: see text] is named hyperedge. So, a hypergraph is a nature generalization of a graph. A hypergraph has a complex structure, thus some researchers try to transform a hypergraph to a graph. In this paper, we define two graphs, Clique graph and Persian graph. These relations are one to one. We can find the shortest path between two vertices in a hypergraph [Formula: see text], by using the Dijkstra algorithm in graph theory on the graphs corresponding to [Formula: see text].

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.

Utilizing Restricted Direction Strategy and Binary Heap Technology to Optimize Dijkstra Algorithm in WebGIS

2009 ◽  
Vol 419-420 ◽  
pp. 557-560 ◽  
Author(s):  
Rui Li
Keyword(s):  
Shortest Path ◽  
Operating Efficiency ◽  
Dijkstra Algorithm ◽  
Shortest Path Algorithm ◽  
Research Focus ◽  
Network Information ◽  
The Core ◽  
Highway Network ◽  
Core Issue ◽  
Storage Structures

Shortest path is the core issue in application of WebGIS. Improving the efficiency of the algorithm is an urgent requirement to be resolved at present. By the lossy algorithm analyzing, which is the current research focus of the shortest path algorithm to optimize, utilizing adjacency table of storage structures, restricted direction strategy and binary heap technology to optimize the algorithm, thereby reduce the scale of algorithm to improve the operating efficiency of algorithm. This scheme has been applied in the simulation of the data downloaded from the Guangdong Provincial Highway Network Information System and satisfactory results have been obtained.

scholarly journals A Relation of Dominance for the Bicriterion Bus Routing Problem

2017 ◽  
Vol 27 (1) ◽  
pp. 133-155 ◽  
Author(s):  
Jacek Widuch
Keyword(s):  
Graph Theory ◽  
Shortest Path ◽  
Experimental Tests ◽  
Partial Solution ◽  
Estimation Methods ◽  
Final Solution ◽  
Routing Problem ◽  
Variable Weights ◽  
Bus Routing ◽  
The Cost

Abstract A bicriterion bus routing (BBR) problem is described and analysed. The objective is to find a route from the start stop to the final stop minimizing the time and the cost of travel simultaneously. Additionally, the time of starting travel at the start stop is given. The BBR problem can be resolved using methods of graph theory. It comes down to resolving a bicriterion shortest path (BSP) problem in a multigraph with variable weights. In the paper, differences between the problem with constant weights and that with variable weights are described and analysed, with particular emphasis on properties satisfied only for the problem with variable weights and the description of the influence of dominated partial solutions on non-dominated final solutions. This paper proposes methods of estimation a dominated partial solution for the possibility of obtaining a non-dominated final solution from it. An algorithm for solving the BBR problem implementing these estimation methods is proposed and the results of experimental tests are presented.

scholarly journals Research on Network Drop Truck Scheduling Based on Dijkstra Algorithm

2019 ◽  
Vol 25 ◽  
pp. 01001
Author(s):  
Yang Li ◽  
Luhua Zhao ◽  
Entong Wang
Keyword(s):  
Shortest Path ◽  
Freight Transportation ◽  
Vehicle Scheduling ◽  
Dijkstra Algorithm ◽  
Vehicle Dispatching ◽  
Truck Scheduling ◽  
Important Link ◽  
Transportation Route ◽  
Network Type

In view of the important link of vehicle dispatching under the network-type trailer-drop transport strategy of vehicle sharing, this paper uses JAVA to implement the Dijkstra algorithm for the transportation route based on the distance between stations and the demand of freight transportation, so as to find the shortest path, and then through the model of trailer-drop transport, an example is given. The advantages of this vehicle scheduling are analyzed.

The Primitive Exponent of a Class of Special Nonnegative Matrix Pairs

2014 ◽  
Vol 915-916 ◽  
pp. 1296-1299
Author(s):  
Mei Jin Luo
Keyword(s):  
Graph Theory ◽  
Nonnegative Matrix ◽  
One To One

There is a one-to-one relationship between nonnegative matrix pairs and two-colored digraph, so the problem of matrices can be changed into that of graphics to be solved. With the knowledge of graph theory, by studying the associated directed digraph of a class of special nonnegative matrix pairs, that is a class of two-colored digraphs whose uncolored digraph have vertices and consists of one-cycle and one-cycle are considered. The exponent and characteristic of extreme two-colored digraphs are given.

An Efficient K-Shortest Paths Based Routing Algorithm

2012 ◽  
Vol 532-533 ◽  
pp. 1775-1779
Author(s):  
Jian Lian ◽  
Yan Zhang ◽  
Cheng Jiang Li
Keyword(s):  
Computer Networks ◽  
Shortest Path ◽  
Traffic Engineering ◽  
Routing Algorithm ◽  
Shortest Paths ◽  
Routing Algorithms ◽  
Dijkstra Algorithm ◽  
Link State

We present an efficient K-shortest paths routing algorithm for computer networks. This Algorithm is based on enhancements to currently used link-state routing algorithms such as OSPF and IS-IS, which are only focusing on finding the shortest path route by adopting Dijkstra algorithm. Its desire effect to achieve is through the use of K-shortest paths algorighm, which has been implemented successfully in some fileds like traffic engineering. The correctness of this Algorithm is discussed at the same time as long as the comparison with OSPF.

The Study of Diffraction Ray Tracing on the Surface of Airplane

2012 ◽  
Vol 433-440 ◽  
pp. 6345-6349
Author(s):  
Li Peng Deng ◽  
Xiao Ying Zhao ◽  
You Feng Chen ◽  
Wang Jing
Keyword(s):  
Ray Tracing ◽  
Shortest Path ◽  
Convex Surface ◽  
Local Algorithm ◽  
Dijkstra Algorithm ◽  
End Point

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.

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