The one-to-one shortest-path problem: An empirical analysis with the two-tree Dijkstra algorithm

1993 ◽  
Vol 2 (1) ◽  
pp. 47-75 ◽  
Author(s):  
Richard V. Helgason ◽  
Jeffery L. Kennington ◽  
B. Douglas Stewart
Keyword(s):  
Empirical Analysis ◽  
Shortest Path ◽  
Shortest Path Problem ◽  
Dijkstra Algorithm ◽  
One To One ◽  
The One

scholarly journals An Efficient Label-Correcting Algorithm for the Multiobjective Shortest Path Problem

2021 ◽  
Author(s):  
Yannick Kergosien ◽  
Antoine Giret ◽  
Emmanuel Néron ◽  
Gaël Sauvanet
Keyword(s):  
Shortest Path ◽  
Exact Algorithm ◽  
Research Problem ◽  
Shortest Path Problem ◽  
Theoretical Computer Science ◽  
Computational Experiments ◽  
Discrete Mathematics ◽  
Large Graphs ◽  
One To One ◽  
The One

This paper proposes an exact algorithm to solve the one-to-one multiobjective shortest path problem. The solution involves determining a set of nondominated paths between two given nodes in a graph that minimizes several objective functions. This study is motivated by the application of this solution method to determine cycling itineraries. The proposed algorithm improves upon a label-correcting algorithm to rapidly solve the problem on large graphs (i.e., up to millions of nodes and edges). To verify the performance of the proposed algorithm, we use computational experiments to compare it with the best-known methods in the literature. The numerical results confirm the efficiency of the proposed algorithm. Summary of Contribution: The paper deals with a classic operations research problem (the one-to-one multiobjective shortest path problem) and is motivated by a real application for cycling itineraries. An efficient method is proposed and is based on a label-correcting algorithm into which several additional improvement techniques are integrated. Computational experiments compare this algorithm with the best-known methods in the literature to validate the performance on large-size graphs (Center for Discrete Mathematics and Theoretical Computer Science (DIMACS) instances from the ninth DIMACS challenge). New instances from the context of cycling itineraries are also proposed.

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].

Research on Composite Web Services Selection Based on Dijkstra Algorithm

2014 ◽  
Vol 596 ◽  
pp. 861-867 ◽  
Author(s):  
Yu Qiang Li ◽  
Yu Wen Li ◽  
Lei Che
Keyword(s):  
Web Services ◽  
Shortest Path ◽  
Feasible Solution ◽  
Optimal Path ◽  
Shortest Path Problem ◽  
Dijkstra Algorithm ◽  
Relevant Theory ◽  
Composite Web Services

Services composing have played an important role in the industry and academia in recent years. Based on the relevant theory and experience of the shortest path problem in a DAG, we propose the method of dijkstra algorithm implementing services composing way selection. Then we provide the pseudo code description of the algorithm implementing the optimal path selecting process and test the correctness of algorithm through the contrast experiment to offer a feasible solution for services composing way selection.

Fuzzy Dijkstra algorithm for shortest path problem under uncertain environment

2012 ◽  
Vol 12 (3) ◽  
pp. 1231-1237 ◽  
Author(s):  
Yong Deng ◽  
Yuxin Chen ◽  
Yajuan Zhang ◽  
Sankaran Mahadevan
Keyword(s):  
Shortest Path ◽  
Shortest Path Problem ◽  
Dijkstra Algorithm ◽  
Uncertain Environment

scholarly journals Optimization of Shortest Path Problem using Dijkstra’s Algorithm in Imprecise Environment

2021 ◽  
Vol 10 (10) ◽  
pp. 216-221
Author(s):  
Samir Dey ◽  
Sriza Malakar ◽  
Shibnath Rajak
Keyword(s):  
Shortest Path ◽  
Shortest Path Problem ◽  
Dijkstra’S Algorithm ◽  
Dijkstra Algorithm ◽  
Numerical Example ◽  
Network Problem ◽  
Dijkstra's Algorithm

Dijkstra algorithm is a widely used algorithm to find the shortest path between two specified nodes in a network problem. In this paper, a generalized fuzzy Dijkstra algorithm is proposed to find the shortest path using a new parameterized defuzzification method. Here, we address most important issue like the decision maker’s choice. A numerical example is used to illustrate the efficiency of the proposed algorithm.

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