The Minimum Spanning Tree with Node Index ≤ 2 Is Equivalent to the Minimum Traveling Salesman Tour

2019 ◽  
pp. 227-244
Author(s):  
Santosh Kumar ◽  
Elias Munapo ◽  
Caston Sigauke ◽  
Masar Al-Rabeeah
Keyword(s):  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Traveling Salesman ◽  
Index 2

Comparison of Heuristics for Resolving the Traveling Salesman Problem with Information Technology

2014 ◽  
Vol 886 ◽  
pp. 593-597 ◽  
Author(s):  
Wei Gong ◽  
Mei Li
Keyword(s):  
Information Technology ◽  
Traveling Salesman Problem ◽  
Spanning Tree ◽  
Nearest Neighbor ◽  
Minimum Spanning Tree ◽  
Optimal Solution ◽  
Traveling Salesman ◽  
Problem Class ◽  
The Traveling Salesman Problem ◽  
Random Insertion

Traveling Salesman Problem (Min TSP) is contained in the problem class NPO. It is NP-hard, means there is no efficient way to solve it. People have tried many kinds of algorithms with information technology. Thus in this paper we compare four heuristics, they are nearest neighbor, random insertion, minimum spanning tree and heuristics of Christofides. We dont try to find an optimal solution. We try to find approximated short trips via these heuristics and compare them.

scholarly journals Budgeted Prize-Collecting Traveling Salesman and Minimum Spanning Tree Problems

2020 ◽  
Vol 45 (2) ◽  
pp. 576-590
Author(s):  
Alice Paul ◽  
Daniel Freund ◽  
Aaron Ferber ◽  
David B. Shmoys ◽  
David P. Williamson
Keyword(s):  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Traveling Salesman ◽  
Prize Collecting

scholarly journals A return to the traveling salesman model: a network branch and bound approach

2013 ◽  
Vol 16 (1) ◽  
pp. 52-63 ◽  
Author(s):  
Elias Munapo
Keyword(s):  
Linear Programming ◽  
Traveling Salesman Problem ◽  
Branch And Bound ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Traveling Salesman ◽  
Tree Model ◽  
The Traveling Salesman Problem ◽  
Assignment Models

This paper presents a network branch and bound approach for solving the traveling salesman problem. The problem is broken into sub-problems, each of which is solved as a minimum spanning tree model. This is easier to solve than either the linear programming-based or assignment models. 

scholarly journals Prim and Genetic Algorithms Performance in Determining Optimum Route on Graph

2018 ◽  
Author(s):  
Andysah Putera Utama Siahaan ◽  
Rusiadi
Keyword(s):  
Genetic Algorithm ◽  
Genetic Algorithms ◽  
Traveling Salesman Problem ◽  
Spanning Tree ◽  
Minimum Spanning Tree ◽  
Traveling Salesman ◽  
Maximum Value ◽  
Optimum Route ◽  
Crossover And Mutation ◽  
Active Vertex

Performance is a process of assessment of the algorithm. Speed and security is the performance to be achieved in determining which algorithm is better to use. In determining the optimum route, there are two algorithms that can be used for comparison. The Genetic and Primary algorithms are two very popular algorithms for determining the optimum route on the graph. Prim can minimize circuit to avoid connected loop. Prim will determine the best route based on active vertex. This algorithm is especially useful when applied in a minimum spanning tree case. Genetics works with probability properties. Genetics cannot determine which route has the maximum value. However, genetics can determine the overall optimum route based on appropriate parameters. Each algorithm can be used for the case of the shortest path, minimum spanning tree or traveling salesman problem. The Prim algorithm is superior to the speed of Genetics. The strength of the Genetic algorithm lies in the number of generations and population generated as well as the selection, crossover and mutation processes as the resultant support. The disadvantage of the Genetic algorithm is spending to much time to get the desired result. Overall, the Prim algorithm has better performance than Genetic especially for a large number of vertices.

Minimalist Approaches to Figurative Maze Design

2015 ◽  
Author(s):  
Robert Bosch ◽  
Tim Chartier ◽  
Michael Rowan
Keyword(s):  
Traveling Salesman Problem ◽  
Spanning Tree ◽  
Optimization Problem ◽  
Minimum Spanning Tree ◽  
Hybrid Approach ◽  
Traveling Salesman ◽  
Image Mosaic ◽  
Target Image ◽  
Mathematical Methods

This chapter demonstrates that simple mathematical methods can be used to design mazes that resemble user-supplied target images. The first approach discussed here is the TSP method, which involves converting the target image into a stipple drawing, and then treating the dots as the cities of a Traveling Salesman Problem (TSP). Another approach involves replacing the TSP with a much easier optimization problem—the problem of finding a minimum spanning tree (MST). The chapter then introduces a hybrid approach that produces mazes that have both the random textures of the original TSP Art and MST Art mazes and also the directional textures of the phyllotactic mazes. Finally, the chapter describes how to form a maze by constructing an image mosaic out of the vortex tiles.

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