# For a given set of delivery destinations, is there a practical method for determining a minimal cost route visiting all of them and returning to a 'hub' distribution depot?

**Main topic:**Science

Short answer:

The 'Traveling Salesman Problem' is the name of this type of problem, and various approaches have been used to solve it.

Depth-First-Search traversal can be used to identify a number route in a directed graph that has a minimal cost (although not necessarily fully optimised). DFS is widely used to discover which pathways in a network are the shortest, and the DFS algorithm may compute the minimal distance that separates any node in the graph from its source, any intermediate nodes, or any destination nodes.The strategy of using Depth-First-Search traversal to handle the issue is a technique that is used to identify the route in a directed graph that has the lowest possible cost.^{[1]} DFS is widely used to discover which pathways in a network are the shortest, and the DFS algorithm may compute the minimal distance that separates any node in the graph from its source, any intermediate nodes, or any destination nodes.^{[2]}

## Advantages of using DFS[edit]

- Anyone could achieve the required answer on the very first try, it's possible that it will discover a solution without having to examine a significant portion of the search results.
^{[3]} - If it follows the correct route, it will arrive at the target node in a shorter amount of time compared to the BFS algorithm.
^{[4]} - Only the nodes that are now being traversed are being saved, depth-first search consumes less memory than other methods.
^{[5]}

## References[edit]

- ↑ Yang, Bohua; Wen, Dong; Qin, Lu; Zhang, Ying; Wang, Xubo; Lin, Xuemin (2019-10-01). "Fully dynamic depth-first search in directed graphs".
*Proceedings of the VLDB Endowment*.**13**(2): 142–154. doi:10.14778/3364324.3364329. ISSN 2150-8097. - ↑ "Depth First Search (DFS): Concept, Implementation, Advantages, Disadvantages".
*BrainKart*. Retrieved 2022-10-09. - ↑ Baswana, Surender; Chaudhury, Shreejit Ray; Choudhary, Keerti; Khan, Shahbaz (2016-01-10). "Dynamic DFS in undirected graphs: breaking the O(m) barrier".
*Proceedings of the twenty-seventh annual ACM-SIAM symposium on Discrete algorithms*. SODA '16. Arlington, Virginia: Society for Industrial and Applied Mathematics: 730–739. doi:10.5555/2884435.2884487 Check`|doi=`

value (help). ISBN 978-1-61197-433-1. - ↑ Reif, John H. (1985-06-12). "Depth-first search is inherently sequential".
*Information Processing Letters*.**20**(5): 229–234. doi:10.1016/0020-0190(85)90024-9. ISSN 0020-0190. - ↑ Chakraborty, Sankardeep; Mukherjee, Anish; Raman, Venkatesh; Satti, Srinivasa Rao (2022-02-01). "Frameworks for designing in-place graph algorithms".
*Journal of Computer and System Sciences*.**123**: 1–19. doi:10.1016/j.jcss.2021.07.004. ISSN 0022-0000.