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Worst Case Analyses of Nearest Neighbor Heuristicfor Finding the Minimum Weight k - cycle |
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| รหัสดีโอไอ | |
| Creator | Piyashat Sripratak |
| Title | Worst Case Analyses of Nearest Neighbor Heuristicfor Finding the Minimum Weight k - cycle |
| Contributor | Tanapat Chalarux |
| Publisher | King Mongkut's Institute of Technology Ladkrabang |
| Publication Year | 2563 |
| Journal Title | Current Applied Science and Technology |
| Journal Vol. | 20 |
| Journal No. | 2 |
| Page no. | 178-185 |
| Keyword | minimum weight k - cycle, worst case analysis, nearest neighbor heuristic |
| URL Website | https://www.tci-thaijo.org/index.php/cast |
| Website title | https://www.tci-thaijo.org/index.php |
| ISSN | 2586-9396 |
| Abstract | Given a weighted complete graph ( , w), where w is an edge weight function, the minimum weight k - cycle problem is to find a cycle of k vertices whose total weight is minimum among all k - cycles. Traveling salesman problem (TSP) is a special case of this problem when k = n. Nearest neighbor algorithm (NN) is a popular greedy heuristic for TSP that can be applied to this problem. To analyze the worst case of the NN for the minimum weight k - cycle problem, we prove that it is impossible for the NN to have an approximation ratio. An instance of the minimum weight k - cycle problem is given, in which the NN finds a k - cycle whose weight is worse than the average value of the weights of all k - cycles in that instance. Moreover, the domination number of the NN when k = n and its upper bound for the case k = n 1 is established. |
