Article ID: | iaor20041854 |
Country: | United States |
Volume: | 42 |
Issue: | 3 |
Start Page Number: | 154 |
End Page Number: | 159 |
Publication Date: | Oct 2003 |
Journal: | Networks |
Authors: | Speranza M. Grazia, Bertazzi Luca, Archetti Claudia |
In this paper, we study the reoptimization problems which arise when a new node is added to an optimal solution of a traveling salesman problem (TSP) instance or when a node is removed. We show that both reoptimization problems are NP-hard. Moreover, we show that while the cheapest insertion heuristic has a tight worst-case ratio equal to 2 when applied to a TSP instance, it guarantees, in linear time, a tight worst-case ratio equal to 3/2 when used to add the new node and that also the simplest heuristic to remove a node from the optimal tour guarantees a tight ratio equal to 3/2 in constant time.