Parameterized algorithms and complexity for the traveling purchaser problem and its variants

The traveling purchaser problem (TPP), a generalization of the traveling salesman problem, is to determine a tour of suppliers and purchase needed products from suppliers while minimizing the traveling and purchasing cost. This problem finds applications in the routing and scheduling contexts and its variants with different constraints have been widely studied. Motivated by the phenomenon that most real-world instances of TPP have a small parameter (such as the number of suppliers, the number of products to purchase, and others), we study TPP and its variants from the view of parameterized complexity. We show that TPP and some variants are fixed-parameter tractable by taking the numberkof products or the numbermof suppliers as the parameter, and W[2]-hard by taking the numberqof visited suppliers as the parameter. Furthermore, we implement some of our fixed-parameter tractable algorithms to show that they are practically effective when the parameters are not very large.