The traveling salesman problem is one of the most famous combinatorial problems. We identify a natural parameter for the two-dimensional Euclidean traveling salesman problem. We show that for random problems there is a rapid transition between soluble and insoluble instances of the decision problem at a critical value of this parameter. Hard instances of the traveling salesman problem are assoc...

In this research, we discuss the intermittent traveling salesman problem (ITSP), which extends the traditional traveling salesman problem (TSP) by imposing temperature restrictions on each node. These additional constraints limit the maximum allowable visit time per node, and result in multiple visits for each node which cannot be serviced in a single visit. We discuss three different temperatu...

We introduce a new combinatorial optimization problem, which is a generalization of the Traveling Salesman Problem (TSP) and which we call Traveling Salesman Problem of Second Order (2-TSP). It is motivated by an application in bioinformatics, especially the Permuted Variable Length Markov model. We propose seven elementary heuristics and two exact algorithms for the 2-TSP, some of which are ge...

The Quota Traveling Salesman Problem is a generalization of the well known Traveling Salesman Problem. The goal of the traveling salesman is, in this case, to reach a given quota of the sales, minimizing the amount of time. In this paper we address the on-line version of the problem, where requests are given over time. We present algorithms for various metric spaces, and analyze their performan...