Continuous line drawings via the traveling salesman problem

Continuous line drawings via the traveling salesman problem

We describe how to use the traveling salesman problem (TSP) to create continuous line drawings of target pictures.

Continuous Relaxations for the Traveling Salesman Problem

In this work, we construct heuristic approaches for the traveling salesman problem (TSP) based on embedding the discrete optimization problem into continuous spaces. We explore multiple embedding techniques – namely, the construction of dynamical flows on the manifold of orthogonal matrices and associated Procrustes approximations of the TSP cost function. In particular, we find that the Procru...

The On-line Asymmetric Traveling Salesman Problem

We consider two on-line versions of the asymmetric traveling salesman problem with triangle inequality. For the homing version, in which the salesman is required to return in the city where it started from, we give a 3+ √ 5 2 -competitive algorithm and prove that this is best possible. For the nomadic version, the on-line analogue of the shortest asymmetric hamiltonian path problem, we show tha...

The traveling salesman problem

The Traveling Salesman Problem

The Traveling Salesman Problem (TSP) is perhaps the most studied discrete optimization problem. Its popularity is due to the facts that TSP is easy to formulate, difficult to solve, and has a large number of applications. It appears that K. Menger [31] was the first researcher to consider the Traveling Salesman Problem (TSP). He observed that the problem can be solved by examining all permutati...