Travelling salesman problem

The travelling salesman problem (TSP) asks the following question: Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each city exactly once and returns to the origin city? It is an NP-hard problem in combinatorial optimization, important in operations research and theoretical computer science.

TSP is a special case of the travelling purchaser problem and the Vehicle routing problem.

In the theory of computational complexity, the decision version of the TSP (where, given a length L, the task is to decide whether the graph has any tour shorter than L) belongs to the class of NP-complete problems. Thus, it is possible that the worst-case running time for any algorithm for the TSP increases superpolynomially (perhaps, specifically, exponentially) with the number of cities.

The problem was first formulated in 1930 and is one of the most intensively studied problems in optimization. It is used as a benchmark for many optimization methods. Even though the problem is computationally difficult, a large number of heuristics and exact methods are known, so that some instances with tens of thousands of cities can be solved completely and even problems with millions of cities can be approximated within a small fraction of 1%.

Travelling salesman

A travelling salesman is a travelling Door-to-door seller of goods.

Travelling salesman may also refer to:

See also

Travelling Salesman (2012 film)

Travelling Salesman is a 2012 intellectual thriller film about four mathematicians solving the P versus NP problem, one of the most challenging mathematical problems in history. The title refers to the Travelling salesman problem, an optimization problem that acts like a key to solving other mathematical problems that are thought to be hard; it has been proven that a quick travelling salesman algorithm, if one exists, could be converted into quick algorithms for many other difficult tasks, such as factoring large numbers. Since many cryptographic schemes rely on the difficulty of factoring integers to protect their data, this would allow access to private data like personal correspondence, bank accounts and, possibly, government secrets.

The story is written and directed by Timothy Lanzone and premiered at the International House in Philadelphia on Saturday, June 16. After screenings in 8 countries, spanning 4 continents, including screenings at the University of Pennsylvania and the University of Cambridge, the film was released globally on September 10, 2013.