Massively Parallel Approximation Algorithms for the Traveling Salesman Problem

The traveling salesman problem (TSP) describes a salesman who needs to travel through a list of given cities exactly once by taking the shortest possible tour. The problem is NP-Complete since there are no known polynomial time algorithms to solve it. The main motivation to solve this problem is that the applications of Traveling Salesman are immense. It can be used by banks to find an optimal route for updating cash in ATMs, by delivery companies to chalk out the best possible route between the delivery centers and save up on fuel and man hours. It can be used outside of delivery based applications too. For example it can be used for drilling holes in circuits. The easiest way to solve the traveling salesman problem would be by using brute force search which is also called as exhaustive search. The algorithm involves going through each possible ordered permutation of cities and finding out the cheapest route. The running time for this approach is O(n!) which is the factorial of the number of cities. One can easily say that this kind of solution is not feasible even for computing the route between 20 cities. This is a serious limitation. Recent advances by vendors like Amazon, Google and Microsoft have made cloud services easily accessible to the public. One can easily harness the power of the cloud to solve huge problems at a fraction of the cost in parallel by making use of multiple cores on multiple nodes. Traveling salesman is one such problem that can be modified for such infrastructure.