Parallelized solution to the asymmetric travelling salesman problem using central processing unit acceleration

Abstract

Travelling salesman problem is a well researched problem in computer science and has many practical applications. It is classified as a NP-hard problem as its exact solution can only be obtained in exponential time unless P = NP. There are different variants of the travelling salesman problem (TSP) and in this paper, asymmetric travelling salesman problem is addressed since this variant is quite often observed in real world scenarios. There are a number of heuristic approaches to this problem which provides approximate solutions in polynomial time, however this paper proposes an exact optimal solution which is accelerated with the help of multi-threading-based parallelization. In order to find the exact optimal solution, we have used the held-karp algorithm involving dynamic programming and to reduce the time taken to find the optimal path, we have used a multi-threaded approach to parallelize the processing of sub-problems by leveraging the central processing unit cores (CPUs). This method is an extension of a well researched solution to the TSP; however, this method shows that solutions to computationally intensive problems involving sub-problems such as the asymmetic travelling salesman problem (ATSP) can be accelerated with the help of modern CPUs.