A GPU-Based Backtracking Algorithm for Permutation Combinatorial Problems

This work presents a GPU-based backtracking algorithm for permutation combinatorial problems based on the Integer-Vector-Matrix (IVM) data structure. IVM is a data structure dedicated to permutation combinatorial optimization problems. In this algorithm, the load balancing is performed without intervention of the CPU, inside a work stealing phase invoked after each node expansion phase. The proposed work stealing approach uses a virtual n-dimensional hypercube topology and a triggering mechanism to reduce the overhead incurred by dynamic load balancing. We have implemented this new algorithm for solving instances of the Asymmetric Travelling Salesman Problem by implicit enumeration, a scenario where the cost of node evaluation is low, compared to the overall search procedure. Experimental results show that the dynamically load balanced IVM-algorithm reaches speed-ups up to 17\(\times \) over a serial implementation using a bitset-data structure and up to 2\(\times \) over its GPU counterpart.