Improving the computational efficiency of ripple-spreading algorithm for the k shortest paths problem

The k shortest paths problem (k-SPP) has a wide application background. Inspired by the natural ripple-spreading phenomenon that occurs on a water surface, we have recently proposed an original ripple-spreading algorithm (RSA) for the k-SPP. However, the computational efficiency of the reported algorithm is poor. This paper is concerned with how to improve the scalability of RSA for the k-SPP. To this end, two methods are proposed in this study. One is to impose an upper bound of k as the maximal number of ripples a node may generate. The other is to start ripple relay race from both the source and the destination simultaneously. Some theoretical analyses on the optimality and time complexity of improved RSA for the k-SPP are given. Surprisingly, the improved RSA can be extended from one-to-one k-SPP to one-to-all k-SPP, with no increase in computational complexity. The experimental results demonstrate the effectiveness and efficiency of the proposed methods.