A ripple-spreading algorithm to calculate the k shortest paths in a network with time-windows

This paper is concerned with finding the k shortest routes or paths in a network where each node has some specific time windows only within which is the node accessible. Because of such time windows at nodes, classical methods for the k shortest paths problem (k-SPP) is not applicable to the k shortest paths problem in a time-window network (k-SPPTW). Taking inspiration from the natural ripple-spreading phenomenon, we propose a novel ripple-spreading algorithm (RSA) for the k-SPPTW. By conducting a purpose-designed ripple relay race in a time-window network, the reported RSA can resolve not only one-to-one k-SPPTW, but also one-to-all k-SPPTW, where all the k shortest paths from a given source node to every other node in the network need to be found. The computational complexity of RSA is just 0(k×NATU×NL), where NL is the number of links in the network, and NATU is the average simulated time units for a ripple to travel through a link. Experimental results demonstrate the effectiveness and efficiency of the proposed RSA for the k-SPPTW.