An effective method to find the k shortest paths in a generalized time-window network

It is a challenging task to find the k shortest paths in a time-window network, where a node may have some specific time windows only within which is the node accessible. Existing research assumes that a traveller can pass through an accessible node immediately or wait to pass at start times of future time windows at the node. This paper targets at a more general case where a traveller, once arriving at a node, may choose to pass through the node at any discrete time in the time windows of the node. In such a generalized time-window network, the degree of complexity increases significantly, as the size of solution space soars up exponentially. By mimicking the natural ripple-spreading phenomenon on a liquid surface, we propose an effective ripple-spreading algorithm (RSA) for the k shortest paths problem in a generalized time-window network (k-SPPGTW). Besides one-to-one k-SPPGTW, the RSA is also extended to one-to-all k-SPPGTW, where all the k shortest paths from a given source to every other node in the network need to be found. The new method has a theoretical guarantee of optimality. The computational complexity of the reported RSA is just 0(k×N
_ATU
×N
_L
), where N
_l
is the number of links in the network, and Natu is the average simulated time units for a ripple to travel through a link. The effectiveness and efficiency of the reported RSA for the k-SPPGTW are demonstrated by some preliminary experimental results.