A Time Impulse Neural Network Framework for Solving the Minimum Path Pair Problems of the Time-Varying Network

The minimum path pair (MPP) query problem is to find the optimal meeting point of two minimum paths for two users in a network, where each user's minimum path has its own departure and destination nodes. However, the MPP query problem on a time-varying network that generally exists in the world remains open. In this study, we investigate the time-varying minimum path pair (TMPP) query problem, where the arcs of the network are time dependent. We first model the TMPP and then propose a time impulse neural network (TINN) to solve the TMPP. In the design of the TINN, the entire network topology is considered as the architecture of the neural network, and each node is viewed as a neuron. The core of an impulse-based neuron consists of six parts: input, impulse receiver, time window selector, neuron storage, impulse sender, and output. Unlike the traditional neural network, the whole neural network does not require a training process but is implemented through an impulse mechanism. The TINN consists of two stages; the first stage is to find the two minimum paths of two users, while the second stage is to calculate the distance between these two minimum paths. The underlying idea of the TINN is to find the minimum path using an impulse mechanism. The minimum path relies on the earliest time impulse stemming from the depart node that arrives at the destination node. With this mechanism, both the minimum path of the network and the distance between two paths can be addressed. Furthermore, theoretical analysis demonstrates the correctness and provides the complexity of the TINN. Experiments of the TINN are carried out based on the well-known New York City Map. A comparative study illustrates the effectiveness of the TINN.