Shortest Path Search in Large-Scale Graphs with Cox-Distributed Edge Weights

Keywords: Shortest path algorithms, Cox distribution, Graph dimensionality reduction, ALT algorithm, Principal Component Analysis (PCA), Large-scale graphs

Abstract:

Graphs are extensively utilized in network communications to optimize data transmission routes, in social networks to model user interactions, in data storage and processing, in artificial intelligence, and in computer graphics. Graph-based structures are particularly prominent in search algorithms, including those employed by logistics companies.
A significant challenge in the application of graph structures lies in the quest for the shortest path and the reduction of dimensionality within large-scale dynamic graphs governed by a Cox distribution, all while minimizing computational time. The Cox distribution serves as a generalization of the exponential distribution, facilitating the modeling of complex processes - such as heterogeneous inter-event times or systems characterized by varying event intensities - and yielding exclusively positive real-valued outcomes. Consequently, a vital research avenue involves the exploration of existing shortest-path algorithms in conjunction with graph dimensionality reduction techniques to identify the most efficient solutions. This paper provides a comprehensive review of the primary methodologies currently employed to address this issue.

Submission Number: 44