A Solution for Finding Quasi-Shortest Path with Graph Coarsening

Abstract

In recent years, different types of large-scale data with a graph structure, such as communication networks, transportation networks, and large-scale integrated circuits, are being commonly used, and it is expected that large-scale graphs will be used to represent such data. However, various graph algorithms for analyzing graphs cannot easily deal with large-scale graphs. To solve this problem, graph sparsification and graph coarsening, which are graph mining techniques, have been actively studied. We believe that a graph coarsening algorithm that reduces the number of dimensions of data while preserving the features of large-scale graphs can be applied not only to complex problems such as node clustering, graph partitioning, and graph visualization but also to the shortest path problem on graphs. In this study, we propose a quasi-shortest path algorithm with coarsening (QSPC) that uses a typical graph coarsening algorithm for finding the quasi-shortest path, that is, an approximate shortest path between two vertices in a large-scale graph. Furthermore, we investigate the effectiveness of QSPC through several experiments with different scales. Our findings indicate that QSPC can find the quasi-shortest path a constant time faster than Dijkstra’s algorithm, and the quasi-shortest path between two vertices in a tree graph or scale-free graph is equal to the shortest path.