Stepping Stone Graph

Abstract

There are many real world applications that require identifying public movements such as identifying movement corridors in cities and most popular paths. If one is not given user trajectories but rather sporadic location data, such as location-based social network data, finding movement related information becomes difficult. Rather than processing all points in a dataset given a query, a clever approach is to construct a graph, based on user locations, and query this graph to answer questions such as shortest paths, most popular paths, and movement corridors. Shortest path graph is one of the popular graphs. However, the shortest path graph can be inefficient and ineffective for analysing movement data, as it calculates the graph edges considering the shortest paths over all the points in a dataset. Therefore, edge sets resulting from shortest path graphs are usually very restrictive and not suitable for movement analysis because of its global view of the dataset. We propose the stepping stone graph, which calculates the graph considering point pairs rather than all points; the stepping stone graph focuses on possible local movements, making it both efficient and effective for location-based social network related data. We demonstrate its capabilities by applying it in the Location-Based Social Network domain and comparing with the shortest path graph. We also compare its properties to a range of other graphs and demonstrate how stepping stone graph relates to Gabriel graph, relative neighbourhood graph, and Delaunay triangulation.