Hierarchical and Dynamic k-Path Covers

Recently, a metric-independent data structure for road netoworks named k-all-path cover (k-APC) has been proposed, which is a set of vertices that covers all the paths of size k. It has a wide range of application in route planning, path subsampling, and various path-related problems. Although it is a useful tool, an existing greedy algorithm cannot construct k-APCs for large k. To address the issue, we propose a new k-APC construction algorithm. Our algorithm recursively constructs layers of APCs, which we name k-all-path cover hierarchy, utilizing vertex cover heuristics, and we can extract k-APCs for various k values from a hierarchy. Further, we devise an algorithm for maintaining k-APC hierarchies on dynamic road networks. Our experiments demonstrate that our construction algorithm attains high solution quality and fast running time for large k value, and our dynamic algorithm can handle an edge weight change within 40 microseconds.