Hierarchical and Dynamic k-Path Covers

A metric-independent data structure for spatial networks called k-all-path cover (k-APC) has recently been proposed. It involves a set of vertices that covers all paths of size k, and is a general indexing technique that can accelerate various path-related processes on spatial networks, such as route planning and path subsampling to name a few. Although it is a promising tool, it currently has drawbacks pertaining to its construction and maintenance. First, k-APCs, especially for large values of k, are computationally too expensive. Second, an important factor related to quality is ignored by a prevalent construction algorithm. Third, an existing algorithm only focuses on static networks. To address these issues, we propose novel k-APC construction and maintenance algorithms. Our algorithms re-cursively construct the layers of APCs, which we call the k-all-path cover hierarchy, by using vertex cover heuristics. This allows us to extract k-APCs for various values of k from the hierarchy. We also devise an algorithm to maintain k-APC hierarchies on dynamic networks. Our experiments showed that our construction algorithm can yield high solution quality, and has a short running time for large values of k. They also verified that our dynamic algorithm can handle an edge weight change within 40 ms.