Finding shortest paths on terrains by killing two birds with one stone

Abstract

With the increasing availability of terrain data, e.g., from aerial laser scans, the management of such data is attracting increasing attention in both industry and academia. In particular, spatial queries, e.g., k-nearest neighbor and reverse nearest neighbor queries, in Euclidean and spatial network spaces are being extended to terrains. Such queries all rely on an important operation, that of finding shortest surface distances. However, shortest surface distance computation is very time consuming. We propose techniques that enable efficient computation of lower and upper bounds of the shortest surface distance, which enable faster query processing by eliminating expensive distance computations. Empirical studies show that our bounds are much tighter than the best-known bounds in many cases and that they enable speedups of up to 43 times for some well-known spatial queries.

New lower and upper bounds for shortest distance queries on terrains

“…Applications Queries on terrains are important in diverse applications, and the database community has recently studied the efficient support for, e.g., distance, kNN, and range queries on terrains [4,6,12,19,24,29,30]. We proceed to cover some applications.…”

“…The motivation behind using distance bounds is that they are inexpensive to compute in comparison to the exact surface shortest path Π(s, t). Kaul et al [12] show that a surface shortest path computation on a triangulation with 20K vertices, takes nearly 7.2 hours, while computing the shortest network path on the same triangulation takes only 0.04 seconds in comparison. However, the lower bound |E| was shown to be nearly 9 times smaller than |Π(s, t)| [12], which was a very loose bound.…”

“…Kaul et al [12] propose a tighter lower bound that captures the information about the surface of the underlying terrain. Both lower and upper bounds are derived from the shortest network distance |ΠG(s, t)|.…”

“…The quality of the state-of-the-art bounds proposed in [12] depends on the minimum interior angle θmin of all faces in the terrain. Observe that a larger θmin improves the tightness of the lower bound, while decreasing θmin results in a looser lower bound.…”

“…Therefore, they are more expensive to compute than the existing bounds [12]. However, the new bounds are tighter, and for kNN and range queries, more objects are pruned, resulting in fewer expensive exact shortest distance computations.…”