We consider the problem of finding an obstacle-avoiding path between two points s and t in the plane, amidst a set of disjoint polygonal obstacles with a total of n vertices. The length of this path should be within a small constant factor c of the length of the shortest possible obstacle-avoiding s-t path measured in the Lv-metric. Such an approximate shortest path is called a c-short path, or a short path with stretch]actor c. The goal is to preprocess the obstacle-scattered plane by creating an efficient data structure that enables fast reporting of a c-short path (or its length). In this paper, we give a family of algorithms for the above problem that achieve an interesting trade-off between the stretch factor, the query time and the preprocessing bounds. Our main results are algorithms that achieve logarithmic length query time, after subquadratic time and space preprocessing.
CITATION STYLE
Arikati, S., Chen, D. Z., Paul Chew, L., Das, G., Staid, M., & Zaroliagis, C. D. (1996). Planar spanners and approximate shortest path queries among obstacles in the plane. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1136, pp. 514–528). Springer Verlag. https://doi.org/10.1007/3-540-61680-2_79
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