Abstract
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 L p -metric. Such an approximate shortest path is called a c-short path, or a short path with stretch factor 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.
Part of this work was done while the authors were with the Max-Planck-Institut für Informatik in Saarbrücken, Germany. Gautam Das was partially supported by NSF Grant CCR-9306822.
The research of this author was supported in part by the National Science Foundation under Grant CCR-9623585.
This author was supported by ONR Grant N00014-89-J-1946, by ARPA under ONR contract N00014-88-K-0591, by the U.S. Army Research Office through the Math. Sciences Institute of Cornell Univ. under contract DAAL03-91-C-0027, and by the Cornell Theory Center which receives funding from its Corporate Research Institute, NSF, New York State, ARPA, NIH, and IBM.
Part of this work was done while the author was with the Max-Planck-Institut für Informatik, Saarbrücken, Germany.
This author was partially supported by the EU ESPRIT LTR Project No. 20244 (ALCOM-IT).
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Arikati, S., Chen, D.Z., Chew, L.P., Das, G., Smid, M., Zaroliagis, C.D. (1996). Planar spanners and approximate shortest path queries among obstacles in the plane. In: Diaz, J., Serna, M. (eds) Algorithms — ESA '96. ESA 1996. Lecture Notes in Computer Science, vol 1136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61680-2_79
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DOI: https://doi.org/10.1007/3-540-61680-2_79
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