Abstract
The problem of computing shortest paths in obstacle environments has received considerable attention recently. We study this problem for a new metric that generalizes the L 1 metric and the link metric. In this combined metric, the length of a path is defined as its L 1 length plus some non-negative constant C times the number of turns the path makes.
Given an environment of n axis parallel line segments and a target point, we present a data structure in which an obstacle free shortest rectilinear path from a query point to the target can be computed efficiently. The data structure uses O(n log n) storage and its construction takes O(n 2) time. Queries can be performed in O(log n) time, and the shortest path can be reported in additional time proportional to its size.
This research was supported by the ESPRIT II Basic Research Actions Program of the EC under contract No. 3075 (project ALCOM). Work of the first author was supported by the Dutch Organization for Scientific Research (N.W.O.). The research was done while the third author was visiting Utrecht University.
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© 1990 Springer-Verlag Berlin Heidelberg
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de Berg, M., van Kreveld, M., Nilsson, B.J., Overmars, M.H. (1990). Finding shortest paths in the presence of orthogonal obstacles using a combined L 1 and link metric. In: Gilbert, J.R., Karlsson, R. (eds) SWAT 90. SWAT 1990. Lecture Notes in Computer Science, vol 447. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-52846-6_91
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DOI: https://doi.org/10.1007/3-540-52846-6_91
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