L1 Shortest Paths with Isothetic Roads
نویسندگان
چکیده
We present a nearly optimal (O(ν min(ν, n)n log n) time and O(n) space) algorithm that constructs a shortest path map with n isothetic roads of speed ν under the L1 metric. The algorithm uses the continuous Dijkstra method and its efficiency is based on a new geometric insight; the minimum in-degree of any nearest neighbor graph for points with roads of speed ν is Θ(ν min(ν, n)), which is first shown in this paper. Also, this algorithm naturally extends to the multi-source case so that the Voronoi diagram for m sites can be computed in O(ν min(ν, n)(n + m) log(n + m)) time and O(n + m) space, which is also nearly optimal.
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