Lower bounds for computing geometric spanners and approximate shortest paths
نویسندگان
چکیده
منابع مشابه
Lower Bounds for Computing Geometric Spanners and Approximate Shortest Paths
We consider the problems of constructing geometric spanners, possibly containing Steiner points, for sets of points in the d-dimensional space IR d , and constructing spanners and approximate shortest paths among a collection of polygonal obstacles in the plane. The complexities of these problems are shown to be (n log n) in the algebraic computation tree model. Since O(n log n)-time algorithms...
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The algorithms for computing a shortest path on a polyhedral surface are slow, complicated, and numerically unstable. We have developed and implemented a robust and efficient algorithm for computing approximate shortest paths on a convex polyhedral surface. Given a convex polyhedral surface P in R3, two points s, t ∈ P , and a parameter ε > 0, it computes a path between s and t on P whose lengt...
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1 This paper studies algorithmic and combinatorial properties of shortest paths of different homo2 topy types in a polygonal domain with holes. We define the “second shortest path” to be the shortest 3 path that is homotopically different from the (first) shortest path; the kth shortest path for an arbitrary 4 integer k is defined analogously. We introduce the “kth shortest path map”—a structur...
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ژورنال
عنوان ژورنال: Discrete Applied Mathematics
سال: 2001
ISSN: 0166-218X
DOI: 10.1016/s0166-218x(00)00280-8