Computing homotopic shortest paths in the plane

We address the problem of computing homotopic shortest paths in the presence of obstacles in the plane. Problems on homotopy of paths received attention very recently [Cabello et al., in: Proc. 18th Annu. ACM Sympos. Comput. Geom., 2002, pp. 160–169; Efrat et al., in: Proc. 10th Annu. European Sympo...

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Vydáno v:Journal of algorithms Ročník 49; číslo 2; s. 284 - 303
Hlavní autor: Bespamyatnikh, Sergei
Médium: Journal Article
Jazyk:angličtina
Vydáno: San Diego, CA Elsevier Inc 01.11.2003
Elsevier
Témata:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Classical combinatorial problems
Combinatorics
Combinatorics. Ordered structures
Computer science; control theory; systems
Convex and discrete geometry
Exact sciences and technology
Geometry
Graph theory
Homotopy
Mathematics
Output-sensitive algorithm
Sciences and techniques of general use
Shortest path
Theoretical computing
Shortest path
Homotopy
Output-sensitive algorithm
Output sensitive algorithm
Graph theory
Computer theory
Computing
ISSN:0196-6774, 1090-2678
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Shrnutí:We address the problem of computing homotopic shortest paths in the presence of obstacles in the plane. Problems on homotopy of paths received attention very recently [Cabello et al., in: Proc. 18th Annu. ACM Sympos. Comput. Geom., 2002, pp. 160–169; Efrat et al., in: Proc. 10th Annu. European Sympos. Algorithms, 2002, pp. 411–423]. We present two output-sensitive algorithms, for simple paths and non-simple paths. The algorithm for simple paths improves the previous algorithm [Efrat et al., in: Proc. 10th Annu. European Sympos. Algorithms, 2002, pp. 411–423]. The algorithm for non-simple paths achieves O(log 2 n) time per output vertex which is an improvement by a factor of O( n/log 2 n) of the previous algorithm [Hershberger, Snoeyink, Comput. Geom. Theory Appl. 4 (1994) 63–98], where n is the number of obstacles. The running time has an overhead O( n 2+ ε ) for any positive constant ε. In the case k< n 2+ ε , where k is the total size of the input and output, we improve the running to O(( n+ k+( nk) 2/3)log O(1) n).
ISSN:0196-6774
1090-2678
DOI:10.1016/S0196-6774(03)00090-7