## A New Algorithm for Computing Shortest Paths in Weighted Planar Subdivisions (Extended Abstract) (1997)

Venue: | In Proc. 13th Annu. ACM Sympos. Comput. Geom |

Citations: | 33 - 3 self |

### BibTeX

@INPROCEEDINGS{Mata97anew,

author = {Cristian S. Mata and J.S.B. Mitchell},

title = {A New Algorithm for Computing Shortest Paths in Weighted Planar Subdivisions (Extended Abstract)},

booktitle = {In Proc. 13th Annu. ACM Sympos. Comput. Geom},

year = {1997},

pages = {264--273},

publisher = {ACM Press}

}

### Years of Citing Articles

### OpenURL

### Abstract

) Cristian S. Mata Joseph S. B. Mitchell y Abstract We present a practical new algorithm for the problem of computing low-cost paths in a weighted planar subdivision or on a weighted polyhedral surface. The algorithm is based on constructing a relatively sparse graph, a "pathnet", that links selected pairs of subdivision vertices with locally optimal paths. The pathnet can be searched for paths that are provably close to optimal and approach optimal, as one varies the parameter that controls the sparsity of the pathnet. We analyze our algorithm both analytically and experimentally. We report on the results of a set of experiments comparing the new algorithm with other standard methods. 1 Introduction For a given weight function, F : ! 2 ! !, the weighted length of an s-t path ß in the plane is the path integral, R ß F (x; y)doe, of the weight function along the path ß, linking the start s to the goal t. The weighted region metric associated with F defines the distance dF (...

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Citation Context ...fl) of optimal, where ffl = O( W=w k` min ). Our approach is strongly motivated by results on approximating Euclidean shortest paths among obstacles (as in Clarkson [3] and Mitchell [16]), t-spanners =-=[9]-=-, and approximation methods devised for minimum spanning trees [24]. 5 Other Algorithms In order to determine the practicality and relative effectiveness of our new algorithm, we implemented several o... |

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Citation Context ...ted terrain maps. We refer the reader to the survey [15] for pointers to the literature. The main theoretical results known for the weighted region problem are presented in Mitchell and Papadimitriou =-=[17]. They giv-=-e an algorithm, based on the "continuous Dijkstra method", to find a path whose weighted length is guaranteed to be within a factor (1 + ffl) of optimal, where ffl ? 0 is any user-specified ... |

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Citation Context ...e of terrain has an assigned weight equal to the reciprocal of the maximum speed of traversal for the robot. It also arises in numerous other applications involving route planning in geographic data (=-=[5, 15, 23]-=-), military mission planning and decision support ([1, 10, 11, 13, 14, 15, 21, 22]), and fluid flow in injection molding [8]. We assume that f is specified by a triangulation having n vertices, with e... |

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