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A Near-Linear Algorithm for the Planar Segment Center Problem (1996)  (Make Corrections)  (10 citations)
Alon Efrat, Micha Sharir
SODA: ACM-SIAM Symposium on Discrete Algorithms (A Conference on Theoretical and Experimental Analysis of Discrete Algorithms)



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Abstract: Let P be a set of n points in the plane and let e be a segment of fixed length. The segment center problem is to find a placement of e (allowing translation and rotation) which minimizes the maximum euclidean distance from e to the points of P . We present an algorithm that solves the problem in time O(n 1+" ), for any " ? 0, improving the previous solution of Agarwal et al. [3] by nearly a factor of O(n). 1 Introduction The problem considered in this paper is: "Given a set S of n... (Update)

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BibTeX entry:   (Update)

A. Efrat and M. Sharir, A near-linear algorithm for the planar segment center problem, Discrete Comput. Geom., 16 (1996), 239--257. http://citeseer.ist.psu.edu/efrat96nearlinear.html   More

@inproceedings{ efrat94nearlinear,
    author = "Efrat and Sharir",
    title = "A Near-Linear Algorithm for the Planar Segment Center Problem",
    booktitle = "{SODA}: {ACM}-{SIAM} Symposium on Discrete Algorithms (A Conference on Theoretical and Experimental Analysis of Discrete Algorithms)",
    year = "1994",
    url = "citeseer.ist.psu.edu/efrat96nearlinear.html" }
Citations (may not include all citations):
214   Davenport-Schinzel Sequences and Their Geometric Application.. - Sharir, Agarwal
185   Applying parallel computation algorithms in the design of se.. (context) - Megiddo - 1983
114   Optimal point location in a monotone subdivision (context) - Edelsbrunner, Guibas et al. - 1986
48   Geometric pattern matching under euclidean motion - Chew, Goodrich et al. - 1993
47   Almost tight upper bounds for lower envelopes in higher dime.. (context) - Sharir - 1994
44   Static and dynamic algorithms for k-point clustering problem.. (context) - Datta, Lenhof et al. - 1993
43   Approximations and optimal geometric divide-and-conquer (context) - Matousek - 1991
38   The polygon containment problem (context) - Chazelle - 1983
36   A singly exponential stratification scheme for real semi--al.. (context) - Chazelle, Edelsbrunner et al. - 1991
33   Vertical decomposition of shallow levels in 3-dimensional ar.. - Agarwal, Efrat et al. - 1995
29   Geometric complexity of some location problems (context) - Lee, Wu - 1986
29   Extremal polygon containment problems - Sharir, Toledo - 1994
22   Parallel transitive closure and point location in planar str.. (context) - Tamassia, Vitter - 1991
22   A deterministic algorithm for the three-dimensional diameter.. - Matousek, Schwarzkopf - 1993
22   the number of critical free contacts of a convex polygonal o.. (context) - Leven, Sharir - 1987

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Documents on the same site (http://www.cs.arizona.edu/~alon/CV/cv3.html):   More
On Incremental Rendering of Silhouette Maps of a.. - Zhang, Efrat, Guibas.. (1999)   (Correct)
On the Complexity of the Union of Fat Objects in the Plane - Efrat, Sharir (1998)   (Correct)
Sweeping Simple Polygons with a Chain of Guards - Efrat, Guibas, Har-Peled.. (1999)   (Correct)

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