Tamás Lukovszki, Anil Maheshwari, Norbert Zeh  Home/Search
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Abstract: We present an algorithm to answer a set Q of range counting queries over a point set P in d dimensions. The algorithm takes O sort(jP j + jQj) + (jP j+jQj) (jP j) DB log d 1 M=B jP j+jQj B 1 I/Os and uses linear space. For an important special case, the α(|P|) term in the I/O-complexity of the algorithm can be eliminated. We apply this algorithm to constructing t-spanners for point sets in R^d and polygonal obstacles in the plane, and finding the K closest pairs of a point set in R^d. (Update)
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BibTeX entry: (Update)
@article{ lukovszki01ioefficient,
author = "Tam{\'a}s Lukovszki and Anil Maheshwari and Norbert Zeh",
title = "{I/O}-Efficient Batched Range Counting and Its Applications to Proximity Problems",
journal = "Lecture Notes in Computer Science",
volume = "2245",
pages = "244+",
year = "2001",
url = "citeseer.ist.psu.edu/467712.html" }
Citations (may not include all citations):133 Geometric range searching and its relatives - Agarwal, Erickson - 1999
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62 Optimal dynamic interval management in external memory - Arge, Vitter - 1996
62 Classes of graphs which approximate the complete Euclidean g.. (context) - Keil, Gutwin - 1992
50 External-memory algorithms for processing line segments in g.. - Arge, Vengro et al. - 1995
50 External memory algorithms (context) - Vitter - 1998
49 Euclidean spanners: Short (context) - Arya, Das et al. - 1995
46 Approximation algorithms for shortest path motion planning - Clarkson - 1987
31 dimensional complete Euclidean graph (context) - Ruppert, Seidel et al. - 1991
30 On two-dimensional indexability and optimal range search ind.. - Arge, Samoladas et al. - 1999
22 range searching in external memory (context) - Vengro, Vitter et al. - 1996
14 On showing lower bounds for external-memory computational ge.. - Arge, Miltersen - 1999
13 er tree: A new technique for optimal I/O-algorithms (context) - Arge - 1995
11 New results on fault tolerant geometric spanners - Lukovszki - 1999
9 Geometric searching in walkthrough animations with weak span.. - Fischer, Lukovszki et al. - 1998
8 Sparse communication networks and ecient routing in the plan.. (context) - Hassin, Peleg - 2000
5 Ecient algorithms for constructing fault-tolerant geometric .. - Levcopoulos, Narasimhan et al. - 1998
3 Theory and practice of I/O-ecient algorithms for multidimens.. (context) - Arge, Procopiuc et al. - 1998
1 ecient well-separated pair decomposition and its application.. (context) - Govindarajan, Lukovszki et al. - 2000
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