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 \( O\left( {sort(\left| P \right| + \left| Q \right|) + \tfrac{{(\left| P \right| + \left| Q \right|)\alpha (\left| P \right|)}} {{DB}}\log _{M/B}^{d - 1} \tfrac{{\left| P \right| + \left| Q \right|}} {B}} \right)^1 \) I/Os and uses linear space. For an important special case, the α(∣P∣) term in the I/Ocomplexity of the algorithm can be eliminated. We apply this algorithm to constructing t-spanners for point sets in ℝd and polygonal obstacles in the plane, and finding the K closest pairs of a point set in ℝd.
Research supported by NSERC, NCE GEOIDE, and DFG-SFB376.
sort(N) denotes the I/O-complexity of sorting N data items in external memory. See Model of Computation.
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Lukovszki, T., Maheshwari, A., Zeh, N. (2001). I/O-Efficient Batched Range Counting and Its Applications to Proximity Problems. In: Hariharan, R., Vinay, V., Mukund, M. (eds) FST TCS 2001: Foundations of Software Technology and Theoretical Computer Science. FSTTCS 2001. Lecture Notes in Computer Science, vol 2245. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45294-X_21
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