Abstract
The problem of finding the closest pair among a collection of points in \(\Re^d\) is a well-known problem. There are better-than-naive-solutions for constant d and approximate solutions in general. We propose the first better-than-naive-solutions for the problem for large d. In particular, we present algorithms for the metrics L 1 and L ∞ with running times of O(n (ω + 3)/2) and O(n (ω + 3)/2logD) respectively, where O(n ω) is the running time of matrix multiplication and D is the diameter of the points.
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This work was supported by the German-Israel Foundation (G.I.F.) young scientists program research grant agreement no. 2055-1168.6/2002.
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Indyk, P., Lewenstein, M., Lipsky, O., Porat, E. (2004). Closest Pair Problems in Very High Dimensions. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds) Automata, Languages and Programming. ICALP 2004. Lecture Notes in Computer Science, vol 3142. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-27836-8_66
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DOI: https://doi.org/10.1007/978-3-540-27836-8_66
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