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J.L. Bentley. Multidimensional binary search in database applications. IEEE Trans. Softw. Eng., 4(5):333-340, 1979.

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Multidimensional Access Methods - Gaede, Günther (1997)   (262 citations)  (Correct)

....The MBB m8, for example, provides a fairly tight fit, whereas r5 is only about half as large as its MBB m5. p2 p8 p10 p1 p3 p4 p5 p6 p9 p7 r2 r10 r3 r5 r7 r9 r6 r8 r1 m1 m10 m2 m4 m5 m3 m7 m9 m6 m8 r4 Figure 9: Running Example 16 3.2. 1 The K D Tree (Bentley 1975; Bentley 1979) One of the most prominent d dimensional data structures is the k d tree. The k dtree is a binary search tree that represents a recursive subdivision of the universe into subspaces by means of (d Gamma 1) dimensional hyperplanes. The hyperplanes are isooriented, and their direction alternates ....

Bentley, J. L. (1979). Multidimensional binary search in database applications. IEEE Trans. Software Eng. 4 (5), 333--340.


Multidimensional Access Methods - Gaede, Günther (1997)   (262 citations)  (Correct)

....approximation varies considerably. The MBB m8, for example, provides a fairly tight fit, whereas r5 is only about half as large as its MBB m5. p2 p8 p10 p1 p3 p4 p5 p6 p9 p7 r2 r10 r4 r3 r5 r7 r9 r6 r8 r1 m1 m10 m2 m4 m5 m3 m7 m9 m6 m8 Figure 9: Running Example 3.2. 1 The K D Tree (Bentley 1975; Bentley 1979) One of the most prominent d dimensional data structures is the k d tree. The k dtree is a binary search tree that represents the recursive subdivision of the universe into subspaces by means of (d Gamma 1) dimensional hyperplanes. The hyperplanes are iso oriented, and their direction alternates ....

Bentley, J. L. (1979). Multidimensional binary search in database applications. IEEE Trans. Software Eng. 4 (5), 333--340.


Multidimensional Access Methods - Gaede, Günther (1997)   (262 citations)  (Correct)

....often use their centroids ci (not pictured) or their minimum bounding boxes (MBBs) mi. Note that the quality of the MBB approximation varies considerably. The MBB m8, for example, provides a fairly tight fit, whereas r5 is only about half as large as its MBB m5. 3.2. 1 The K D Tree (Bentley 1975; Bentley 1979) One of the most prominent d dimensional data structures is the k d tree. The k dtree is a binary search tree that represents a recursive subdivision of the universe into subspaces by means of (d Gamma 1) dimensional hyperplanes. The hyperplanes are isooriented, and their direction alternates ....

Bentley, J. L. (1979). Multidimensional binary search in database applications. IEEE Trans. Software Eng. 4 (5), 333--340.


Reflected Min-Max Heaps - Christos Makris Athanasios   (Correct)

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J.L. Bentley. Multidimensional binary search in database applications. IEEE Trans. Softw. Eng., 4(5):333-340, 1979.

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