Consider the k-d tree shown in Step 3 of Figure 15.5, constructed out of two dimensional keys {P: (3, 5), Q: (2, 6), R: (5, 8), S: (1, 7), T: (5, 4), U: (4, 5)}. The aim is to find the minimum elements MIN1 and MIN2 across dimensions 1 and 2, respectively. At the end of the FIND MIN operation, MIN1 would be set to 1 and MIN2 would be set to 4.

Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
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Consider the k-d tree shown in Step 3 of Figure 15.5, constructed out of two
dimensional keys {P: (3, 5), Q: (2, 6), R: (5, 8), S: (1, 7), T: (5, 4), U: (4, 5)}. The
aim is to find the minimum elements MIN1 and MIN2 across dimensions 1 and 2,
respectively. At the end of the FIND MIN operation, MIN1 would be set to 1 and
MIN2 would be set to 4. 

Keys: {P: (3,5), Q: (2,6), R: (5,8), S: (1,7), T: (5,4), U: (4,5)}
P
(3,5)
Step 1 (a)
Step 2
(b)
median (6, 7) = 6
Step 3
S(1,7)
Q(2,6)
(2,6)
P
(3,5)
(2,6)
Zas
(1,7)
S
(1,7)
(3,5)
P
(3,5)
DISC=1 median (1, 2, 3 4, 5, 5)=3
DISC = 1
U(4, 5)
R(5,8)
T(5, 4)
URT
T
(5,4)
DISC=1
DISC=2
DISC= 1
U
(4, 5)
R
(5,8)
DISC = 1
DISC = 2 median (4, 5, 8) = 5
DISC = 1
Figure 15.5. Building a k-d tree (method (ii))
Transcribed Image Text:Keys: {P: (3,5), Q: (2,6), R: (5,8), S: (1,7), T: (5,4), U: (4,5)} P (3,5) Step 1 (a) Step 2 (b) median (6, 7) = 6 Step 3 S(1,7) Q(2,6) (2,6) P (3,5) (2,6) Zas (1,7) S (1,7) (3,5) P (3,5) DISC=1 median (1, 2, 3 4, 5, 5)=3 DISC = 1 U(4, 5) R(5,8) T(5, 4) URT T (5,4) DISC=1 DISC=2 DISC= 1 U (4, 5) R (5,8) DISC = 1 DISC = 2 median (4, 5, 8) = 5 DISC = 1 Figure 15.5. Building a k-d tree (method (ii))
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