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between the actions logged with LSN s 105 and 107. Note that p 1 was still a modified
page when the modified-page table was logged at LSN 105. We also assume that in
the disk version of page p 2 , P AGE -LSN .p 2 / < 101, meaning that the page was not
flushed onto disk after the actions logged with LSN s 112 and 117. Also note that
during taking the checkpoint, page p 2 , if buffered, was unmodified, since it does not
appear in the logged modified-page table.
During the log scan, the following actions are performed at LSN s 102-118:
102: Because R EC -LSN .p 1 / D 102 102, the page p 1 must be fixed and write-
latched. The fixing brings page p 1 fromdisktothebuffer.The P AGE -LSN of the page
can now be examined. As the page is unmodified, we set
R EC -LSN .p 1 / max f R EC -LSN .p 1 /; P AGE -LSN .p 1 / C 1 g
D max f 102; 102 C 1 gD 103
in the modified-page table. Because P AGE -LSN .p 1 / D 102 102,the LSN of the log
record, the result of the logged action DŒx 1 ; v 1 is already on the page. Page p 1 is
unlatched and unfixed.
103-106: No action.
107: Because R EC -LSN .p 1 / D 103 107,pagep 1 is fixed and write-latched. As
the page is still unmodified, we again set R EC -LSN .p 1 / 102 C 1 D 103. Because
P AGE -LSN .p 1 / D 102 < 107, the result of the action IŒx 1 ; v 0 1 is missing from the
page. The tuple .x 1 ; v 0 1 / is inserted into the page, and the P AGE -LSN is advanced:
P AGE -LSN .p 1 / 107.Pagep 1 is unlatched and unfixed.
108-109: No action.
110: Because R EC -LSN .p 1 / D 103 110,pagep 1 is fixed and write-
latched. As the page is no longer unmodified, its R EC -LSN is not updated. Because
P AGE -LSN .p 1 / D 107 < 110, the result of the action DŒx 1 ; v 0 1 is missing from
page p 1 . The tuple .x 1 ; v 0 1 / is deleted from page p 1 and P AGE -LSN .p 1 / 110.
Page p 1 is unlatched and unfixed.
111: No action.
112: Because R EC -LSN .p 2 / D 112 112,pagep 2 is fixed and write-latched.
The fixing brings page p 2 from disk to the buffer. As the page is unmodified, we set
R EC -LSN .p 2 / max f R EC -LSN .p 2 /; P AGE -LSN .p 2 / C 1 gD 112.
Recall that P AGE -LSN .p 2 / < 101. Because P AGE -LSN .p 2 / < 112, the result of the
action IŒx 2 ; v 2 is missing from the page. The tuple .x 2 ; v 2 / is inserted into the page
and P AGE -LSN .p 2 / 112.Pagep 2 is unlatched and unfixed.
113: Because R EC -LSN .p 1 / D 103 113,pagep 1 is fixed and write-latched.
Because P AGE -LSN .p 1 / D 110 < 113, the result of the action IŒx 3 ; v 3 is missing
from the page. The tuple .x 3 ; v 3 / is inserted into the page and P AGE -LSN .p 1 / 113.
Page p 1 is unfixed and unlatched.
114: No action.
115: Because R EC -LSN .p 1 / D 103 115,pagep 1 is fixed and write-latched.
Because P AGE -LSN .p 1 / D 113 < 115, the result of the action I 1 Œx 3 ; v 3 is missing
from the page. The tuple .x 3 ; v 3 / is deleted from the page and P AGE -LSN .p 1 / 115.
Page p 1 is unlatched and unfixed.
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