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1. B+ Tree (5 points) Assume the following B-tree exists with d = 2: Draw the B+-tree after each step in the following sequence of insertions and deletions: Insert 28, Insert 4, Delete 38, Delete 14, Delete 7 Note: Please use the insertion and deletion algorithms given in the lecture slides. 2. Disk, File Storage and Organization (5 points) Consider a disk with a sector size of 512 bytes, 2000 tracks per surface, 50 sectors per track, five double-sided platters, and average seek time of 10 msec. Suppose also that a block size of 1024 bytes is chosen. Suppose that a file containing 100,000 records of 100 bytes each is to be stored on such a disk and that no record is allowed to span over two blocks. The disk platters rotate at 5400 rpm (revolutions per minute). We can transfer one track per revolution. 2.1 How many records fit onto a block? 2.2 How many blocks are required to store the entire file? If the file is arranged sequentially on the disk, how many surfaces are needed? 2.3 How many records of 100 bytes each can be stored using this disk? 2.4 What is the transfer time if you are to read a file containing 100,000 records of 100 bytes each sequentially? 3. Buffer management (5 points) Assuming that you have a four frame bufferpool. Please show the bufffer content given the workload listed in the table below using LRU and MRU strategies. We start from T1 and moves forward by one on each page reference. For your solution, highlight or cirle the frame in the bufferpool each time that a memory access caused a “miss” in the buffer pool (i.e., a page is read that is not currently in the buffer pool), when the page is put in the buffer pool. When the buffer pool has unused slots (such as at the beginning, when all four slots are empty), it will put newly read data in the first unused slot. The pages to be read from disk are labelled A through G. For each access the page is pinned, and then immediately unpinned. Assume one page on disk fits perfectly with one frame on the bufferpool. Time Page Read T1 A T2 B T3 C T4 A T5 D T6 E T7 E T8 A T9 B T10 F T11 C T12 G T13 A T14 B T15 B T16 D T17 G T18 F T19 A T20 F T21 C T22 F T23 B T24 G Buffer Pool LRU strategy Time Frame 1 Frame 2 Frame 3 Frame 4 T1 ……. …… …. T2 ….. MRU strategy Time Frame 1 Frame 2 Frame 3 Frame 4 T1 ……. …… …. T2 …..

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Database: Disk, File Storage, Organization And B+ Tree
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