Computer Science 5443 Assignment 1

This assignment should be completed individually. Please make sure that your answer is legible (typing is preferred).

1. [60] A disk drive has 5 double-sided platters, 4000 cylinders, 50 sectors per track, and 512 bytes per sector. It has a speed of 7,200 rpm (revolutions per minute), an average seek time of 10 msec, and a block (or page) size of 1024 bytes. The block address is in the form of (cylinder#, surface#, block#), and the first block of the disk is (0, 0, 0). A file of 200,000 fixed-size records is stored on this disk. The record size is 335 bytes. Answer the following questions.
   • The total capacity of the disk in bytes.
   • The maximum and the average rotational delay of the disk in msec.
   • The transfer rate of the disk in bytes per second.
   • What is the size of the file in pages if it is stored unspanned? What is the size of the file if it were stored spanned?
   • Suppose that the pages of the file are stored contiguously on the disk starting at blockaddress (1,1,2). If the file is stored unspanned, what is the address of the last page of the file? Which page of the file is at block address (2, 2, 2)?
   • If the file is stored unspanned, how many second would it take on average to read theentire file sequentially? What about read randomly?
2. [40] A heap file has 20,000 records stored unspanned on a disk, which has a block size of 1000 bytes and block address (that is, a page id) of 8 bytes. The file has a dense B+ tree index on a candidate key of a size of 45 bytes. Suppose that the index was constructed using the bulk loading algorithm of the textbook, with nodes filled completely. Answer the following questions and show the detail calculation.
   • How many levels would the index have?
   • How many nodes would be at each level?
   • How many levels would the index have if the keys are compressed to 10 bytes or less?
   • How many levels would the index have if the keys are not compressed but all nodes areonly 70% full?