大数据库复习题2(问题详解)

复习题（2）1、试分别判断下列图中G1和G2是否互模拟(bisimulation)，并说明理由:答案：(1) 在图中标出各点的状态，我们构造关系，可知G2可以模拟G1，下面我们讨论abc ab cc G 1 G 2dd daa abccb G 1=G 2=是否可模拟，在G2中有一个a 变换可对应到G1中2个变换，即，。

但有两个变换b ，c ，而在G1中仅存在只有b或只有c 的状态点，可知G1和G2不能互模拟。

(2) 如图，标出各状态点，构造有关系可知其中G1中的点均可由G2中的点模拟，下面我们考虑可知同样其中G2中的点均可由G1中的点模拟. 所以G1和G2为互模拟的。

2、 给定如下数据图(Data Graph)：address r1c1c2s2s3s6s7s10company companyname name url address “Widget ”“Trenton ”“Gadget ”“www.gp.fr ”“Paris ”p2p1p3s0s1s4s5s8s9personperson person “Smith ”name position namephone name position “Manager ”“Jones ”“5552121”“Dupont ”“Sales ”employeemanagesceoworks-for works-for works-for ceo试给出其Strong DataGuide 图答案：Strong DataGuide 图3、 Consider the relation, r , shown in Figure 5.27. Give the result of the following query :Figure 5.27Query 1:select building , room number , time_slo_ id , count (*) from rgroup by rollup (building , room number , time_slo_ id )Query 1:select building , room number, time_slo_ id , count (*) from rgroup by cube (building , room number , time_slo_ id )答案：Query 1Query 2:group by后带rollup子句与group by后带cube子句的唯一区别就是：带cube子句的group by会产生更多的分组统计数据。

cube后的列有多少种组合（注意组合是与顺序无关的）就会有多少种分组。

4、[Disks and Access Time]Consider a disk with a sector扇区 size of 512bytes, 63 sectors per track磁道, 16,383 tracks per surface盘面, 8 double-sided platters柱面 (i.e., 16 surfaces). The disk platters rotate at 7,200 rpm (revolutions per minute). The average seek time is 9 msec, whereas the track-to-track seek time is 1 msec.Suppose that a page size of 4096 bytes is chosen. Suppose that a file containing 1,000,000 records of 256 bytes each is to be stored on sucha disk. No record is allowed to span two pages (use these numbers inappropriate places in your calculation).(a) What is the capacity of the disk?(b) If the file is arranged sequentially on the disk, how many cylinders are needed?(c) How much time is required to read this file sequentially?(d) How much time is needed to read 10% of the pages in the file randomly? Answer:(a) Capacity = sector size * num. of sectors per track * num. of tracks per surface * num of surfaces = 512 * 63 * 16383 * 16 = 8 455 200 768 (b) File: 1,000,000 records of 256 bytes eachNum of records per page: 4096/256 = 161,000,000/ 16 = 62,500 pages or 62,500 * 8 = 500,000 sectorsEach cylinder has 63 * 16 = 1,008 sectorsSo we need 496.031746 cylinders.(c) We analyze the cost using the following three components:Seek time: This access seeks the initial position of the file (whose cost can be approximated using the average seek time) and then seeks between adjacent tracks 496 times (whose cost is the track-to-track seek time). So the seek time is 0.009 + 496*0.001 = 0.505 seconds.Rotational delay:The transfer time of one track of data is 1/ (7200/60) = 0.0083 seconds. For this question, we use 0.0083/2 as an estimate of the rotational delay (other numbers between 0 and 0.00415 are also fine). So the rotational delay for 497 seeks is 0.00415 * 497 = 2.06255.Transfer time: It takes 0.0083*(500000/63) = 65.8730159 seconds totransfer data in 500,000 sectors.Therefore, total access time is 0.505 + 2.06255 + 65.8730159 = 68.4405659 seconds.(d) number of pages = 6250time cost per page: 0.009 (seek) + 0.0083/2 (rotational delay) + 0.0083*8/63 (transfer) = 0.0142 secondstotal cost = 6250 * 0.0142 = 88.77 seconds5、[Disk Page Layout]The figure below shows a page containing variablelength records. The page size is 1KB (1024 bytes). It contains 3 records, some free space, and a slot directory in that order. Each record has its record id, in the form of Rid=(page id, slot number), as well as its start and end addresses in the page, as shown in the figure.Now a new record of size 200 bytes needs to be inserted into this page.Apply the record insertion operation with page compaction, ifnecessary. Show the content of the slot directory after the new record is inserted. Assume that you have only the page, not any other temporary space, to work with.Answer:Content of the slot directory, from left to right, is:[(650, 200), (0, 200), (500, 150), (200, 300)], 4, 8506、[Buffer Management for File and Index Accesses]Consider thefollowing two relations:●student(snum:integer, sname:char(30), major:char(25),standing:char(2), age:integer)●enrolled(snum:integer,ame:char(40))The following index is available:A B+ Tree index on the <snum> attribute of the student relation.Assume that the buffer size is large enough to store multiple paths of each B+ Tree but not an entire tree.(a) Consider Query 1 and Query 2 that retrieve the snum’s of studentswho have taken ‘Database Systems’ and ‘Operating Systems’,respectively, from the enrolled table. We know that Query 1 will be executed before Query 2, and both queries are executed using a file scan of the enrolled table.Which replacement policy would you recommend for the buffer manager to use to support this workload?(b) Now assume that we have retrieved the snum’s of students who havetaken ‘Database Systems’ from the enrolled table. In the exact order of the retrieved snum’s (not necessarily in sorted order),we then retrieve the names of those students via repeated lookups in the B+Tree on <snum>.For these repeated accesses to the index on student.snum, which replacement policy would you recommend for efficient buffermanagement?Query 1:select snumfrom student s, enrolled ewhere s.snum=e.snum and ame like ‘Database Systems’;Query 2:select snumfrom student s, enrolled ewhere s.snum=e.snum and ame like ‘Operating Systems’;Answer:(a) Not LRU. MRU or LRU2.(b) Now we have repeated equality searches over the B+ Tree on <sid>,with no duplicate values in the search key (because the schema does not allow a student to take the same course twice). Two possible answers:- The B+ Tree pages close to the top are repeated accessed but those at the leaf level are rarely reused. So we can use LRU.- LIFO (Last In First Out) is another possible answer. This is because over time, we have cached most nodes close to the top in memory. So the nodes recently read from the disk are mostly close to the leaves.So LIFO will replace those leaf or close-to-leaf nodes to make room for the newly requested nodes.- We also accept other answers if the student can justify well.。