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since the disk wears out Failures do not occur independently either: consider a re in the building, an earthquake, or purchase of a set of disks that come from a bad manufacturing batch) Reliability of a disk array can be increased by storing redundant information If a disk failure occurs, the redundant information is used to reconstruct the data on the failed disk Redundancy can immensely increase the MTTF of a disk array When incorporating redundancy into a disk array design, we have to make two choices First, we have to decide where to store the redundant information We can either store the redundant information on a small number of check disks or we can distribute the redundant information uniformly over all disks The second choice we have to make is how to compute the redundant information Most disk arrays store parity information: In the parity scheme, an extra check disk contains information that can be used to recover from failure of any one disk in the array Assume that we have a disk array with D disks and consider the rst bit on each data disk Suppose that i of the D data bits are one The rst bit on the check disk is set to one if i is odd, otherwise it is set to zero This bit on the check disk is called the parity of the data bits The check disk contains parity information for each set of corresponding D data bits To recover the value of the rst bit of a failed disk we rst count the number of bits that are one on the D 1 nonfailed disks; let this number be j If j is odd and the parity bit is one, or if j is even and the parity bit is zero, then the value of the bit on the failed disk must have been zero Otherwise, the value of the bit on the failed disk must have been one Thus, with parity we can recover from failure of any one disk Reconstruction of the lost information involves reading all data disks and the check disk For example, with an additional 10 disks with redundant information, the MTTF of our example storage system with 100 data disks can be increased to more than 250 years! What is more important, a large MTTF implies a small failure probability during the actual usage time of the storage system, which is usually much smaller than the reported lifetime or the MTTF (Who actually uses 10-year-old disks ) In a RAID system, the disk array is partitioned into reliability groups, where a reliability group consists of a set of data disks and a set of check disks A common redundancy scheme (see box) is applied to each group The number of check disks depends on the RAID level chosen In the remainder of this section, we assume for ease of explanation that there is only one reliability group The reader should keep in mind that actual RAID implementations consist of several reliability groups, and that the number of groups plays a role in the overall reliability of the resulting storage system.

{ ElectronicPhone phone = new ElectronicPhone( ); phone.Ring( ); // accessing the base method } static void Main( ) { Tester t = new Tester( ); t.Run( ); } } }

The integrated database is to have a single Education relation, created from the similar Highschool record and College record relations Since the attribute minor does not exist in the high school record, the constant attribute null is added to the relation Given the relations

Solution to Exercise 11-2. Extend Exercise 11-1 to illustrate a polymorphic method. Have the derived class override the Ring( ) method to display a different message. The only trick here is that you have to make sure to mark the Ring( ) method in the base class as virtual, and be sure to use the override keyword on the Ring( ) method in the derived class. Example A-27 shows how to do that.

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Highschool record: RELATION child, schoolname : subject;

Example A-27. One solution to Exercise 11-2

College record: RELATION child, schoolname : major, minor;

using using using using System; System.Collections.Generic; System.Linq; System.Text;

Education: RELATION = ( Highschool record (schooltype="high school",minor="null") ) ( College record (schooltype="college") ); child, schooltype, schoolname : major, minor;

namespace Exercise_11_2 { public class Telephone { protected string phonetype; public virtual void Ring( ) // now virtual { Console.WriteLine("Ringing the {0} phone. Ring Ring.", phonetype); } } public class ElectronicPhone : Telephone { public ElectronicPhone( ) { this.phonetype = "Digital"; // access protected member } public override void Ring( ) // override { Console.WriteLine("Ringing the {0} phone. Beep Beep.", phonetype); } } public class Tester { public void Run( ) {

Throughout the discussion of the di erent RAID levels, we consider sample data that would just t on four disks That is, without any RAID technology our storage system would consist of exactly four data disks Depending on the RAID level chosen, the number of additional disks varies from zero to four

The new attribute schooltype distinguishes the tuples obtained from the two views when needed Since we do not know whether schoolname is unique in the combined domain, schooltype has to appear in the ruling part

Example A-27. One solution to Exercise 11-2 (continued)

The second, technical solution is again to create subrelations The subrelations contain all those dependent attributes which are not appropriate to the general relation

// assign derived instance to base reference Telephone phone = new ElectronicPhone( ); phone.Ring( ); // accessing the polymorphic method } static void Main( ) { Tester t = new Tester( ); t.Run( ); } } }

Sec 7-5

Solution to Exercise 11-3. Change the Telephone class to abstract, and make Ring( ) an abstract method. Derive two new classes from Telephone: DigitalPhone and TalkingPhone. Each derived class should set the phonetype, and override the Ring( ) method. This time around, the Telephone has become abstract (there may be some social commentary there, but this is just a programming book, so we ll leave it alone). Be sure to mark both the Ring( ) method and the class itself as abstract. Now the derived classes are obligated to override the Ring( ) method appropriately. Example A-28 shows the code.

We nd subrelations of the Employees for Managers with their stock options, for Salesmen with their sales quotas and territories, and for Retirees with the attribute last day worked We note that having subrelations in the database model does not imply having corresponding les There may well be one EMPLOYEE le with a number of variant records Derivable Attributes We may nd in some views attributes which are derivable from other attributes These embody strong connections which are easy to miss Only the enumeration of a more general category, computational functional dependencies, of the F Ds treated earlier will show such redundancy Analysis of the data does not show con icts in a model containing derived values, since the attributes are not comparable with the source attributes Such attributes may have existed within view models or arisen after integration Example 7-15

Example A-28. One solution to Exercise 11-3. Exercise 11-3

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