13.1 through 13.5, 13.10 and 13.11

-.-Chapter 13 Disk Storage, Basic File Structures, and Hashingthen use a new hashing function (based on the new value of M) to redistribute therecords. These reorganizations can be quite time consuming for large files. Newerdynamic file organizations based on hashing allow the number of buckets to varydvnamically with only localized reorganization (see Section 13.8.3).When using external hashing, searching for a record given a value of some fieldother than the hash field is as expensive as in the case of an unordered file. Recorddeletion can be inplemented by removing the record from its bucket. If the buckethas an overflow chain, we can move one of the overflow records into the bucket toreplace the deleted record. If the record to be deleted is already in overflow, we simplyrernove it from the linked list. Notice that rernoving an overflow record impliesthat rve should keep track of emprty positions in overflow. This is done easily bymaintainir-rg a linked list of unused overflow locations.Modiffing a record's field value depends on two factors: the search condition tolocate the record and the field to be modified. If the search condition is an equalitycomparison on the hash field, we can locate the record efficiently by using the hashingfunction; otherwise, we must do a linear search. A nonhash field can be modifiedby changing the record and rewriting it in the same bucket. Modifring the hashfield means that the record can move to another bucket, which requires deletion ofthe old record followed bv insertion of the modified record.13.8.3 Hashing Techniques That Allow DynamicFile ExpansionA major drawback of the srarlc hashing scheme just discussed is that the hashaddress space is fixed. Hence, it is difficult to expand or shrink the file dynamically.The schemes described in this section attempt to remedy this situation. The firstscheme-extendible hashing-stores an acces structure in addition to the fiie, andhence is somewhat sirnilar to indexing (Chapter 14). The main difference is that theaccesstructure is based on the values that result after application ofthe hash functionto the search field. hr indexing, the acces structure is based on the values ofthesearch freld itself. The second technique, called linear hashing, does not requireadditional accesstmctures.These hashing schemes take advantage of the f-acthat the result of applying a hashingfunction is a r.ronnegative integer and hence can be represented as a binary number.The access structure is built on the binary representation of the hashingfunction result, which is a string of bits. We call this the hash value of a record.Records are distributed amons buckets based on the values of the lendirry bits intheir hash values.Extendible Hashing. In extendible hashing, a type of directory-an array of 2'rbucket addresses-is maintained, where d is called the global depth of the directory.The integer value corresponding to the first (high-order) d bits of a hash valueis used as an index to the array to determine a directory entry, and the address inthat entry determines the bucket in which the corresponding records are stored.