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The quadratic split heuristic works this way: First, it picks a pair of entries a and b from S such that putting them in the same node would result in a bounding box with the maximum wasted space; that is, the area of the minimum bounding box of a and b minus the sum of the areas of a and b is the largest The heuristic places the entries a and b in sets S1 and S2 respectively It then iteratively adds the remaining entries, one entry per iteration, to one of the two sets S1 or S2 At each iteration, for each remaining entry e, let ie,1 denote the increase in the size of the bounding box of S1 if e is added to S1 and let ie,2 denote the corresponding increase for S2 In each iteration, the heuristic chooses one of the entries with the maximum difference of ie,1 and ie,2 and adds it to S1 if ie,1 is less than ie,2 , and to S2 otherwise That is, an entry with maximum preference for one of S1 or S2 is chosen at each iteration The iteration stops when all entries have been assigned, or when one of the sets S1 or S2 has enough entries that all remaining entries have to be added to the other set so the nodes constructed from S1 and S2 both have the required minimum occupancy The heuristic then adds all unassigned entries to the set with fewer entries Deletion: Deletion can be performed like a B+ -tree deletion, borrowing entries from sibling nodes, or merging sibling nodes if a node becomes underfull An alternative approach redistributes all the entries of underfull nodes to sibling nodes, with the aim of improving the clustering of entries in the R-tree See the bibliographical references for more details on insertion and deletion operations on R-trees, as well as on variants of R-trees, called R -trees or R+ -trees The storage ef ciency of R-trees is better than that of k-d trees or quadtrees, since a polygon is stored only once, and we can ensure easily that each node is at least half full However, querying may be slower, since multiple paths have to be searched Spatial joins are simpler with quadtrees than with R-trees, since all quadtrees on a region are partitioned in the same manner However, because of their better storage ef ciency, and their similarity to B-trees, R-trees and their variants have proved popular in database systems that support spatial data.

Faculty FacSSN 111-11-1111 222-22-2222 333-33-3333 Faculty PRODUCT Student FacSSN 111-11-1111 111-11-1111 111-11-1111 222-22-2222 222-22-2222 222-22-2222 333-33-3333 333-33-3333 333-33-3333 StdSSN 111-11-1111 444-44-4444 555-55-5555 111-11-1111 444-44-4444 555-55-5555 111-11-1111 444-44-4444 555-55-5555

#Bytes(B->A)

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Multimedia data, such as images, audio, and video an increasingly popular form of data are today almost always stored outside the database, in le systems This kind of storage is not a problem when the number of multimedia objects is relatively small, since features provided by databases are usually not important However, database features become important when the number of multimedia objects stored is large Issues such as transactional updates, querying facilities, and indexing then become important Multimedia objects often have descriptive attributes, such as those indicating when they were created, who created them, and to what category they belong One approach to building a database for such multimedia objects is to use databases for storing the descriptive attributes and for keeping track of the les in which the multimedia objects are stored

The McGraw Hill Companies, 2001

23

"Novell_ Server34" 922 "[132157 18224]" 95 "Novell_ Server34" 88 "[13215 244152]" 29 "[13240 21561]" 675

Student StdSSN 111-11-1111 444-44-4444 555-55-5555

.

However, storing multimedia outside the database makes it harder to provide database functionality, such as indexing on the basis of actual multimedia data content It can also lead to inconsistencies, such as a le that is noted in the database, but whose contents are missing, or vice versa It is therefore desirable to store the data themselves in the database Several issues have to be addressed if multimedia data are to be stored in a database The database must support large objects, since multimedia data such as videos can occupy up to a few gigabytes of storage Many database systems do not support objects larger than a few gigabytes Larger objects could be split into smaller pieces and stored in the database Alternatively, the multimedia object may be stored in a le system, but the database may contain a pointer to the object; the pointer would typically be a le name The SQL/MED standard (MED stands for Management of External Data), which is under development, allows external data, such as les, to be treated as if they are part of the database With SQL/MED, the object would appear to be part of the database, but can be stored externally We discuss multimedia data formats in Section 2341 The retrieval of some types of data, such as audio and video, has the requirement that data delivery must proceed at a guaranteed steady rate Such data are sometimes called isochronous data, or continuous-media data For example, if audio data are not supplied in time, there will be gaps in the sound If the data are supplied too fast, system buffers may over ow, resulting in loss of data We discuss continuous-media data in Section 2342 Similarity-based retrieval is needed in many multimedia database applications For example, in a database that stores ngerprint images, a query ngerprint image is provided, and ngerprints in the database that are similar to the query ngerprint must be retrieved Index structures such as B+ -trees and R-trees cannot be used for this purpose; special index structures need to be created We discuss similarity-based retrieval in Section 2343.

79,377 38,130 6,394 9,354 337,690

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