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Associative file structures are potentiallv valuable for many database and artificial lntelllgence applications, but very 11tt1e information 1s available to database designers trying to choose an appropriate file structure for a particular problem This paper describes an experiment comparlng the retrieval performance of K-d trees, quad-trees, and flat files, as measured by CPU time, wall clock time, and I/O operations Five types of queries are used exact match, partial match, range search, nearest neighbor. and best match The database used in this study 1s a static medical database of half a mllllon characters with the parlent lnrormatlon removed Results suggest that there is no one best type of file structure for all types of assoclatlve queries, quad trees dominated with some query classes, K-d trees wrth others Motlratlon for Assoclatlve File Structures Many data base applications are inherently multldrmenslonal, but data has usually been forced into primary o;ey file structures The main shortcoming primary key structures for information processing applications 1s the absence of support for multlkey retrieval functions Assoc:ative, or multikey, file structures can srmpllfy the mapplng of multlkey data to physical storage as well as support a richer scope of access functions Data retrieval 1s based on content rather than address or file index and involves more substantive relations among the keys being matched It 1s not necessary to sequence a file with a unique key In addltlon to data base appllcatlons, associative f,le structures have found applications in several dreas of artificial intelligence including Image processing, robotics, cartography, pattern recognition, statrstlcs. and lnformatlon retrieval Knowledge-based systems and expert systems are often viewed as data base systems with added :ntelllgence to augment the user interface, multrkey retrieval capability 1s especially attractive for these applications PermIssIon to COPY whout fee all or part of this material IS granted provl&d that the copies are not made or dlstrlbuted for direct commcrclal advantage, the ACM copyrIght notICe and the Us of the pubhc&lon and its date appear, and nottce IS gwen that copYng 1s by permission of the Assoclatlon for Computmg Machmery To COPY otherwse, or to repubhsh, reqmres a fee and/or speclflc PermIssIon @ 1985 ACM 0-89791-160-l/85/005/0291 $00 75 File design 1s not a simple problem [271. there are many relevant factors that can drastically affect performance 121 I and cost. Data base designers faced wrth the chore of choosrng an associative file structure have very few resources with which to attack this difficult task Few studies of the performance and cost characteristics of these new file structures are available This paper is an attempt to address this deficiency w1t.h a study of the performance of K-d trees and quad-trees on secondary storage with a direct access file organization The associative query algorithms for quad-trees that were used for these experiments ale also given because they are not available elsewhere in the literature. Review of Flat Files K-d Trees and Quad-Trees ----f--~Performance and cost characteristics are not always portable across operating environments This 1s partly due to lmplementatlon differences in file access methods Cardenas and Sagamang [ 10,ll I pointed out that another very important performance factor IS the manner in which lists or indexes are actually organized and managed In addition to file structure differences and environmental differences, the “best” or even an appropriate file structure [12] also depends on the data and users Guidelines and methodologies for the comparison of file structures in the targeted production environment are necessary Sequential or “flat” files here chosen as a reasonable standard to use for comparison with other structures It 1s certainly the most basic of any file structure It 1s logically simple and 1t is easy to implement, however, for on-line applications, 1t 1s should be limited to small files because retrlebal 1s slow Intuition would lead one to assume that a sequential file is not worthy of conslderatlon for associative retrieval, but the simpllclty of the structure makes it a viable solution for many applications K-d trees [43 are multldlmenslonal homogeneous blnarv trees At the root lebel, the first key is used as the primary dlscrimrnator for branching declslons At eacn successive level, the next key IS used as the primary drs@riminator If more than k levels are necessary, the process repeats again beginning with the first key at the k+l level This cycle continues for as many levels as necessary When the primary discriminator of a node IS equal to the corresponding query key, secondary dlscrlmlnators are used until a secondary hey does not match the corresponding query key Secondary dlscrlmlnators begin with the key after the primary dlscrlmlnator and continue to the last

Multikey retrieval from K-d trees and QUAD-trees