AD-AIIO 1I" HARVARD UIV CA04BRID MA AIKEN COMPUJTATION LAB F/0O 5/2PREDICATE-ORIENTED DATABASE SEARCH ALSOITM4S.U)MAY 7 D E WILLARD N0001 -76--0914

UNCLASSIFIED TR-20-78 ,

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EIIEEEIIIIII-

1114 0- 1111 .

111111 .25 IIf'~ ~j1.6

MICROCOPY RESOLUTION TEST CHART

PREDICATE-OR! ENTD DATABASE SEARCH ALGOP T INMS

by

Dan E. Willard

TR-20-78 -I

This research wasq supported in part by the Office of Naval Research

under contract NOCO14-76-C-0914.

Tbk d'~tu'w.t , 1

for pubL !

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unclassi fied

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4. 1 :TLE (an~d Sb,ibie) S. TYPE OF RLPor , P. R, C.E . -technical report

Predicate-Oriented Database Search Algorithms technicalreport

6. PERFOPmiNG CkG. rk:C T1 1L .

7. AUTHOR(@,' . CONT RAC OF. GkA%1 N

Willard, Dan E. N00014-76-C-0914

9. PEF:FORMING CN'ANIZATfCN N"-ME AND ADDPL$5. 10. pkj:.Pkv EE !. .- -. -Harvard University AREA A V-OF( UNIT

Aiken Computation. LaboratoryCambridge, Massachusetts 02138

IS. CONTROLLIN OFFICE NA ' AN") A:,DFt 12. REPORT VATL

Office of Naval Research May 1978800 North Quincy Street i. NUME !.E r,.Z S I

Arlington, Virginia 22217 384 pages14. MON4ITORING AGENCY NAME & ADZRESS1j1 aiifrq t Iro,' Conirolljrg Oyit.e) IS. SECIJRITY CLPS. (ot :,,,r r

unclassified

SCRXLCJLE

16. SDITRIB6jTION STATEMENT (ot .a f's Rprt)

unlimited

17. DISTR UTION STATEmENT (oi tme abetrect entered in Biock 20, it d1hereni ltro. Reporf)

IS. SUP-PL~,EM TAkY N%,TES

19. KEy Yi OR $ (Ccnr'nue on revert, *ice i f necessar- .d :!.-nrfy by blork n'. -r

multidimensional searching low-level SUM and COUNT algorithmsrelational databases low-level FIND algorithmsB-tree E-7 algorithms

super-B-tree

20. ABSTRACT (Continue on tverso slde It neicoesaey And . entffy %y blocx nul.bL,)

Let e(x,y) denote an arbitrarily complex (nonatomic) predicate, andlet e(X,y) denote the special form that this prediate will assume when theinitial multi-component variable of x is replaced by the fixed tuple of X?.This thesis will study the question of how the set of y-records that satisfythe condition of e(Xr,y) can be efficiently retrieved. Such retrievals willbe examined in the. context of a "dynamic" environment where new records arebeing continually, inserted, deleted, and updated. This- thesis will show that

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every conceivable predicate of e(x,y) can be assigned a database anda number of D(e) such that

i) For any element of R, the set of y-records that satisfye(x,y) can be retrieved in O(logD(e)N) time (from theinitial N-membered database).

ii) The relevant database will be sufficiently flexible so thatthe user can insert, delete, or modify any of its y-recordsin O(logD(e)N) time.

The above results will be extremely significant because the number ofD(' 4 ill usually assume small values such as zero, one, or two.

The principal application of this thesis will be in the area ofautomatic programming. The purpose of that branch of computer sciencehas been to discover how automatic algorithms can be developed which domuch of the programming that has traditionally been assigned to humanbeings.

Such automatic algorithms have been advocated by many computerscientists (Codd-70, Boehm-72, Date-77)_4ecause these procedures woulddramatically reduce-the cost of writing computer programs. The combinedwork of the cited authors have shown that,

zi) the cost of developing computer software may greatly exceedhardware costs in the 1980's (Boehm has estimated that computerprogrammer labor costs will constitute 90 percent of all theAir Force's 1985 computer-related expenditures),

ii) and that the health of the computer industry requires lowersoftware development costs (even if this is done in the contextof a trade-off that modestly increases the hardware costs).

The importance of automatic database search algorithms was further confirmedin a recent panel discussion.( @ed q5) The members of that panel con-cluded that such automatic search algorithms would be extremely usefulif these algorithms could be made to be moderately efficient. This thesiswill lay the foundations of the theory that should be used in the develop-ment of authomatic predicate searching algorithms.

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