source4/lib/ldb/ldb_sqlite3/trees.ps

   1 %!PS-Adobe-2.0
   2 %%Creator: dvips(k) 5.86 Copyright 1999 Radical Eye Software
   3 %%Title: trees.dvi
   4 %%Pages: 7
   5 %%PageOrder: Ascend
   6 %%BoundingBox: 0 0 596 842
   7 %%EndComments
   8 %DVIPSWebPage: (www.radicaleye.com)
   9 %DVIPSCommandLine: dvips -f trees.dvi
  10 %DVIPSParameters: dpi=600, compressed
  11 %DVIPSSource:  TeX output 2000.05.06:2055
  12 %%BeginProcSet: texc.pro
  13 %!
  14 /TeXDict 300 dict def TeXDict begin/N{def}def/B{bind def}N/S{exch}N/X{S
  15 N}B/A{dup}B/TR{translate}N/isls false N/vsize 11 72 mul N/hsize 8.5 72
  16 mul N/landplus90{false}def/@rigin{isls{[0 landplus90{1 -1}{-1 1}ifelse 0
  17 0 0]concat}if 72 Resolution div 72 VResolution div neg scale isls{
  18 landplus90{VResolution 72 div vsize mul 0 exch}{Resolution -72 div hsize
  19 mul 0}ifelse TR}if Resolution VResolution vsize -72 div 1 add mul TR[
  20 matrix currentmatrix{A A round sub abs 0.00001 lt{round}if}forall round
  21 exch round exch]setmatrix}N/@landscape{/isls true N}B/@manualfeed{
  22 statusdict/manualfeed true put}B/@copies{/#copies X}B/FMat[1 0 0 -1 0 0]
  23 N/FBB[0 0 0 0]N/nn 0 N/IEn 0 N/ctr 0 N/df-tail{/nn 8 dict N nn begin
  24 /FontType 3 N/FontMatrix fntrx N/FontBBox FBB N string/base X array
  25 /BitMaps X/BuildChar{CharBuilder}N/Encoding IEn N end A{/foo setfont}2
  26 array copy cvx N load 0 nn put/ctr 0 N[}B/sf 0 N/df{/sf 1 N/fntrx FMat N
  27 df-tail}B/dfs{div/sf X/fntrx[sf 0 0 sf neg 0 0]N df-tail}B/E{pop nn A
  28 definefont setfont}B/Cw{Cd A length 5 sub get}B/Ch{Cd A length 4 sub get
  29 }B/Cx{128 Cd A length 3 sub get sub}B/Cy{Cd A length 2 sub get 127 sub}
  30 B/Cdx{Cd A length 1 sub get}B/Ci{Cd A type/stringtype ne{ctr get/ctr ctr
  31 1 add N}if}B/id 0 N/rw 0 N/rc 0 N/gp 0 N/cp 0 N/G 0 N/CharBuilder{save 3
  32 1 roll S A/base get 2 index get S/BitMaps get S get/Cd X pop/ctr 0 N Cdx
  33 0 Cx Cy Ch sub Cx Cw add Cy setcachedevice Cw Ch true[1 0 0 -1 -.1 Cx
  34 sub Cy .1 sub]/id Ci N/rw Cw 7 add 8 idiv string N/rc 0 N/gp 0 N/cp 0 N{
  35 rc 0 ne{rc 1 sub/rc X rw}{G}ifelse}imagemask restore}B/G{{id gp get/gp
  36 gp 1 add N A 18 mod S 18 idiv pl S get exec}loop}B/adv{cp add/cp X}B
  37 /chg{rw cp id gp 4 index getinterval putinterval A gp add/gp X adv}B/nd{
  38 /cp 0 N rw exit}B/lsh{rw cp 2 copy get A 0 eq{pop 1}{A 255 eq{pop 254}{
  39 A A add 255 and S 1 and or}ifelse}ifelse put 1 adv}B/rsh{rw cp 2 copy
  40 get A 0 eq{pop 128}{A 255 eq{pop 127}{A 2 idiv S 128 and or}ifelse}
  41 ifelse put 1 adv}B/clr{rw cp 2 index string putinterval adv}B/set{rw cp
  42 fillstr 0 4 index getinterval putinterval adv}B/fillstr 18 string 0 1 17
  43 {2 copy 255 put pop}for N/pl[{adv 1 chg}{adv 1 chg nd}{1 add chg}{1 add
  44 chg nd}{adv lsh}{adv lsh nd}{adv rsh}{adv rsh nd}{1 add adv}{/rc X nd}{
  45 1 add set}{1 add clr}{adv 2 chg}{adv 2 chg nd}{pop nd}]A{bind pop}
  46 forall N/D{/cc X A type/stringtype ne{]}if nn/base get cc ctr put nn
  47 /BitMaps get S ctr S sf 1 ne{A A length 1 sub A 2 index S get sf div put
  48 }if put/ctr ctr 1 add N}B/I{cc 1 add D}B/bop{userdict/bop-hook known{
  49 bop-hook}if/SI save N @rigin 0 0 moveto/V matrix currentmatrix A 1 get A
  50 mul exch 0 get A mul add .99 lt{/QV}{/RV}ifelse load def pop pop}N/eop{
  51 SI restore userdict/eop-hook known{eop-hook}if showpage}N/@start{
  52 userdict/start-hook known{start-hook}if pop/VResolution X/Resolution X
  53 1000 div/DVImag X/IEn 256 array N 2 string 0 1 255{IEn S A 360 add 36 4
  54 index cvrs cvn put}for pop 65781.76 div/vsize X 65781.76 div/hsize X}N
  55 /p{show}N/RMat[1 0 0 -1 0 0]N/BDot 260 string N/Rx 0 N/Ry 0 N/V{}B/RV/v{
  56 /Ry X/Rx X V}B statusdict begin/product where{pop false[(Display)(NeXT)
  57 (LaserWriter 16/600)]{A length product length le{A length product exch 0
  58 exch getinterval eq{pop true exit}if}{pop}ifelse}forall}{false}ifelse
  59 end{{gsave TR -.1 .1 TR 1 1 scale Rx Ry false RMat{BDot}imagemask
  60 grestore}}{{gsave TR -.1 .1 TR Rx Ry scale 1 1 false RMat{BDot}
  61 imagemask grestore}}ifelse B/QV{gsave newpath transform round exch round
  62 exch itransform moveto Rx 0 rlineto 0 Ry neg rlineto Rx neg 0 rlineto
  63 fill grestore}B/a{moveto}B/delta 0 N/tail{A/delta X 0 rmoveto}B/M{S p
  64 delta add tail}B/b{S p tail}B/c{-4 M}B/d{-3 M}B/e{-2 M}B/f{-1 M}B/g{0 M}
  65 B/h{1 M}B/i{2 M}B/j{3 M}B/k{4 M}B/w{0 rmoveto}B/l{p -4 w}B/m{p -3 w}B/n{
  66 p -2 w}B/o{p -1 w}B/q{p 1 w}B/r{p 2 w}B/s{p 3 w}B/t{p 4 w}B/x{0 S
  67 rmoveto}B/y{3 2 roll p a}B/bos{/SS save N}B/eos{SS restore}B end
  68
  69 %%EndProcSet
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1312 %%Page: 1 1
1313 1 0 bop 290 639 a Fo(Genealogical)56 b(Represen)l(tation)e(of)f(T)-13
1314 b(rees)52 b(in)g(Databases)1686 822 y Fn(First)46 b(Draft)1247
1315 1063 y Fm(Miguel)36 b(Sofer)i(<mig@utdt.edu>)1359 1179
1316 y Fl(Univ)m(ersidad)33 b(T)-8 b(orcuato)33 b(Di)f(T)-8
1317 b(ella)1728 1295 y(Buenos)33 b(Aires)1797 1411 y(Argen)m(tina)1746
1318 1606 y(Ma)m(y)h(6,)e(2000)1839 1905 y Fk(Abstract)441
1319 2035 y Fj(blah)25 b(blah)h(.)13 b(.)g(.)118 2310 y Fi(1)131
1320 b(In)l(tro)t(duction)118 2491 y Fh(T)-7 b(rees)28 b(are)h(a)g(v)n(ery)f
1321 (frequen)n(t)h(data)f(structure.)41 b(They)30 b(are)e(the)h(natural)g
1322 (represen)n(tation)e(for)i(instance)g(for)f(organiza-)118
1323 2591 y(tional)f(c)n(harts,)g(threaded)g(discussion)g(groups,)f(some)h
1324 (bills)g(of)h(materials,)e(.)14 b(.)g(.)243 2691 y(A)n(t)28
1325 b(least)f(t)n(w)n(o)f(alternativ)n(e)h(represen)n(tations)e(for)i
1326 (trees)g(in)h(RDBMs)g(are)e(kno)n(wn)h(and)h(used:)220
1327 2857 y(1.)41 b Fg(P)m(oin)m(ters:)k Fh(a)31 b(\034eld)h(in)h(the)f(c)n
1328 (hild)g(record)e(references)h(the)h(paren)n(t)f(no)r(de.)50
1329 b(This)32 b(seems)g(to)f(b)r(e)i(the)f(canonical)326
1330 2956 y(represen)n(tation.)38 b(Some)29 b(DB)g(engines)f(pro)n(vide)g
1331 (sp)r(ecial)g(SQL)g(extensions)g(to)h(simplify)g(tree)g(searc)n(hes;)e
1332 (Oracle)326 3056 y(tree)d(extensions)g(are)g(an)h(example)f(\(see)h
1333 (for)f(instance)g([1]\);)i(DB2's)f(WITH)g(can)f(b)r(e)i(used)e(for)h
1334 (this)g(purp)r(ose)f(to)r(o)326 3156 y(\(see)j([3],)g(pp)h(139-162\).)
1335 220 3322 y(2.)41 b Fg(Nested)35 b(Sets:)43 b Fh(t)n(w)n(o)30
1336 b(n)n(umeric)h(\034elds)g(in)g(ev)n(ery)f(no)r(de)h(record)f(co)r(de)h
1337 (the)g(tree)g(structure.)47 b(I)31 b(can't)g(pro)n(vide)f(a)326
1338 3421 y(b)r(etter)e(or)e(briefer)h(description)g(of)h(this)g(metho)r(d)g
1339 (than)f(the)h(four)f(articles)g([2].)118 3587 y(These)g(t)n(w)n(o)g
1340 (metho)r(ds)h(o\033er)f(di\033eren)n(t)h(adv)-5 b(an)n(tages)25
1341 b(and)j(disadv)-5 b(an)n(tages:)243 3753 y Ff(\017)41
1342 b Fh(P)n(oin)n(ters)30 b(are)g(extremely)g(e\036cien)n(t)h(for)f(no)r
1343 (de)h(insertion)f(and/or)g(deletion,)h(but)h(require)e(recursiv)n(e)f
1344 (table)i(ac-)326 3853 y(cesses)e(to)h(searc)n(h)f(the)h(tree)g(\(I)h
1345 (do)f(not)g(kno)n(w)f(the)i(implemen)n(tation)f(details)g(of)g(the)h
1346 (Oracle)e(tree)g(extensions,)326 3953 y(whic)n(h)e(as)g(far)g(as)g(I)g
1347 (kno)n(w)g(ma)n(y)g(solv)n(e)f(this)i(problem)f(in)n(ternally;)g(they)g
1348 (de\034nitely)h(solv)n(e)f(it)g(for)g(the)h(end)g(user\).)243
1349 4119 y Ff(\017)41 b Fh(Nested)30 b(sets)g(are)f(v)n(ery)f(e\036cien)n
1350 (t)i(for)g(tree)f(searc)n(hes,)g(but)i(are)e(rather)f(exp)r(ensiv)n(e)i
1351 (for)f(no)r(de)h(insertion)f(and/or)326 4218 y(deletion:)37
1352 b(they)27 b(require)g(up)r(dating)g(p)r(oten)n(tially)h(man)n(y)f(no)r
1353 (des.)243 4384 y(W)-7 b(e)30 b(prop)r(ose)f(here)h(a)g(di\033eren)n(t)h
1354 (represen)n(tation,)e(based)g(on)i(no)r(de)f(iden)n(ti\034ers)g(whic)n
1355 (h)g(are)f(\020genealogical)f(iden)n(ti-)118 4484 y(\034ers\021:)44
1356 b(they)32 b(con)n(tain)f(the)h(complete)f(genealogy)f(of)h(the)h(no)r
1357 (de,)h(i.e.,)g(the)f(list)g(of)g(ancestors)d(up)j(to)g(the)g(ro)r(ot)f
1358 (of)g(the)118 4584 y(tree.)243 4683 y(This)j(allo)n(ws)f(to)i(replace)e
1359 (man)n(y)h(searc)n(hes)f(in)h(database)g(tables)g(with)h(string)f(op)r
1360 (erations)f(on)h(the)h(index.)58 b(The)118 4783 y(result,)24
1361 b(as)f(explained)h(in)g(Section)g(3)f(is)h(that)g(tree)f(searc)n(hes)f
1362 (pro)r(ceed)h(at)h(\020nested)f(sets\021)30 b(sp)r(eed,)25
1363 b(while)f(no)r(de)g(insertions)118 4882 y(and)k(deletions)f(are)f(as)h
1364 (fast)h(as)f(with)h(p)r(oin)n(ters.)243 4982 y(The)i(ob)n(vious)f(do)n
1365 (wnside)h(of)h(the)g(metho)r(d)g(is)f(that)h(the)g(primary)f(k)n(ey)f
1366 (in)i(the)g(tree)f(needs)h(to)f(b)r(e)h(a)g(v)-5 b(ariable)29
1367 b(size)118 5082 y(text)j(\034eld,)h(and)f(that)g(the)g(iden)n
1368 (ti\034ers)f(ma)n(y)g(b)r(e)i(extremelly)e(long)g(for)g(deep)h(trees.)
1369 49 b(W)-7 b(e)32 b(will)g(pro)n(vide)e(estimates)i(of)118
1370 5181 y(the)c(size)f(required)g(as)g(a)g(function)h(of)g(the)f
1371 (magnitude)h(of)f(the)h(tree.)1987 5653 y(1)p eop
1372 %%Page: 2 2
1373 2 1 bop 118 291 a Fi(2)131 b(Genealogical)45 b(iden)l(ti\034ers)g(for)f
1374 (trees)118 489 y Fm(2.1)112 b(De\034nition)118 642 y
1375 Fh(W)-7 b(e)28 b(de\034ne)g Fe(gene)l(alo)l(gic)l(al)k(identi\034ers)j
1376 Fh(recursiv)n(ely)25 b(as)i(follo)n(ws:)326 808 y Fg(De\034nition:)59
1377 b Fe(The)42 b(gene)l(alo)l(gic)l(al)h(identi\034er)f(\(gID\))e(of)i(a)f
1378 (no)l(de)h(is)f(obtaine)l(d)h(by)g(app)l(ending)g(a)f(child)326
1379 908 y(identi\034er)30 b(to)g(the)g(gene)l(alo)l(gic)l(al)h
1380 (identi\034er)g(of)f(the)g(p)l(ar)l(ent)f(no)l(de.)243
1381 1074 y Fh(Remark)40 b(that)h(genealogical)e(iden)n(ti\034ers)i(are)f
1382 (rather)g(w)n(ell)h(kno)n(wn)f(and)h(used;)48 b(common)41
1383 b(examples)f(are)g(the)118 1174 y(\020path+\034le-name\021)33
1384 b(in)28 b(a)f(computer)g(\034le)h(system)f(and)h(the)f(URLs)h(within)g
1385 (a)f(WWW.)243 1273 y(The)d(name)g(\020genealogical)e(iden)n
1386 (ti\034er\021)30 b(is)24 b(suggested)g(b)n(y)g(the)g(fact)h(that)f(the)
1387 h(v)-5 b(alue)24 b(of)g(the)h(iden)n(ti\034er)f(con)n(tains)f(the)118
1388 1373 y(complete)30 b(genealogy)d(of)j(the)g(no)r(de:)41
1389 b(it)30 b(con)n(tains)e(as)h(a)h(substring)f(the)h(gID)f(of)h(its)g
1390 (father,)g(whic)n(h)f(in)h(turn)g(con)n(tains)118 1472
1391 y(as)d(a)g(substring)g(the)h(gID)g(of)f(the)h(grandfather,)e(.)14
1392 b(.)g(.)243 1572 y(The)27 b(ro)r(ot)g(no)r(de)h(of)f(the)h(tree)f(has)g
1393 (a)h(gID)f(with)h(v)-5 b(alue)28 b(\021)34 b(\(the)28
1394 b(empt)n(y)g(string\),)f(as)g(it)h(has)f(no)g(paren)n(t.)118
1395 1804 y Fm(2.2)112 b(Child)36 b(iden)m(ti\034ers)118 1958
1396 y Fh(The)26 b(ob)n(vious)e(c)n(hild)i(iden)n(ti\034er)g(is)f(a)h
1397 (zero-based)d(coun)n(ter:)35 b(iden)n(tify)26 b(the)h(c)n(hild)e(b)n(y)
1398 h(the)g(n)n(um)n(b)r(er)f(of)h(older)f(brethren)g(it)118
1399 2057 y(has.)243 2157 y(W)-7 b(e)25 b(could)f(represen)n(t)g(the)h(coun)
1400 n(ter)f(in)h(base)f(10;)h(this)g(ho)n(w)n(ev)n(er)e(is)i(extremely)f(w)
1401 n(asteful)g(of)h(resources.)34 b(It)25 b(is)g(m)n(uc)n(h)118
1402 2257 y(b)r(etter)33 b(to)f(represen)n(t)f(the)h(coun)n(ter)g(in)g(as)g
1403 (large)e(a)i(base)g(as)f(p)r(ossible:)46 b(in)n(terpret)32
1404 b(as)f(n)n(um)n(b)r(ers)h(a)g(set)g(of)g(c)n(haracters)118
1405 2356 y(larger)26 b(than)h({0,1,.)14 b(.)g(.)g(9}.)243
1406 2456 y(As)26 b(tree)f(op)r(erations)f(will)i(in)n(v)n(olv)n(e)f(string)
1407 g(op)r(erations)f(on)i(the)g(indices,)g(in)g(order)f(to)g(a)n(v)n(oid)g
1408 (a)g(\020quoting)g(hell\021)33 b(it)26 b(is)118 2555
1409 y(desirable)d(to)h(a)n(v)n(oid)e(using)h(an)n(y)g(c)n(haracter)f(with)i
1410 (a)g(sp)r(ecial)f(meaning)h(in)g(LIKE)g(expressions)e(or)g(regular)g
1411 (expressions;)118 2655 y(i.e.,)28 b(w)n(e)f(will)h(not)f(use)h(an)n(y)f
1412 (of)g(the)h(sym)n(b)r(ols)70 b Fd(.)44 b(*)f(^)g(\\)g([)g(])g({)h(})f
1413 (\()g(\))g(<)g(>)71 b Fh(?)37 b(|)28 b(&)f($)243 2755
1414 y(W)-7 b(e)28 b(prop)r(ose)e(to)h(reserv)n(e)f(also)g(/)i(as)f(a)g
1415 (separator)e(\(see)i(\020V)-7 b(ariable)27 b(Sized)g(gID\021)34
1416 b(b)r(elo)n(w\).)243 2854 y(If)g(w)n(e)f(limit)i(ourselv)n(es)d(to)i
1417 (ascii)f(c)n(haracters,)g(and)h(a)n(v)n(oid)e(to)i(b)r(e)g(safe)f(a)h
1418 (lot)g(of)g(other)f(c)n(haracters,)g(w)n(e)g(can)h(use)118
1419 2954 y(n)n(um)n(b)r(ers)27 b(in)h(base)f(64)g(b)n(y)g(represen)n(ting)
1420 243 3120 y Ff(\017)41 b Fh(0-9)26 b(with)i('0'-'9')f(\(dec)g(ascii)g
1421 (co)r(de)h(48-57\))243 3286 y Ff(\017)41 b Fh(10)26 b(with)i(':')37
1422 b(\(dec)28 b(ascii)f(co)r(de)h(58\))243 3452 y Ff(\017)41
1423 b Fh(11)26 b(with)i(';')g(\(dec)g(ascii)f(co)r(de)g(59\))243
1424 3618 y Ff(\017)41 b Fh(12-37)25 b(with)j('A'-'Z')g(\(dec)f(ascii)g(co)r
1425 (de)h(65-90\))243 3784 y Ff(\017)41 b Fh(38-63)25 b(with)j('a'-'z')f
1426 (\(dec)h(ascii)f(co)r(de)g(97-122\))118 3950 y(By)g(using)g(base)f(64,)
1427 h(up)g(to)h(4096)d(c)n(hildren)i(can)f(b)r(e)i(represen)n(ted)e(using)h
1428 (t)n(w)n(o)f(suc)n(h)h(digits,)g(up)h(to)f(262144)d(with)k(three)118
1429 4050 y(digits,)g(and)f(up)h(to)f(16777216)d(with)k(four)f(digits.)243
1430 4149 y(If)37 b(the)g(RDBMs)g(supp)r(orts)f(in)n(ternational)g(c)n
1431 (haracters,)h(it)g(is)g(p)r(ossible)f(to)h(further)f(increase)g(the)h
1432 (base;)k(as)36 b(an)118 4249 y(example,)30 b(b)n(y)f(using)g(the)h(95)f
1433 (additional)g(c)n(haracters)e(of)i(the)h(latin-1)f(c)n(haracter)e(set,)
1434 k(w)n(e)e(could)g(co)r(de)g(n)n(um)n(b)r(ers)g(in)h(a)118
1435 4349 y(base)f(up)g(to)g(160)f(\025)g(remark)g(that)h(ev)n(ery)f(single)
1436 h(digit)g(is)g(still)h(one)e(b)n(yte)h(in)h(this)f(represen)n(tation.)
1437 40 b(This)29 b(means)f(that)118 4448 y(w)n(e)f(expand)h(the)f(sym)n(b)r
1438 (ols)g(ab)r(o)n(v)n(e)f(b)n(y)i(represen)n(ting)243 4614
1439 y Ff(\017)41 b Fh(64-159)25 b(with)j(dec)f(latin1)g(co)r(de)h(160-255)
1440 243 4780 y(In)23 b(base)g(160,)g(up)g(to)h(25600)d(c)n(hildren)i(can)f
1441 (b)r(e)i(represen)n(ted)e(using)h(t)n(w)n(o)g(digits,)h(up)g(to)f
1442 (4096000)d(with)k(three)f(digits,)118 4880 y(and)28 b(up)f(to)h
1443 (6.5E+08)e(with)i(four)f(digits.)243 4980 y(Remark)g(that)h(base)f(con)
1444 n(v)n(ersions)f(only)h(need)i(to)e(b)r(e)i(p)r(erformed)e(at)h
1445 (insertion)g(time,)g(when)h(the)f(index)g(of)g(a)g(new)118
1446 5079 y(no)r(de)g(is)f(computed.)37 b(They)28 b(will)f(therefore)g(only)
1447 g(ha)n(v)n(e)f(an)i(impact)f(on)h(insertion)f(timings.)1987
1448 5653 y(2)p eop
1449 %%Page: 3 3
1450 3 2 bop 118 291 a Fm(2.3)112 b(Coun)m(ters:)50 b(\020delimited\021)44
1451 b(vs.)51 b(\020\034xed)38 b(size\021)118 444 y Fh(The)33
1452 b(standard)g(represen)n(tation)e(of)i(gID)h(uses)e(a)h(v)-5
1453 b(ariable)32 b(size)h(c)n(hild)h(iden)n(ti\034er,)g(and)f(delimiters)g
1454 (to)h(separate)d(the)118 543 y(gID)f(of)g(the)h(c)n(hild)f(no)r(de)g
1455 (from)f(the)i(gID)f(of)g(its)g(paren)n(t.)43 b(F)-7 b(or)30
1456 b(example,)g(w)n(e)g(can)f(represen)n(t)g(the)i(\034fth)g(c)n(hild)f
1457 (of)g(no)r(de)118 643 y('/23/27/1')24 b(as)j('/23/27/1/4'.)32
1458 b(Let)c(us)f(call)g(this)h(a)f Fg(vgID)h Fh(represen)n(tation)e(\(V)-7
1459 b(ariable)27 b(Size)h(Genealogical)d(ID\).)243 743 y(This)30
1460 b(represen)n(tation)f(allo)n(ws)f(for)i(an)n(y)g(n)n(um)n(b)r(er)g(of)g
1461 (c)n(hildren)g(of)h(a)f(no)r(de,)h(sub)5 b(ject)30 b(only)g(to)g(the)h
1462 (limitations)f(the)118 842 y(RDBMS)e(ma)n(y)f(ha)n(v)n(e)f(as)h(to)h
1463 (the)g(length)f(of)h(a)f(v)-5 b(ariable)27 b(sized)g(string.)243
1464 942 y(Alternativ)n(ely)-7 b(,)24 b(w)n(e)f(could)h(c)n(ho)r(ose)f(to)h
1465 (limit)g(from)g(the)g(outset)g(the)g(quan)n(tit)n(y)g(of)f(c)n(hildren)
1466 h(that)g(a)g(no)r(de)g(ma)n(y)f(ha)n(v)n(e;)118 1042
1467 y(this)28 b(limit)g(w)n(ould)f(dep)r(end)i(of)e(course)f(on)i(the)g
1468 (application.)36 b(Let)27 b(us)h(call)f(this)h(a)f Fg(fgID)h
1469 Fh(represen)n(tation.)243 1141 y(F)-7 b(or)25 b(example,)h(if)g(no)g
1470 (no)r(de)f(is)h(allo)n(w)n(ed)f(to)g(ha)n(v)n(e)g(more)g(than)h(25600)d
1471 (c)n(hildren,)j(w)n(e)g(could)f(represen)n(t)g(the)h(coun)n(ters)118
1472 1241 y(alw)n(a)n(ys)36 b(with)i(2)f(digits.)67 b(The)38
1473 b(no)r(de)f(whic)n(h)h(w)n(as)f(previously)f('/23/27/1/4')d(is)k(no)n
1474 (w)g('23270104'.)64 b(If)38 b(w)n(e)f(require)118 1340
1475 y(a)g(three)g(digit)h(represen)n(tation)d(of)i(no)r(des)g(\(up)h(to)f
1476 (ab)r(out)h(4)f(million)g(c)n(hildren\),)j(then)d(it)h(will)g(b)r(e)f
1477 (represen)n(ted)f(as)118 1440 y('023027001004'.)118 1672
1478 y Fm(2.4)112 b(Ordering)37 b(of)h(no)s(des)118 1825 y
1479 Fh(F)-7 b(or)35 b(some)g(applications)g(it)h(is)f(necessary)f(to)i
1480 (obtain)f(subtrees)g(ordered)f(according)g(to)i(some)f(sp)r(ecial)g
1481 (rules.)60 b(F)-7 b(or)118 1925 y(instance:)220 2090
1482 y(1.)41 b(the)34 b(complete)g(subtree)f(starting)g(at)h(a)f(no)r(de)h
1483 (is)g(listed)g(immediately)g(after)f(the)i(no)r(de)f(in)g(question)f
1484 (\(\020depth)326 2189 y(\034rst\021\))220 2354 y(2.)41
1485 b(no)r(des)27 b(with)h(a)f(common)g(paren)n(t)g(are)g(listed)g(c)n
1486 (hronologically)243 2519 y(F)-7 b(or)39 b(instance,)k(the)d(displa)n(y)
1487 f(of)h(an)f(organization)f(c)n(hart)h(is)g(usually)h(required)e(to)i
1488 (satisfy)g(at)f(least)h(the)g(\034rst)118 2619 y(condition.)h(In)29
1489 b(a)g(threaded)f(discussion)h(group)e(one)i(wishes)g(to)f(satisfy)h(b)r
1490 (oth)h(conditions)e(to)h(displa)n(y)f(the)h(messages)118
1491 2718 y(in)20 b(a)g(thread)g(\025)f(the)i(threads)e(themselv)n(es)h
1492 (\(i.e.,)i(c)n(hildren)e(of)g(the)g(ro)r(ot)f(no)r(de\))i(are)e
1493 (usually)g(listed)i(in)f(in)n(v)n(erse)f(c)n(hronolical)118
1494 2818 y(order.)243 2917 y(T)-7 b(o)35 b(mak)n(e)f(a)h(particular)f
1495 (ordering)g(e\036cien)n(t,)j(it)f(w)n(ould)f(b)r(e)h(a)f(nice)g
1496 (feature)g(if)h(it)g(could)f(b)r(e)h(made)f(to)g(coincide)118
1497 3017 y(with)28 b(a)f(lexicographic)f(ordering)f(of)j(the)g(indices)f
1498 (\025i.e.,)g(as)g(pro)r(duced)g(b)n(y)h(an)f(\020ORDER)h(BY)f(id)h
1499 (ASC\021)35 b(in)27 b(SQL.)h(The)118 3117 y(lexicographic)d(ordering)h
1500 (of)h(fgID)h(satis\034es)e(b)r(oth)i(conditions.)36 b(The)27
1501 b(lexicographic)f(ordering)f(of)i(vgID)g(as)g(describ)r(ed)118
1502 3216 y(ab)r(o)n(v)n(e)34 b(satis\034es)g(the)h(\034rst)g(requisite)f
1503 (if)i(the)f(separator)d(has)j(the)g(minimal)g(binary)g(represen)n
1504 (tation)e(of)i(all)f(allo)n(w)n(ed)118 3316 y(sym)n(b)r(ols)c(in)h(an)f
1505 (index)h(\025)f(this)h(is)g(wh)n(y)f(w)n(e)g(reserv)n(ed)f(/)h(for)g
1506 (the)i(separator.)43 b(But)31 b(the)g(second)f(prop)r(ert)n(y)g(is)g
1507 (missing:)118 3416 y(for)d(instance,)g(the)h(index)g('/1/10')d(is)j
1508 (lexicographically)d(b)r(efore)i('/1/2'.)243 3515 y(If)c(the)h(second)e
1509 (prop)r(ert)n(y)g(is)i(also)e(required)g(for)h(vgID,)g(w)n(e)f(can)h
1510 (sp)r(ecify)h(the)f(c)n(hild)h(iden)n(ti\034ers)e(with)i(coun)n(ters)e
1511 (built)118 3615 y(in)28 b(the)g(follo)n(wing)e(w)n(a)n(y:)36
1512 b(represen)n(t)26 b(a)h(n)n(um)n(b)r(er)h(b)n(y)f(a)g(string)g(of)g
1513 (digits,)h(where)243 3779 y Ff(\017)41 b Fh(the)25 b(\034rst)g(digit)h
1514 Fc(D)896 3791 y Fb(0)958 3779 y Fh(represen)n(ts)e(the)i(length)f(in)h
1515 (digits)f(of)g(the)h(decimal)f(expansion)f(of)i(the)f(n)n(um)n(b)r(er,)
1516 h(min)n(us)f(one)243 3945 y Ff(\017)41 b Fh(the)28 b(follo)n(wing)e
1517 Fa(\()p Fc(D)920 3957 y Fb(0)976 3945 y Fa(+)18 b(1\))27
1518 b Fh(digits)h(are)e(the)i(decimal)g(expansion)e(of)i(the)g(n)n(um)n(b)r
1519 (er)118 4109 y(Let)g(us)f(call)h(these)f(iden)n(ti\034ers)g
1520 Fg(m-vgID)p Fh(,)g(\020m\021)34 b(for)27 b(mo)r(di\034ed.)243
1521 4209 y(As)e(an)f(example,)h(the)g(no)r(de)g(whic)n(h)g(w)n(as)f
1522 (previously)f(represen)n(ted)h(b)n(y)g(/15/3/182)d(will,)k(after)g
1523 (this)g(mo)r(di\034cation,)118 4309 y(ha)n(v)n(e)h(the)i(index)g
1524 (/115/03/2182.)243 4408 y(The)37 b(lexicographic)f(ordering)g(of)i
1525 (m-vgID)f(is)h(the)g(desired)f(ordering)f(of)h(the)h(tree)g(no)r(des.)
1526 67 b(The)38 b(cost)f(of)g(this)118 4508 y(prop)r(ert)n(y)31
1527 b(is)i(that)f(\(a\))h(the)g(ID)f(are)g(no)n(w)g(longer,)g(\(b\))h(no)f
1528 (no)r(de)g(can)g(ha)n(v)n(e)g(more)f(than)i Fa(160)3106
1529 4478 y Fb(160)3240 4508 y Fh(c)n(hildren)f(\(actually)-7
1530 b(,)118 4607 y(this)32 b(is)g(a)f(non-issue\),)h(and)f(\(c\))h(the)g
1531 (index)g(structure)f(is)h(redundan)n(t,)g(some)f(formally)f(correct)h
1532 (indices)g(are)g(in)n(v)-5 b(alid)118 4707 y(\025e.g.,)24
1533 b(/316/013/11.)30 b(The)24 b(third)g(issue)g(can)g(b)r(e)g(addressed)f
1534 (b)n(y)g(k)n(eeping)g(a)h(strict)g(con)n(trol)e(on)i(the)g(generation)f
1535 (of)h(new)118 4807 y(indices)k(to)f(insure)g(that)h(all)f(indices)h
1536 (are)e(formally)h(correct.)243 4906 y(The)32 b(issue)f(of)h(the)g(rev)n
1537 (erse)e(c)n(hronological)f(indexing)j(of)f(threads)h(in)g(threaded)f
1538 (discussion)g(groups)g(can)g(b)r(e)h(ad-)118 5006 y(dressed)d(easily)f
1539 (enough)h(in)h(fgID:)f(coun)n(t)g(\020do)n(wn\021)36
1540 b(instead)29 b(of)g(\020up\021)36 b(the)30 b(c)n(hildren)f(of)g(the)h
1541 (ro)r(ot)e(no)r(de)i(\025)f(this)h(implies)118 5106 y(only)e(an)g
1542 (inconsequen)n(tial)f(mo)r(di\034cation)h(of)g(the)g(no)r(de)h
1543 (insertion)e(routine,)h(as)g(sho)n(wn)f(b)r(elo)n(w.)38
1544 b(The)29 b(problem)e(is)h(less)118 5205 y(trivial)i(with)g(vgID;)h(in)f
1545 (this)h(case,)f(ma)n(yb)r(e)f(a)h(thread)g(iden)n(ti\034er)g(should)g
1546 (b)r(e)h(k)n(ept)f(in)g(a)g(di\033eren)n(t)g(\034eld)h(-)f(i.e.,)h
1547 (repre-)118 5305 y(sen)n(ting)h(the)h(structure)f(as)g(a)h(forest)f
1548 (rather)f(than)i(a)f(tree,)i(where)e(the)h(thread_id)f(\034eld)h
1549 (selects)f(the)h(\020tree\021)38 b(in)33 b(the)118 5404
1550 y(forest.)1987 5653 y(3)p eop
1551 %%Page: 4 4
1552 4 3 bop 118 291 a Fi(3)131 b(T)-11 b(ree)45 b(op)t(erations)e(using)h
1553 (genealogical)g(indices)118 472 y Fh(In)32 b(this)f(section)g(w)n(e)g
1554 (sho)n(w)g(ho)n(w)g(to)g(implemen)n(t)h(v)-5 b(arious)30
1555 b(tree)h(op)r(erations)f(using)h(gID)g(as)g(the)h(primary)e(k)n(ey)h
1556 (in)g(the)118 572 y(no)r(de)d(table.)243 672 y(Some)h(implemen)n
1557 (tation)h(issues)g(are)f(relev)-5 b(an)n(t)29 b(here,)h(esp)r(ecially)f
1558 (concerning)g(the)h(utilisation)g(of)g(indices)g(b)n(y)f(the)118
1559 771 y(DB)f(engine.)243 871 y(W)-7 b(e)28 b(discuss)f(a)g(tree)g
1560 (represen)n(ted)f(in)i(a)f(table)h(of)f(the)h(form)326
1561 1034 y Fd(CREATE)41 b(TABLE)g(tree)h(\()456 1134 y(gid)304
1562 b(text)42 b(PRIMARY)f(KEY,)456 1234 y(nchildren)f(integer)h(DEFAULT)f
1563 (0,)456 1333 y(\\ldots)h(the)i(actual)e(node)h(data)326
1564 1433 y(\);)118 1597 y Fh(The)26 b(\034eld)g(\020nc)n(hildren\021)32
1565 b(is)26 b(a)f(coun)n(ter)g(for)g(the)i(n)n(um)n(b)r(er)e(of)h(c)n
1566 (hildren)f(that)h(the)h(no)r(de)f(has)f Fe(ever)35 b
1567 Fh(had;)27 b(w)n(e)e(assume)g(here)118 1696 y(it)j(is)g(not)f(up)r
1568 (dated)h(when)g(no)r(des)f(or)g(subtrees)g(are)f(deleted.)243
1569 1796 y(Section)h(4)g(pro)n(vides)f(a)i(complete)f(implemen)n(tation)h
1570 (of)f(these)h(op)r(erations)e(for)h(fgID)h(in)g(P)n(ostgreSQL.)118
1571 2028 y Fm(3.1)112 b(Computing)37 b(the)g(lev)m(el)f(of)h(a)h(no)s(de)
1572 118 2181 y Fg(Cost:)f Fe(string)30 b(op)l(er)l(ations)g(\(no)g(table)g
1573 (ac)l(c)l(ess\))243 2280 y Fh(This)d(is)h(a)f(pure)g(string)g(op)r
1574 (eration,)f(no)i(table)f(access)g(is)g(required.)243
1575 2460 y Ff(\017)41 b Fg(vgID:)27 b Fh(coun)n(t)h(the)g(n)n(um)n(b)r(er)f
1576 (of)g(separators)e(\('/'\))j(in)g(the)g(PK)243 2625 y
1577 Ff(\017)41 b Fg(fgID:)27 b Fh(coun)n(t)g(the)h(n)n(um)n(b)r(er)g(of)f
1578 (c)n(haracters)e(in)j(the)g(PK,)g(divide)g(b)n(y)f(the)h(\034xed)f
1579 (size)h(of)f(the)h(coun)n(ters.)118 2857 y Fm(3.2)112
1580 b(Selecting)36 b(or)h(deleting)f(a)i(subtree)118 3010
1581 y Fg(Cost:)f Fe(index)30 b(sc)l(an)g(of)g(the)g(tr)l(e)l(e)243
1582 3173 y Ff(\017)41 b Fg(vgID:)27 b Fh(The)h(subtree)f(ro)r(oted)g(at)g
1583 (/26/5/7)e(is)i(selected)g(b)n(y)508 3338 y Fd(...)43
1584 b(WHERE)e(id)i(LIKE)f('/26/5/7\045')d(AND)j(id)h(<)g('/26/5/70')243
1585 3503 y Ff(\017)e Fg(m-vgID:)26 b Fh(The)h(subtree)h(ro)r(oted)e(at)i
1586 (/126/05/07)22 b(is)28 b(selected)f(b)n(y)508 3668 y
1587 Fd(...)43 b(WHERE)e(id)i(LIKE)f('/126/06/07\045')243
1588 3833 y Ff(\017)f Fg(fgID:)27 b Fh(The)h(subtree)f(ro)r(oted)g(at)g
1589 (260507)e(is)i(selected)h(b)n(y)508 3997 y Fd(...)43
1590 b(WHERE)e(id)i(LIKE)f('260507\045')118 4229 y Fm(3.3)112
1591 b(Selecting)36 b(the)h(direct)f(c)m(hildren)g(of)i(a)g(no)s(de)118
1592 4382 y Fg(Cost:)f Fe(index)30 b(sc)l(an)g(of)g(the)g(tr)l(e)l(e)243
1593 4562 y Ff(\017)41 b Fg(vgID:)27 b Fh(The)h(direct)f(c)n(hildren)g(of)h
1594 (/26/5/7)c(are)j(selected)g(b)n(y)508 4727 y Fd(...)43
1595 b(WHERE)e(id)i(LIKE)f('/26/5/7/\045')d(AND)j(id)h(NOT)f(LIKE)g
1596 ('26/5/7/\045/\045')243 4892 y Ff(\017)f Fg(m-vgID:)26
1597 b Fh(The)h(direct)h(c)n(hildren)f(of)g(/26/5/7)e(are)h(selected)i(b)n
1598 (y)508 5056 y Fd(...)43 b(WHERE)e(id)i(LIKE)f('/126/06/07/\045')37
1599 b(AND)43 b(id)f(NOT)h(LIKE)f('/126/05/07/\045/\045)o(')243
1600 5221 y Ff(\017)f Fg(fgID:)27 b Fh(The)h(direct)f(c)n(hildren)g(of)h
1601 (260507)c(are)j(selected)g(b)n(y)508 5386 y Fd(...)43
1602 b(WHERE)e(id)i(LIKE)f('260507\045')d(AND)k(char_length\(id\))37
1603 b(=)43 b(\(char_length\('26)o(05)o(07')o(\)+)o(2\))1987
1604 5653 y Fh(4)p eop
1605 %%Page: 5 5
1606 5 4 bop 118 291 a Fm(3.4)112 b(Inserting)37 b(a)h(no)s(de)g(or)f(a)h
1607 (subtree)118 444 y Fg(Cost:)f Fe(index)30 b(sc)l(an)g(of)g(the)g(tr)l
1608 (e)l(e)f(+)h(string)f(and)h(math)g(op)l(er)l(ations)243
1609 543 y Fh(Insertion)f(is)g(a)h(pro)r(cedural)e(op)r(eration.)42
1610 b(As)30 b(eac)n(h)f(RDBMS)h(has)f(a)h(di\033eren)n(t)f(w)n(a)n(y)g(of)g
1611 (de\034ning)h(pro)r(cedures,)f(w)n(e)118 643 y(will)f(just)g(describ)r
1612 (e)f(here)g(the)h(necessary)e(steps.)37 b(Examples)27
1613 b(for)g(P)n(ostgreSQL)f(are)h(pro)n(vided)f(in)i(4.)243
1614 743 y(In)22 b(order)f(to)h(insert)g(a)g(new)g(c)n(hild)h(of)f
1615 (\020daddy\021)28 b(\(either)23 b(one)f(of)g(/26/5/7,)e(/126/05/07)d
1616 (or)22 b(260507)d(in)k(the)f(examples)118 842 y(ab)r(o)n(v)n(e\))27
1617 b(y)n(ou)f(ha)n(v)n(e)h(to)220 1008 y(1.)41 b(add)27
1618 b(one)g(to)h(the)g(n)n(um)n(b)r(er)f(of)g(c)n(hildren)h(of)f
1619 (\020daddy\021)508 1174 y Fd(UPDATE)41 b(tree)h(SET)h(nchildren)c(=)k
1620 (\(nchildren)d(+)j(1\))g(WHERE)e(ID)i(=)g(``daddy'';)220
1621 1340 y Fh(2.)e(enco)r(de)27 b(the)h(n)n(um)n(b)r(er)f(of)g(c)n(hildren)
1622 g(of)h(\020daddy\021)33 b(in)28 b(base)f(160,)f(bring)h(it)h(to)f(the)h
1623 (correct)e(format)h(dep)r(ending)h(on)326 1440 y(the)c(v)-5
1624 b(arian)n(t)23 b(of)h(gID)g(\(pad)g(with)h(0)e(or)g(not,)i(prep)r(end)f
1625 (a)g(digit)g(coun)n(ter)f(or)g(not,)i(prep)r(end)f(/)g(or)f(not,)i
1626 (coun)n(t)e(do)n(wn)326 1540 y(or)j(up,)i(.)14 b(.)g(.)g(\))37
1627 b(and)28 b(app)r(end)f(it)h(to)g(daddy's)f(gID)g(to)h(obtain)f(the)h
1628 (new)g(no)r(de's)f(gID.)220 1706 y(3.)41 b(insert)27
1629 b(the)h(new)f(no)r(de)243 1872 y(When)35 b(inserting)g(a)f(subtree,)j
1630 (the)e(index)g(of)g(the)h(ro)r(ot)e(of)h(the)g(subtree)g(has)f(to)h(b)r
1631 (e)h(computed)f(as)f(ab)r(o)n(v)n(e,)i(and)118 1971 y(prep)r(ended)28
1632 b(to)f(the)h(index)g(of)f(eac)n(h)g(no)r(de)h(of)f(the)h(subtree)f(b)r
1633 (efore)h(insertion.)243 2071 y(Remark)e(that)i(only)f(the)h(paren)n(t)f
1634 (no)r(de)h(has)f(to)g(b)r(e)h(up)r(dated)g(on)f(insertion.)118
1635 2303 y Fm(3.5)112 b(Selecting)36 b(the)h(ancestors)h(of)g(a)g(no)s(de)
1636 118 2457 y Fg(Cost:)f Fe(index)30 b(sc)l(an)g(of)g(the)g(tr)l(e)l(e)243
1637 2556 y Fh(Y)-7 b(ou)27 b(can)g(sp)r(ecify)h(all)g(ancestors)d(of)j(a)f
1638 (no)r(de)h(in)f(a)h(single)f(SQL)g(statemen)n(t;)g(for)g(instance)h
1639 (for)f(vgID)326 2722 y Fd(...)42 b(WHERE)f('/25/6/7')f(LIKE)i(\(id)g
1640 (||)h('/\045'\))f(AND)g(id)h(<)g('/25/6/7')118 2888 y
1641 Fh(The)31 b(second)e(part)h(of)h(the)g(clause,)f(while)h(logically)e
1642 (redundan)n(t,)h(is)h(a)f(\020hin)n(t\021)37 b(to)30
1643 b(the)h(optimizer.)45 b(A)n(t)31 b(least)f(in)g(P)n(ost-)118
1644 2988 y(greSQL,)c(without)i(it)g(the)g(optimizer)f(will)h(c)n(ho)r(ose)e
1645 (a)i(sequen)n(tial)e(scan)h(of)h(the)g(table)f(and)h(disregard)d(the)j
1646 (index.)118 3220 y Fm(3.6)112 b(Selecting)36 b(all)g(lea)m(v)m(es)118
1647 3374 y Fg(Cost:)h Fe(sc)l(an)30 b(of)g(the)g(tr)l(e)l(e)243
1648 3473 y Fh(A)e(leaf)f(is)g(a)h(no)r(de)f(without)h(descendan)n(ts:)36
1649 b(it)28 b(has)f(0)g(c)n(hildren.)37 b(Hence)326 3639
1650 y Fd(...)42 b(WHERE)f(nchildren)f(=)j(0)118 3805 y Fh(If)28
1651 b(this)g(t)n(yp)r(e)g(of)f(query)g(is)h(often)f(necessary)-7
1652 b(,)26 b(y)n(ou)h(ma)n(y)g(b)r(e)h(w)n(ell)f(advised)g(to)g(k)n(eep)g
1653 (an)h(index)f(on)h(tree\(nc)n(hildren\).)118 4038 y Fm(3.7)112
1654 b(Determining)35 b(if)i(A)g(is)g(a)h(descendan)m(t)g(of)g(B)118
1655 4191 y Fg(Cost:)f Fe(string)30 b(op)l(er)l(ations,)h(no)f(table)g(ac)l
1656 (c)l(ess)243 4291 y Fh(This)d(is)h(a)f(pure)g(string)g(op)r(eration)f
1657 (on)i(the)g(indices,)f(no)g(table)h(access)e(is)i(necessary)-7
1658 b(.)118 4565 y Fi(4)131 b(Putting)45 b(it)f(all)h(together:)57
1659 b(a)44 b(P)l(ostgreSQL)f(implemen)l(tation)118 4747 y
1660 Fh(h)n(ttp://www.p)r(ostgresql.org/mhonarc/pgsq)o(l-sql/)o(20)o(00)o
1661 (-0)o(4/)o(msg0)o(02)o(67)o(.h)n(tml)243 4847 y(W)-7
1662 b(e)30 b(describ)r(e)g(here)g(a)g(small)f(pac)n(k)-5
1663 b(age)29 b(that)i(can)e(b)r(e)i(used)f(for)g(implemen)n(ting)g(gID)g
1664 (on)g(P)n(ostgreSQL.)f(It)i(can)e(b)r(e)118 4946 y(found)f(at)f(<h)n
1665 (ttp://...>)243 5046 y(The)21 b(pac)n(k)-5 b(age)21 b(uses)g(the)h(pro)
1666 r(cedural)e(language)h(PL/PGsql.)35 b(A)22 b(b)r(etter)g(implemen)n
1667 (tation)g(w)n(ould)f(probably)g(de\034ne)118 5145 y(the)28
1668 b(gID)g(as)f(new)g(P)n(ostgres)f(t)n(yp)r(es,)i(and)f(co)r(de)g(all)h
1669 (this)g(in)f(C.)243 5245 y(The)g(\034les)h(should)f(b)r(e)h(loaded)f
1670 (in)h(alphab)r(etical)f(order.)1987 5653 y(5)p eop
1671 %%Page: 6 6
1672 6 5 bop 118 291 a Fm(4.1)112 b(tree0_enco)s(ding.sql)118
1673 444 y Fh(This)28 b(\034le)f(de\034nes)h(and)f(p)r(opulates)h(the)f
1674 (table)h(_b160_digits)d(of)j(\020digits\021)33 b(in)28
1675 b(base)f(160,)326 604 y Fd(CREATE)41 b(TABLE)g(\\_b160\\_digits)d
1676 (\(deci)j(integer,)f(code)i(char\);)118 764 y Fh(and)28
1677 b(the)f(t)n(w)n(o)g(functions)326 924 y Fd(CREATE)41
1678 b(FUNCTION)f(\\_b160\\_encode\(i)o(nt)o(eg)o(er\))d(RETURNS)j(string)
1679 413 1024 y(AS)j('....')e(LANGUAGE)f('plpgsql';)326 1124
1680 y(CREATE)h(FUNCTION)f(\\_b160\\_encode\(i)o(nt)o(eg)o(er,)o(in)o(te)o
1681 (ger)o(\))d(RETURNS)k(string)413 1223 y(AS)i('....')e(LANGUAGE)f
1682 ('plpgsql';)118 1384 y Fh(The)22 b(\034rst)h(function)f(returns)g(a)g
1683 (v)-5 b(ariable)21 b(size)h(enco)r(ding;)i(the)f(second)e(a)h(\034xed)h
1684 (size)f(enco)r(ding)g(\(the)h(second)e(parameter)118
1685 1483 y(is)g(the)h(size\),)g(and)f(raises)e(an)i(exception)g(if)h(the)f
1686 (n)n(um)n(b)r(er)g(is)g(to)r(o)g(large)e(to)i(b)r(e)h(represen)n(ted)e
1687 (with)h(the)h(requested)e(n)n(um)n(b)r(er)118 1583 y(of)28
1688 b(digits.)118 1814 y Fm(4.2)112 b(tree1_de\034ne.sql)118
1689 1967 y Fh(This)28 b(\034le)f(pro)n(vides)f(a)i(function)326
1690 2127 y Fd(CREATE)41 b(FUNCTION)f(_tree_create\(tex)o(t,)o(in)o(teg)o
1691 (er)o(,t)o(ext)o(,t)o(ex)o(t\))d(RETURNS)k(bpchar)413
1692 2227 y(AS)i('....')e(LANGUAGE)f('plpgsql';)118 2387 y
1693 Fh(that)e(creates)f(a)h(tree)f(infrastructure)g(of)h(either)g(fgID)g
1694 (or)f(vgID.)h(Assuming)f(y)n(ou)g(ha)n(v)n(e)g(a)h(table)f(\020m)n
1695 (ytable\021)44 b(with)118 2487 y(primary)26 b(k)n(ey)h(\020m)n
1696 (yid\021,)g(then)h(calling)326 2647 y Fd(SELECT)41 b(_tree_create\('m)o
1697 (yt)o(ree)o(',)o(2,')o(my)o(ta)o(ble)o(',)o('m)o(yid)o('\))o(;)118
1698 2807 y Fh(will)28 b(cause:)220 2967 y(1.)41 b(the)28
1699 b(creation)e(of)i(a)f(table)508 3131 y Fd(CREATE)41 b(TABLE)h
1700 (mytree_bkg\()683 3230 y(gid)g(text)g(PRIMARY)e(KEY,)683
1701 3330 y(nchildren)f(int,)683 3429 y(sid)j(integer)f(REFERENCES)e
1702 (mytable\(myid\))508 3529 y(\);)508 3629 y(CREATE)i(UNIQUE)g(INDEX)h
1703 (mytree_bkg_sid)37 b(ON)43 b(mytree_bkg\(sid\);)326 3792
1704 y Fh(for)27 b(the)h(tree)f(structure.)220 3955 y(2.)41
1705 b(the)28 b(creation)e(of)i(a)f(view)508 4118 y Fd(CREATE)41
1706 b(VIEW)h(mytree)f(AS)639 4218 y(SELECT)g(t.gid,n.*)900
1707 4317 y(FROM)h(mytable)f(n,)i(mytree_bkg)c(t)900 4417
1708 y(WHERE)j(t.sid=n.myid;)326 4580 y Fh(with:)35 b(a)23
1709 b(trigger)e(on)i(UPD)n(A)-7 b(TE)25 b(that)e(blo)r(c)n(ks)g(up)r
1710 (dating)g(the)h(gid)f(and)g(allo)n(ws)f(up)r(dating)h(the)g(no)r(de)h
1711 (data,)f(a)g(rule)326 4680 y(on)k(DELETE)i(that)f(deletes)f(the)h
1712 (corresp)r(onding)e(en)n(try)h(b)r(oth)h(in)g(m)n(ytree_bkg)d(and)j(m)n
1713 (ytable,)f(and)g(a)g(trigger)326 4779 y(ON)h(INSER)-7
1714 b(T)30 b(that)f(raises)e(an)h(exception)g(and)g(informs)h(the)f(user)g
1715 (to)h(use)f(the)h(insertion)f(function)h(describ)r(ed)326
1716 4879 y(b)r(elo)n(w.)220 5042 y(3.)41 b(t)n(w)n(o)26 b(insertion)h
1717 (functions)h(that)g(compute)g(automatically)e(the)i(gID)g(of)f(the)h
1718 (new)g(no)r(de:)425 5205 y Ff(\017)41 b Fh(a)27 b(function)i(m)n
1719 (ytree_insert\(text,text,in)n(teger,text\))d(for)h(insertion)g(sim)n
1720 (ultaneosly)f(in)i(b)r(oth)g(tables:)508 5305 y(m)n
1721 (ytree_insert\('2201','hello',0,'not)15 b(m)n(uc)n(h'\))j(inserts)g(a)g
1722 (new)g(c)n(hild)h(of)f(2201)f(with)h(data1='hello',)h(data2=0)508
1723 5404 y(and)28 b(data3='not)e(m)n(uc)n(h')1987 5653 y(6)p
1724 eop
1725 %%Page: 7 7
1726 7 6 bop 425 291 a Ff(\017)41 b Fh(a)27 b(function)i(m)n
1727 (ytree_insert_no)r(de\(text,in)n(teger\))c(for)i(insertion)g(in)h(m)n
1728 (ytree_bkg)508 390 y(m)n(ytree_insert\('2201',25\))c(inserts)j(in)h(m)n
1729 (ytree_bkg)e(a)h(new)h(c)n(hild)f(of)h(2201)d(with)j(sid=25)220
1730 556 y(4.)41 b(a)27 b(function)h(m)n(ytree_mo)n(v)n(e\(text,text\))e
1731 (that)i(mo)n(v)n(es)e(subtrees:)326 656 y(m)n(ytree_mo)n(v)n
1732 (e\('2201','23'\))d(mo)n(v)n(es)j(the)i(subtree)f(ro)r(oted)g(at)g
1733 (2201)f(to)h(a)h(place)f(b)r(elo)n(w)g(23)f(\(ma)n(yb)r(e)i(2307\))220
1734 822 y(5.)41 b(a)c(function)g(m)n(ytree_len\(\))g(that)h(returns)e(the)i
1735 (length)f(of)g(the)h(enco)r(dings)f(used)g(in)h(the)f(gID)g(\(2)h
1736 (here;)j(0)c(if)326 922 y(v)-5 b(ariable)26 b(size\).)118
1737 1196 y Fi(5)131 b(Non-tree)44 b(hierarc)l(hies)118 1378
1738 y Fh(sequence)22 b(as)f(id,)j(table)e(with)h(\(id,g-index\))f(with)g(p)
1739 r(ossibly)g(man)n(y)g(g-indices)f(for)h(eac)n(h)f(id)h(\(if)h(TOO)f
1740 (man)n(y)-7 b(,)23 b(bad)f(mo)r(del:)118 1478 y(list)28
1741 b(all)f(genealogies,)f(i.e.,)h(paths)h(from)f(the)h(ro)r(ot\))118
1742 1752 y Fi(References)160 1934 y Fh([1])41 b(Philip)28
1743 b(Greenspun,)g Fe(T)-6 b(r)l(e)l(es)29 b(in)h(Or)l(acle)g(SQL)p
1744 Fh(,)d(in)h Fg(SQL)k(for)g(W)-8 b(eb)31 b(Nerds)289 2033
1745 y Fh(<h)n(ttp://photo.net/sql/trees.h)n(tml>)160 2200
1746 y([2])41 b(Jo)r(e)27 b(Celk)n(o,)f Fe(SQL)j(for)i(Smarties)p
1747 Fh(,)d(in)g Fg(DBMS)j(Online)p Fh(,)26 b(Marc)n(h)h(to)g(June)h(1996)
1748 289 2299 y(<h)n(ttp://www.dbmsmag.com/9603d06.h)n(tml>)289
1749 2399 y(<h)n(ttp://www.dbmsmag.com/9604d06.h)n(tml>)289
1750 2498 y(<h)n(ttp://www.dbmsmag.com/9605d06.h)n(tml>)289
1751 2598 y(<h)n(ttp://www.dbmsmag.com/9606d06.h)n(tml>)160
1752 2764 y([3])41 b(Graeme)26 b(Birc)n(hall,)h Fg(DB2)32
1753 b(UDB)g(V6.1)f(SQL)h(Co)s(okb)s(o)s(ok)p Fh(,)289 2864
1754 y(<h)n(ttp://ourw)n(orld.compuserv)n(e.com/homepag)o(es/)o(Gra)o
1755 (eme_Bir)o(c)n(ha)o(ll/HTM_CO)o(OK)o(.HTM>)1987 5653
1756 y(7)p eop
1757 %%Trailer
1758 end
1759 userdict /end-hook known{end-hook}if
1760 %%EOF