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Diffstat (limited to 'ldb/ldb_sqlite3/trees.ps')
| -rw-r--r-- | ldb/ldb_sqlite3/trees.ps | 1760 |
1 files changed, 0 insertions, 1760 deletions
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-(kno)n(w)g(ma)n(y)g(solv)n(e)f(this)i(problem)f(in)n(ternally;)g(they)g -(de\034nitely)h(solv)n(e)f(it)g(for)g(the)h(end)g(user\).)243 -4119 y Ff(\017)41 b Fh(Nested)30 b(sets)g(are)f(v)n(ery)f(e\036cien)n -(t)i(for)g(tree)f(searc)n(hes,)g(but)i(are)e(rather)f(exp)r(ensiv)n(e)i -(for)f(no)r(de)h(insertion)f(and/or)326 4218 y(deletion:)37 -b(they)27 b(require)g(up)r(dating)g(p)r(oten)n(tially)h(man)n(y)f(no)r -(des.)243 4384 y(W)-7 b(e)30 b(prop)r(ose)f(here)h(a)g(di\033eren)n(t)h -(represen)n(tation,)e(based)g(on)i(no)r(de)f(iden)n(ti\034ers)g(whic)n -(h)g(are)f(\020genealogical)f(iden)n(ti-)118 4484 y(\034ers\021:)44 -b(they)32 b(con)n(tain)f(the)h(complete)f(genealogy)f(of)h(the)h(no)r -(de,)h(i.e.,)g(the)f(list)g(of)g(ancestors)d(up)j(to)g(the)g(ro)r(ot)f -(of)g(the)118 4584 y(tree.)243 4683 y(This)j(allo)n(ws)f(to)i(replace)e -(man)n(y)h(searc)n(hes)f(in)h(database)g(tables)g(with)h(string)f(op)r -(erations)f(on)h(the)h(index.)58 b(The)118 4783 y(result,)24 -b(as)f(explained)h(in)g(Section)g(3)f(is)h(that)g(tree)f(searc)n(hes)f -(pro)r(ceed)h(at)h(\020nested)f(sets\021)30 b(sp)r(eed,)25 -b(while)f(no)r(de)g(insertions)118 4882 y(and)k(deletions)f(are)f(as)h -(fast)h(as)f(with)h(p)r(oin)n(ters.)243 4982 y(The)i(ob)n(vious)f(do)n -(wnside)h(of)h(the)g(metho)r(d)g(is)f(that)h(the)g(primary)f(k)n(ey)f -(in)i(the)g(tree)f(needs)h(to)f(b)r(e)h(a)g(v)-5 b(ariable)29 -b(size)118 5082 y(text)j(\034eld,)h(and)f(that)g(the)g(iden)n -(ti\034ers)f(ma)n(y)g(b)r(e)i(extremelly)e(long)g(for)g(deep)h(trees.) -49 b(W)-7 b(e)32 b(will)g(pro)n(vide)e(estimates)i(of)118 -5181 y(the)c(size)f(required)g(as)g(a)g(function)h(of)g(the)f -(magnitude)h(of)f(the)h(tree.)1987 5653 y(1)p eop -%%Page: 2 2 -2 1 bop 118 291 a Fi(2)131 b(Genealogical)45 b(iden)l(ti\034ers)g(for)f -(trees)118 489 y Fm(2.1)112 b(De\034nition)118 642 y -Fh(W)-7 b(e)28 b(de\034ne)g Fe(gene)l(alo)l(gic)l(al)k(identi\034ers)j -Fh(recursiv)n(ely)25 b(as)i(follo)n(ws:)326 808 y Fg(De\034nition:)59 -b Fe(The)42 b(gene)l(alo)l(gic)l(al)h(identi\034er)f(\(gID\))e(of)i(a)f -(no)l(de)h(is)f(obtaine)l(d)h(by)g(app)l(ending)g(a)f(child)326 -908 y(identi\034er)30 b(to)g(the)g(gene)l(alo)l(gic)l(al)h -(identi\034er)g(of)f(the)g(p)l(ar)l(ent)f(no)l(de.)243 -1074 y Fh(Remark)40 b(that)h(genealogical)e(iden)n(ti\034ers)i(are)f -(rather)g(w)n(ell)h(kno)n(wn)f(and)h(used;)48 b(common)41 -b(examples)f(are)g(the)118 1174 y(\020path+\034le-name\021)33 -b(in)28 b(a)f(computer)g(\034le)h(system)f(and)h(the)f(URLs)h(within)g -(a)f(WWW.)243 1273 y(The)d(name)g(\020genealogical)e(iden)n -(ti\034er\021)30 b(is)24 b(suggested)g(b)n(y)g(the)g(fact)h(that)f(the) -h(v)-5 b(alue)24 b(of)g(the)h(iden)n(ti\034er)f(con)n(tains)f(the)118 -1373 y(complete)30 b(genealogy)d(of)j(the)g(no)r(de:)41 -b(it)30 b(con)n(tains)e(as)h(a)h(substring)f(the)h(gID)f(of)h(its)g -(father,)g(whic)n(h)f(in)h(turn)g(con)n(tains)118 1472 -y(as)d(a)g(substring)g(the)h(gID)g(of)f(the)h(grandfather,)e(.)14 -b(.)g(.)243 1572 y(The)27 b(ro)r(ot)g(no)r(de)h(of)f(the)h(tree)f(has)g -(a)h(gID)f(with)h(v)-5 b(alue)28 b(\021)34 b(\(the)28 -b(empt)n(y)g(string\),)f(as)g(it)h(has)f(no)g(paren)n(t.)118 -1804 y Fm(2.2)112 b(Child)36 b(iden)m(ti\034ers)118 1958 -y Fh(The)26 b(ob)n(vious)e(c)n(hild)i(iden)n(ti\034er)g(is)f(a)h -(zero-based)d(coun)n(ter:)35 b(iden)n(tify)26 b(the)h(c)n(hild)e(b)n(y) -h(the)g(n)n(um)n(b)r(er)f(of)h(older)f(brethren)g(it)118 -2057 y(has.)243 2157 y(W)-7 b(e)25 b(could)f(represen)n(t)g(the)h(coun) -n(ter)f(in)h(base)f(10;)h(this)g(ho)n(w)n(ev)n(er)e(is)i(extremely)f(w) -n(asteful)g(of)h(resources.)34 b(It)25 b(is)g(m)n(uc)n(h)118 -2257 y(b)r(etter)33 b(to)f(represen)n(t)f(the)h(coun)n(ter)g(in)g(as)g -(large)e(a)i(base)g(as)f(p)r(ossible:)46 b(in)n(terpret)32 -b(as)f(n)n(um)n(b)r(ers)h(a)g(set)g(of)g(c)n(haracters)118 -2356 y(larger)26 b(than)h({0,1,.)14 b(.)g(.)g(9}.)243 -2456 y(As)26 b(tree)f(op)r(erations)f(will)i(in)n(v)n(olv)n(e)f(string) 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b(with)i(':')37 -b(\(dec)28 b(ascii)f(co)r(de)h(58\))243 3452 y Ff(\017)41 -b Fh(11)26 b(with)i(';')g(\(dec)g(ascii)f(co)r(de)g(59\))243 -3618 y Ff(\017)41 b Fh(12-37)25 b(with)j('A'-'Z')g(\(dec)f(ascii)g(co)r -(de)h(65-90\))243 3784 y Ff(\017)41 b Fh(38-63)25 b(with)j('a'-'z')f -(\(dec)h(ascii)f(co)r(de)g(97-122\))118 3950 y(By)g(using)g(base)f(64,) -h(up)g(to)h(4096)d(c)n(hildren)i(can)f(b)r(e)i(represen)n(ted)e(using)h -(t)n(w)n(o)f(suc)n(h)h(digits,)g(up)h(to)f(262144)d(with)k(three)118 -4050 y(digits,)g(and)f(up)h(to)f(16777216)d(with)k(four)f(digits.)243 -4149 y(If)37 b(the)g(RDBMs)g(supp)r(orts)f(in)n(ternational)g(c)n -(haracters,)h(it)g(is)g(p)r(ossible)f(to)h(further)f(increase)g(the)h -(base;)k(as)36 b(an)118 4249 y(example,)30 b(b)n(y)f(using)g(the)h(95)f -(additional)g(c)n(haracters)e(of)i(the)h(latin-1)f(c)n(haracter)e(set,) -k(w)n(e)e(could)g(co)r(de)g(n)n(um)n(b)r(ers)g(in)h(a)118 -4349 y(base)f(up)g(to)g(160)f(\025)g(remark)g(that)h(ev)n(ery)f(single) -h(digit)g(is)g(still)h(one)e(b)n(yte)h(in)h(this)f(represen)n(tation.) -40 b(This)29 b(means)f(that)118 4448 y(w)n(e)f(expand)h(the)f(sym)n(b)r -(ols)g(ab)r(o)n(v)n(e)f(b)n(y)i(represen)n(ting)243 4614 -y Ff(\017)41 b Fh(64-159)25 b(with)j(dec)f(latin1)g(co)r(de)h(160-255) -243 4780 y(In)23 b(base)g(160,)g(up)g(to)h(25600)d(c)n(hildren)i(can)f -(b)r(e)i(represen)n(ted)e(using)h(t)n(w)n(o)g(digits,)h(up)g(to)f -(4096000)d(with)k(three)f(digits,)118 4880 y(and)28 b(up)f(to)h -(6.5E+08)e(with)i(four)f(digits.)243 4980 y(Remark)g(that)h(base)f(con) -n(v)n(ersions)f(only)h(need)i(to)e(b)r(e)i(p)r(erformed)e(at)h -(insertion)g(time,)g(when)h(the)f(index)g(of)g(a)g(new)118 -5079 y(no)r(de)g(is)f(computed.)37 b(They)28 b(will)f(therefore)g(only) -g(ha)n(v)n(e)f(an)i(impact)f(on)h(insertion)f(timings.)1987 -5653 y(2)p eop -%%Page: 3 3 -3 2 bop 118 291 a Fm(2.3)112 b(Coun)m(ters:)50 b(\020delimited\021)44 -b(vs.)51 b(\020\034xed)38 b(size\021)118 444 y Fh(The)33 -b(standard)g(represen)n(tation)e(of)i(gID)h(uses)e(a)h(v)-5 -b(ariable)32 b(size)h(c)n(hild)h(iden)n(ti\034er,)g(and)f(delimiters)g -(to)h(separate)d(the)118 543 y(gID)f(of)g(the)h(c)n(hild)f(no)r(de)g -(from)f(the)i(gID)f(of)g(its)g(paren)n(t.)43 b(F)-7 b(or)30 -b(example,)g(w)n(e)g(can)f(represen)n(t)g(the)i(\034fth)g(c)n(hild)f -(of)g(no)r(de)118 643 y('/23/27/1')24 b(as)j('/23/27/1/4'.)32 -b(Let)c(us)f(call)g(this)h(a)f Fg(vgID)h Fh(represen)n(tation)e(\(V)-7 -b(ariable)27 b(Size)h(Genealogical)d(ID\).)243 743 y(This)30 -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 -(c)n(hildren)g(of)h(a)f(no)r(de,)h(sub)5 b(ject)30 b(only)g(to)g(the)h -(limitations)f(the)118 842 y(RDBMS)e(ma)n(y)f(ha)n(v)n(e)f(as)h(to)h -(the)g(length)f(of)h(a)f(v)-5 b(ariable)27 b(sized)g(string.)243 -942 y(Alternativ)n(ely)-7 b(,)24 b(w)n(e)f(could)h(c)n(ho)r(ose)f(to)h -(limit)g(from)g(the)g(outset)g(the)g(quan)n(tit)n(y)g(of)f(c)n(hildren) -h(that)g(a)g(no)r(de)g(ma)n(y)f(ha)n(v)n(e;)118 1042 -y(this)28 b(limit)g(w)n(ould)f(dep)r(end)i(of)e(course)f(on)i(the)g -(application.)36 b(Let)27 b(us)h(call)f(this)h(a)f Fg(fgID)h -Fh(represen)n(tation.)243 1141 y(F)-7 b(or)25 b(example,)h(if)g(no)g -(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 -(c)n(hildren,)j(w)n(e)g(could)f(represen)n(t)g(the)h(coun)n(ters)118 -1241 y(alw)n(a)n(ys)36 b(with)i(2)f(digits.)67 b(The)38 -b(no)r(de)f(whic)n(h)h(w)n(as)f(previously)f('/23/27/1/4')d(is)k(no)n -(w)g('23270104'.)64 b(If)38 b(w)n(e)f(require)118 1340 -y(a)g(three)g(digit)h(represen)n(tation)d(of)i(no)r(des)g(\(up)h(to)f -(ab)r(out)h(4)f(million)g(c)n(hildren\),)j(then)d(it)h(will)g(b)r(e)f -(represen)n(ted)f(as)118 1440 y('023027001004'.)118 1672 -y Fm(2.4)112 b(Ordering)37 b(of)h(no)s(des)118 1825 y -Fh(F)-7 b(or)35 b(some)g(applications)g(it)h(is)f(necessary)f(to)i -(obtain)f(subtrees)g(ordered)f(according)g(to)i(some)f(sp)r(ecial)g -(rules.)60 b(F)-7 b(or)118 1925 y(instance:)220 2090 -y(1.)41 b(the)34 b(complete)g(subtree)f(starting)g(at)h(a)f(no)r(de)h -(is)g(listed)g(immediately)g(after)f(the)i(no)r(de)f(in)g(question)f -(\(\020depth)326 2189 y(\034rst\021\))220 2354 y(2.)41 -b(no)r(des)27 b(with)h(a)f(common)g(paren)n(t)g(are)g(listed)g(c)n -(hronologically)243 2519 y(F)-7 b(or)39 b(instance,)k(the)d(displa)n(y) -f(of)h(an)f(organization)f(c)n(hart)h(is)g(usually)h(required)e(to)i -(satisfy)g(at)f(least)h(the)g(\034rst)118 2619 y(condition.)h(In)29 -b(a)g(threaded)f(discussion)h(group)e(one)i(wishes)g(to)f(satisfy)h(b)r -(oth)h(conditions)e(to)h(displa)n(y)f(the)h(messages)118 -2718 y(in)20 b(a)g(thread)g(\025)f(the)i(threads)e(themselv)n(es)h -(\(i.e.,)i(c)n(hildren)e(of)g(the)g(ro)r(ot)f(no)r(de\))i(are)e -(usually)g(listed)i(in)f(in)n(v)n(erse)f(c)n(hronolical)118 -2818 y(order.)243 2917 y(T)-7 b(o)35 b(mak)n(e)f(a)h(particular)f -(ordering)g(e\036cien)n(t,)j(it)f(w)n(ould)f(b)r(e)h(a)f(nice)g 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