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14.6 VisitedFlags
177
14.6 VisitedFlags
The booleanvisited ags areavailablefor/ineachgraphelement;they may be usedfor
markingalreadyvisitedgraphelementsduringgraphwalksorforpartitioningagraph.They
can be e queried d with a functionof the e expressions, , can be set t withanassignment of f the
statements,andcanbereset,allocated,anddeallocatedwithproceduresofthestatements.
Thevisited agsarestoredinsomeexcessbitsofthegraphelements,ifthispoolisexceeded
theyarestoredinadditionaldictionaries,onepervisited agrequested.Thisiswhythe ags
mustgetallocated/deallocated,andall agrelatedoperationsrequireanintegernumber{the
agid{specifyingthe agtooperateon(withexceptionoftheallocationoperationreturning
this agid).Ifyoutrytoaccessanotpreviouslyallocatedvisited ag,anexceptionisthrown.
ThefollowingsyntaxdiagramgivesanextensionstotheExpression clauseofchapter6and
anextensiontothecomputationStatementsofchapter12:
Expression
-
VisitedFlag
-
VisitedAssignment
-
VisitedFlag
-
=
-
BoolExpr
-
;
-
VisitedFlag
-
NodeOrEdge
-
.
-
visited
-
[
-
IntExpr
-
]
-
Flagreading:
By e.visited[f]{thefunctionreturnsthebooleanvisitedstatusofthe aggiven
bythe agidvariablefofthegraphelemente(visited agsarenormallyreadbyif
conditionsoftherulelanguage). Ifnoint agnumberisgiven,thedefaultnumberfor
therstvisited agof0isused;itstillmusthavebeenallocatedbefore.
Flagassignment:
Bye.visited[f] = b{setsthevisitedstatusofthe aggivenbythe agidvariable
fofthegraphelement etothegivenbooleanvalueb ascomputedbyanexpression
(visited agsarenormallywrittenbyevalpartsoftherulelanguage). Ifnoint ag
numberisgiven,thedefaultnumberfortherstvisited agof0isused;itstillmust
havebeenallocatedbefore.
ProcedureName
-
valloc
-
vfree
-
vreset
-
vfreenonreset
-
Thesignaturesoftheproceduresvalloc,vfree,vreset,vfreenonresetformanaging
thevisited agsaredenedin12.4. Theirsemanticsare:
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178
GraphTypeandComputations
Flagallocation:
Byvalloc(){allocatesspaceforavisited agintheelementsofthegraphandreturns
theidofthevisited ag(integernumber),startingat0.Afterwards,thevisited agof
theidcanbereadandwrittenbythevisited-expressionandthevisited-assignment.
Therstvisited agsarestoredinsomeexcessbitsofthegraphelementsandarethus
essentiallyforfree,butifthisimplementationdenedspaceisusedupcompletely,the
informationisstoredingraphelementexternaldictionaries.
Flagdeallocation:
Byvfree{freesthespacepreviouslyallocatedforthevisited ag;afterwardsyoumust
notaccessitanymore. Thevaluepassedinvfree(IntExpr)mustbeofintegertype,
stemmingfromapreviousallocation. Thisfunctioninternallycallsavresettoensure
thatnocorrespondingvisited agissetinthegraph.
Flagresetting:
Byvreset{resetsthevisitor aggivenbythe agidvariableinall graphelements.
Flagdeallocationwithoutreset:
Withvfreenonresetthespacepreviously allocatedfor the visited agis freed,too,
buttheimplicitinternalvreset(id)ofvfreeisnotexecuted.Itisyourdutytoensure
the agisfalseinallgraphelements{otherwiseafterafollowingallocationelements
maystartas beingmarked. . This s saves usanO(n) operation,but opensthedoor to
nastybugsifyoucan’tdesignyouralgorithminawaywhichrendersunmarkingtrivial.
EXAMPLE(89)
Anexampleshowinghowtocomputethelengthofthelongestpathstartingatsomenode.
1
procedurelengthOfLongestPath(start:Node,varlengthReached:int, varflag:int) : (int)
2
{
3
defvarmaxLength:int= lengthReached;
4
start.visited[flag] =true;
5
for(child:Nodeinadjacent(start)){
6
if(!child.visited[flag]){
7
def varlengthOfLongestPathStartingAtChild:int;
8
(lengthOfLongestPathStartingAtChild)=lengthOfLongestPath(child,lengthReached+1,
flag);
9
maxLength =Math::max(maxLength,lengthOfLongestPathStartingAtChild);
10
}
11
}
12
start.visited[flag] =false;
13
return(maxLength);
14
}
15
16
rulegetLolp(start:Node): (int)
17
{
18
modify{
19
defvarlolp:int;
20
eval{
21
(defvarflag:int)= valloc();
22
(yield lolp)= lengthOfLongestPath(start, 0, flag;)
23
vfree(flag);
24
}
25
return(lolp);
26
}
27
}
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14.7 GraphProcessingEnvironmentProcedures
179
14.7 GraphProcessingEnvironmentProcedures
14.7.1 TransactionHandling
Inadditiontotheproceduresimplementeddirectlyinthegraph,therearetransactionman-
agerproceduresavailable,implementedinthegraphprocessingenvironment. Whileatrans-
actionisunderway,anundologislledwithcommandstoundothechangesthatoccurredin
thegraphinthemeantime.Thosetransactionhandlingproceduresfromthebuilt-inpackage
Transaction(formoreonpackagessee16.2.2)are:
Transaction::start()
startsatransactionandreturnsitstransactionid(asnumberoftypeint).
Transaction::pause()
pausestransactionhandlingsochangesarenotrecordedandcan’tbeundone.
Transaction::resume()
resumespausedtransactionhandling.
Transaction::commit(.)
keepsthechangesofthetransactionofthegivenid(oftypeint)inthegraph,removing
undoinformation.
Transaction::rollback(.)
reverts thechanges ofthe transactionof thegiven n id(oftype int) ) inthegraphby
executingtheundolog.
Please notethattransactions maybe nested;thosefunctions areusedinimplementing
thetransactionandbacktrackingconstructsexplainedin18.2.
14.7.2 Misc. . GlobalProcedures
Besidesthereareprocedurestoemittextorrecordgraphchangesavailable:
emit(.(,.)*)
writestheargumentvalue,orthecommaseparatedlistofargumentvalues,tostdout,or
toaleifoutputwasredirected.Theargument(s)mustbeofstringtype,butanytypeis
automaticallycastedintoitsstringrepresentationasneeded.Prefercommaseparated
arguments over string concatenation, , they y are are more ecient t as s no intermediate
stringsneedtobecomputed,justtobegarbagecollectedthereafter.
record(.)
writestheargumentvalue,typicallyatextstring,tothegraphchangerecord.
Aremarkonthegraphglobalvariables: theyareinfactglobaltothegraphprocessing
environment. This s dierence becomes clear whenyou u store graphs s in n attributes s ofgraph
typeofanothergraph,see16.3foradiscussionofthisstyleofprogramming.
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180
GraphTypeandComputations
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CHAPTER 15
FILTERING AND SORTING OF F MATCHES
Filtersareusedtoprocessthematcheslistofaruleallapplication(includingtheone-element
matches list ofasingle rule application)after allmatches werefound,butbefore theyare
rewritten.Theyallowyoutofollowonlythemostpromisingmatchesduringasearchtask.
Youmayimplementltersintheformoflterfunctionsonyourown.Alternatively,you
maydeclarecertainltersattheirrules,theyarethenauto-generated foryou. Somelters
areauto-suppliedandmayjustbeused. Allltersareusedbyltercallsfromthesequences
(normallytogetherwitharuleallapplication).
15.1 FilterFunctions
Filterfunctionsneedtobedened,i.e. declaredandimplementedbeforetheycanbeused.
FilterFunctionDenition
-
filter
-
FilterIdent
-
<
-
RuleIdent
-
>
-
Parameters
-
f
-
Statement
-
g
-
Alterfunctiondenitionisgiveninbetweentherulesasaglobalconstruct. Itspecies
thenameofthelterandtheparameterssupported,furthermoreitspecieswhichrulethe
lterappliesto,anditsuppliesalistofstatementsinthebody.
Therestrictionsofafunctionbodyapplyhere,i.e.youarenotallowedtomanipulatethe
graph. Incontrasttothefunctionbodyisathisvariablepredened,whichgivesaccessto
thematchesarraytolter,oftypearray<match<r>>,whererdenotesthenameoftherule
thelter isdenedfor. . Alltheoperations s knownforvariablesofarraytype(cf. 13.4)are
available.
181
182
FilteringandSortingofMatches
EXAMPLE(90)
Thefollowinglterfffortherulefooclones the lastmatchinthearray ofmatches,and
addsittothearray. Sothelastmatchwouldberewrittentwice(whichisneforfoothat
onlycreates anode,buttakecarewhendeletingor retypingnodes). . Butinthefollowing
therstentryandthelastentryaredeleted(again);therstinanecientin-placewayby
assigningnull.
1
rulefoo
2
{
3
n:Node;
4
modify{
5
nn:Node;
6
}
7
}
8
9
filterff<foo>
10
{
11
this.add(copy(this.peek()));//note the copyonmatch<foo>
12
this[0]= null;//removes firstentryinmatchesarray,efficiently
13
this.rem();
14
}
Thematch type match<r> > itself provides member access in n dot t notation n (readingand
writing),andacopyoperationtogetaclone(forinsertionintothematchesarray).
EXAMPLE(91)
Thefollowingruleincidencyyieldsforeachnodenmatchedthenumberofincidentedges
toadefvariableiandassignsitintheevalontoanattributej.ThelterfilterMultiply
modiesthedefvariableiinthematcheswiththefactorfhandedinaslterparameter.
1
ruleincidency
2
{
3
n:N;
4
defvari:int;
5
yield {yieldi =incident(n).size(); }
6
7
modify{
8
eval{ n.j = i;}
9
}
10
}
11
12
filterfilterMultiply<incidency>(var f:int)
13
{
14
for(m:match<incidency> inthis)
15
{
16
m.i = m.i *f;
17
}
18
}
Thefollowingcalltriplesthecountofincidentedgesthatisnallywrittentotheattributej
foreachnodenmatchedbyincidency:
1
exec[incidency\ filterMultiply(3)]
15.2 Auto-GeneratedFilters
183
YoumaydeclareexternalltersyoumustimplementtheninaC#accompanyingle,see
25.4formoreonthat. Withlterfunctionsandexternallterfunctions,youmayimplement
matches-listmodicationsexceedingtheavailablepre-implementedfunctionality.
15.2 Auto-GeneratedFilters
Auto-generated lters s needtobe declared d at t their rule beforethey canbe used, , they y are
implementedbyGrGen.NET.
FiltersDecl
-
\
-
FilterDecl
,
-
FilterDecl
-
FilterIdent
-
<
-
VariableIdent
-
>
-
auto
-
Theauto-generatedltersmustbedeclaredattheendofaruledenition(cf.5.2).With
exceptionoftheautolterforremovalofautomorphicmatchestheyhavetospecifythename
ofadef varvariablecontainedinthepattern,ofinteger, oatingpoint,orstringtype;you
yieldavaluecomputedfromtheelementsandtheirattributestoit,permatchedpattern.
Theylterbasedoncertainconditionsregardingthatvariable;lteringmaymeantoreorder
amatcheslistalongsidethechosendefvariable.
orderAscendingBy<v>
orders thematches list ascendingly(from m lowest t ot highest value according to the e <
operator),alongsidethevcontainedineachmatch.
orderDescendingBy<v>
ordersthematcheslistdescendingly,alongsidethevcontainedineachmatch.
keepSameAsFirst<v>
lters away all l matches s withv values that are not equal l to the v v value of the rst
match. Maybeusedtoensureallmatchesofanindeterministically y chosenvalueare
rewritten,buttypicallyyouwanttoorderthematcheslistbefore.
keepSameAsLast<v>
ltersawayallmatcheswithvvaluesthatarenotequaltothevvalueofthelastmatch.
keepOneForEach<v>
ltersawayallmatcheswithduplicatevvalues,i.e. onlyone(prototypical)matchis
keptper vvalue. . Thelistmust t havebeengroupedor orderedbefore, , otherwise the
resultisundened.
Besidesthosevariable-basedltersyoumayusetheautomorphicmatchesltertopurge
symmetric matches. . In n order to do so specify y the e special l lter named auto at the e rule
declaration,anduseit withthesamenameat theanapplicationof thataction(withthe
known backslash syntax). . Thelter r is removingmatches duetoanautomorphic pattern,
matches which h are e covering the same spot in the e host t graph h with a permutation of f the
nodes,theedges,orsubpatternsofthesametypeatthesamelevel. Othernestedpattern
184
FilteringandSortingofMatches
constructswhicharestructurallyidenticalarenotrecognizedtobeidenticalwhentheyappear
as commuted d subparts; ; but t they y are e so when n they y are e factored d into a subpattern which
is instantiated multiple e times. . It t is s highly y recommended d touse this s symmetry reduction
technique when building state spaces including isomorphic state collapsing, as puringthe
matcheswhichleadtoisomorphicstatesearlysavesexpensivegraphcomparisons{andoften
itgivesthesemanticsyouareinterestedinanyway.
15.3 Auto-SuppliedFilters
Afewlters (that donot needinformationfromaspecicmatch) areauto-supplied,they
canbe usedwithoutimplementationandevenwithoutdeclaration. . They y allowtokeepor
removeacertainnumberofmatchesfromthebeginningortheendofthematcheslist.
Thefollowingauto-suppliedltersmaybeuseddirectly:
keepFirst(count)
keeps the rst countmatches fromthebeginofthematches list, , count t must be an
integernumber.
keepLast(count)
keepstherstcountmatchesfromtheendofthematcheslist,countmustbeaninteger
number.
keepFirstFraction(fraction)
keepsthefractionofthematchesfromthebeginofthematcheslist,fractionmust
bea oatingpointnumberinbetween0.0and1.0.
keepLastFraction(fraction)
keepsthefractionofthematchesfromtheendofthematcheslist,fractionmustbe
a oatingpointnumberinbetween0.0and1.0.
removeFirst(count)
removestherstcountmatchesfromthebeginofthematcheslist,countmustbean
integernumber.
removeLast(count)
removestherst count matches fromthe endofthematcheslist, , countmustbean
integernumber.
removeFirstFraction(fraction)
removes the fraction of the matches fromthe begin n of the matches s list, , fraction
mustbea oatingpointnumberinbetween0.0and1.0.
removeLastFraction(fraction)
removesthefractionofthematchesfromtheendofthematcheslist,fractionmust
bea oatingpointnumberinbetween0.0and1.0.
15.4 Filtercalls
FilterCalls
-
\
-
FilterCall
-
15.4 Filtercalls
185
FilterCall
-
FilterIdent
-
(
-
Arguments
-
)
-
FilterIdent
-
<
-
VariableIdent
-
>
-
auto
-
Filters areemployedwithr\fnotationatrulecallsfromthesequenceslanguage. . This
holdsforuser-implemented,auto-generated,andauto-suppliedlters.
EXAMPLE(92)
ThefollowingruledeleteNode yields to adefvariable theamount of outgoingedges of a
node,anddeletesthenode. Withoutlteringthisbehaviourwouldbepointless,butalter
orderingbasedonthedefvariableisalreadydeclaredforit.
1
ruledeleteNode
2
{
3
defvari:int;
4
5
n:Node;
6
7
yield {
8
yield i=outgoing(n).size();
9
}
10
11
modify{
12
delete(n);
13
}
14
} \orderAscendingBy<i>
Therulemaythenbeappliedwithasequencelikethefollowing:
1
exec[deleteNode \orderAscendingBy<i> \keepFirstFraction(0.5)]
Thisway,the50%ofthenodeswiththesmallestnumberofoutgoingedgesaredeletedfrom
thehost graph(becausethey don’tgetlteredaway),orrephrased: : the50%ofthenodes
withthehighestnumberofoutgoingedgesarekept(theirmatchesattheendoftheordered
matcheslistarelteredaway).
186
FilteringandSortingofMatches
orderAscendingBy<def var:int|double|string>
orderDescendingBy<def var:int|double|string>
keepSameAsFirst<def var:int|double|string>
keepSameAsLast<def var>:int|double|string
keepOneForEach<def var:int|double|string>
auto
keepFirst(int-Number)
keepLast(int-Number)
keepFirstFraction(double-Number)
keepLastFraction(double-Number)
removeFirst(int-Number)
removeLast(int-Number)
removeFirstFraction(double-Number)
removeLastFraction(double-Number)
Table15.1: Auto-generatedandthenauto-suppliedltersataglance
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