Garbage Collection in Ob ject Or iente d Databas e s Us ing
Transactional Cyclic Reference Counting
S Ashwin Prasan Roy S Se shadr i Avi Silb erschatz
S Sudarshan
1 2
Indian Institute of Technology Bell Lab orator ie s
Mumbai India Murray Hill NJ
sashwin cs wi sc e du avi b ell labs com
fprasan s e shadr i sudarshag cs e iitb er net in
Intro duction
Ob ject or iente d databas e s OODBs unlike relational
Ab stract
databas e s supp ort the notion of ob ject identity and
ob jects can refer to other ob jects via ob ject identi
ers Requir ing the programmer to wr ite co de to track
Garbage collection i s imp ortant in ob ject
ob jects and the ir reference s and to delete ob jects that
or iente d databas e s to f ree the programmer
are no longer reference d i s error prone and leads to
f rom explicitly deallo cating memory In thi s
common programming errors such as memory leaks
pap er we pre s ent a garbage collection al
garbage ob jects that are not referre d to f rom any
gor ithm calle d Transactional Cyclic Refer
where and haven t b een delete d and dangling ref
ence Counting TCRC for ob ject or iente d
erence s While the s e problems are pre s ent in tradi
databas e s The algor ithm i s bas e d on a var i
tional programming language s the e ect of a memory
ant of a reference counting algor ithm pro
leak i s limite d to individual runs of programs s ince
p os e d for functional programming language s
all garbage i s implicitly collecte d when the program
The algor ithm keeps track of auxiliary refer
terminate s The problem b ecome s more s er ious in p er
ence count information to detect and collect
s i stent ob ject store s s ince ob jects outlive the programs
cyclic garbage The algor ithm works correctly
that create and acce ss them Automate d garbage col
in the pre s ence of concurrently running trans
lection i s e ss ential in an ob ject or iente d databas e to
actions and system f ailure s It do e s not ob
protect f rom the errors mentione d ab ove In f act
tain any long term lo cks thereby minimizing
the Smalltalk binding for the ODMG ob ject databas e
interference with transaction pro ce ss ing It
standard require s automate d garbage collection
us e s recovery subsystem logs to detect p ointer
We mo del an OODB in the standard way as an ob
up date s thus exi sting co de nee d not b e re
ject graph where in the no de s are the ob jects and the
wr itten Finally it exploits schema informa
arcs are the reference s b etween ob jects The graph has
tion if available to re duce costs We have im
a p ers i stent root All ob jects that are reachable f rom
plemente d the TCRC algor ithm and pre s ent
the p ers i stent ro ot or f rom the trans ient program state
re sults of a p erformance study of the imple
of an on going transaction are live while the re st are
mentation
garbage We often call ob ject reference s as pointers
There have b een two approache s to garbage collec
Currently at the University of Wisconsin Madison
tion in ob ject or iente d databas e s Copying Col lector
Permission to copy without fee al l or part of this material is
bas e d YNY and Mark and Sweep bas e d AFG
granted provided that the copies are not made or distributed for
direct commercial advantage the VLDB copyright notice and
The copying collector algor ithm travers e s the entire ob
the title of the publication and its date appear and notice is
ject graph and copie s live ob jects into a new space the
given that copying is by permission of the Very Large Data Base
entire old space i s then reclaime d In contrast the
Endowment To copy otherwise or to republish requires a fee
Mark and Sweep algor ithm marks all live ob jects by
and or special permission from the Endowment
travers ing the ob ject graph and then travers e s sweeps
Pro cee dings of the rd VLDB Conference
Athens Greece the entire databas e and delete s all ob jects that are un
marke d The copying collector algor ithm reclusters ob ing algor ithm to handle cyclic data have b een prop os e d
jects dynamically the recluster ing can improve lo cality in the programming language community including
of reference in some cas e s but may de stroy program Bro Bro PvEP More recent work in thi s
mer sp eci e d cluster ing re sulting in wors e p erformance area include s Lin MWL JL
in other cas e s The garbage collection algor ithms of In thi s pap er we cons ider a vers ion of reference
YNY as well as AFG handle concurrency con counting prop os e d by Brownbr idge Bro Bro
trol and recovery i ssue s for functional programming language s which handle s
s elf referential cycle s of garbage We pre s ent an al
With b oth the ab ove algor ithms the cost of tra
gor ithm calle d Transactional Cyclic Reference Count
vers ing the entire ob ject graph can b e prohibitively
ing TCRC bas e d on Brownbr idge s algor ithm which
exp ens ive for databas e s larger than the memory s ize
i s suitable for garbage collection in an OODB The sa
particularly if there are many cross page reference s
lient feature s of the TCRC algor ithm are
In the worst cas e when the bu er s ize i s a small f rac
tion of the databas e s ize and ob jects in a page refer to
It detects all s elf referential cycle s of garbage un
ob jects in other page s only there may b e an I O for
like bas ic reference counting and the partitione d
every p ointer in the databas e To alleviate thi s prob
garbage collection algor ithms
lem earlier work YNY AFG has attempte d to
divide the databas e into partitions cons i sting of a few
It p erforms a very lo calize d vers ion of mark and
page s Each partition store s inter partition reference s
sweep to handle cyclic data with each mark and
that i s reference s to ob jects in the partition f rom ob
sweep likely to acce ss f ar fewer ob jects than a
jects in other partitions in a p ers i stent data structure
global mark and sweep Thus it do e s not have
Ob jects referre d to f rom other partitions are treate d
to examine the entire databas e while collecting
as if they are reachable f rom the p ers i stent ro ot and
garbage except in the worst cas e
are not garbage collecte d even if they are not referre d
to f rom within the partition Each partition i s garbage It allows transactions to run concurrently and
collecte d indep endent of other partitions reference s to
do e s not obtain any long term lo cks thereby min
ob jects in other partitions are not followe d Thus par
imizing interference with transaction pro ce ss ing
titioning make s the traversal more e cient the smal
It i s integrate d with recovery algor ithms and
ler the partition the more e cient the traversal with
works correctly in spite of system crashe s It also
maximum e ciency o ccurr ing if the whole partition ts
us e s recovery subsystem logs to detect p ointer up
into the bu er space
date s thus exi sting application co de nee d not b e
Unfortunately small partitions increas e the probab
rewr itten
ility of s elf referential cycle s of garbage that cross par
tition b oundar ie s such cyclic garbage i s not detecte d
It exploits schema information if available to re
by the partitione d garbage collection algor ithms Pre
duce costs In particular if the schema graph i s
vious work has maintaine d that such cross cycle struc
acyclic no cyclic reference s are p oss ible in the
ture s will b e few and will probably not b e a prob
databas e and TCRC b ehave s identically to refer
lem However s imulations by CWZ showe d that
ence counting
even small increas e s in databas e connectivity can pro
duce s igni cant amounts of such garbage Therefore
A pro of of correctne s s of the TCRC algor ithm i s
+
it i s not clear that partition s ize s can b e made very
pre s ente d in ARS De s igning a cyclic referencing
small without e ither f ailing to collect large amounts
counting algor ithm which allows concurrent up date s
of garbage or employing sp ecial and exp ens ive tech
and handle s system crashe s i s rather non tr ivial and
nique s to detect such cyclic garbage
to our knowle dge has not b een done b efore we b elieve
thi s i s one of the central contr ibutions of our pap er
A natural alter native i s Reference Counting Refer
A problem often cite d against reference counting
ence Counting i s bas e d on the idea of keeping a count of
the numb er of p ointers p ointing to each ob ject When scheme s i s the overhead of up dating reference counts
the reference count of the ob ject b ecome s zero it i s However each p ointer up date can only re sult in at
garbage and eligible for collection Reference count most one reference count b e ing up date d Thi s over
ing has the attractive prop ertie s of lo calize d and in head will have only a small impact on p erformance if
as we exp ect i s true in any reali stic scenar io p ointer
cremental pro ce ss ing Unfortunately bas ic reference
up date s are only a small f raction of the overall up
counting cannot deal with s elf referential cycle s of ob
jects each ob ject could have a p os itive reference count date s For TCRC moreover the overhead i s o s et by
yet all the ob jects in the cycle may b e unreachable f rom the re duce d cost of traversals while collecting garbage
the p ers i stent ro ot and therefore b e garbage However We have implemente d a prototyp e of the TCRC al
a numb er of extens ions of the bas ic referencing count gor ithm as well as the partitione d mark and sweep
algor ithm on a storage manager calle d Brahm a de and are delete d
velop e d in I IT Bombay We pre s ent a p erformance However pr ior cyclic reference counting algor ithms
study of TCRC bas e d on the implementation the study including Brownbr idge s algor ithm were de s igne d for
clearly illustrate s the b ene ts of TCRC a s ingle us er system They cannot b e us e d in a multi
us er environment with concurrent up date s to ob jects
and do not deal with p ers i stent data and f ailure s Our
Brownbr idge s Cyclic Reference
contr ibutions lie in extending Brownbr idge s algor ithm
Counting Algor ithm
to a us e logs of up date s to detect change s to ob ject
Our Transactional Cyclic Reference Counting al reference s b to work in an environment with con
gor ithm i s bas e d on the Cyclic Reference Counting current up date s c to work on p ers i stent data in the
CRC algor ithm prop os e d by Brownbr idge Bro pre s ence of system f ailure s and transaction ab orts d
Bro in the context of functional programming lan handle a batch of up date s at a time rather than one up
guage s date at a time and e optimize the lo calize d mark and
sweep s igni cantly by following only strong p ointers
The bas ic idea b ehind the Cyclic Reference Count
ing CRC algor ithm of Brownbr idge Bro Bro i s
to lab el e dge s in the ob ject graph as strong or weak System Mo del and As sumptions
The lab elling i s done such that a cycle in the ob ject
In thi s s ection we de scr ib e our system mo del and
graph cannot cons i st of strong e dge s alone it must
outline the architectural assumptions on which our
have at least one weak e dge Two s eparate reference
garbage collector i s bas e d which i s very s imilar to the
counts for strong and for weak e dge s denote d SRefC
mo del and assumptions in AFG
and WRefC re sp ectively are maintaine d p er ob ject It
In our mo del transactions log undo and re do in
i s not p oss ible in general to cheaply determine whether
formation for all up date s Undo and re do records
lab elling a new e dge as strong create s a cycle of strong
are repre s ente d as undo tid oid o s et old value and
e dge s or not Hence in the abs ence of further informa
re do tid oid o s et new value where tid denote s a
tion the algor ithm take s the cons ervative view that la
transaction identi er and oid an ob ject identi er Ob
b elling a new e dge strong could create a cycle of strong
ject creation i s logge d as object allo cation tid oid The
e dge s and lab els the new e dge weak
commit log i s repre s ente d as commit tid and the
The SRefC and WRefC are up date d as e dge s are
ab ort log i s repre s ente d as ab ort tid We require that
create d and delete d If for an ob ject S the SrefC as
f rom the oid we can identify the typ e of the ob ject p er
well as WrefC i s zero then S i s garbage and S and
haps by rst fetching the ob ject and f rom the o s et
the e dge s f rom it are delete d If the SrefC i s zero but
we can determine if the value that has b een up date d
WrefC i s non zero there i s a chance that S i s involve d
i s a p ointer eld The s e requirements are sati s e d by
in a s elf referential cycle of garbage If the SrefC of
most databas e systems
an ob ject S i s greater than zero then S i s guarantee d
We make the following imp ortant assumption ab out
to b e reachable f rom the ro ot however our TCRC
transactions
algor ithm do e s not guarantee thi s last prop erty
As sumption Transactions fol low strict two
If the ob ject graph did not have any garbage b e
phase locking on objects That is transactions acquire
fore the deletion of an e dge to S then the only p oten
read or write locks on objects as appropriate and hold
tial candidate s for b ecoming garbage are S and ob jects
read as wel l as write locks until end of transaction 2
reachable f rom S If SrefC of S i s zero and WrefC of
S i s nonzero a lo calize d mark and sweep algor ithm
As with any other garbage collection scheme we as
detects whether S and any of the ob jects reachable
sume that an ob ject identi er i s valid only if it i s e ither
f rom S are indee d garbage The lo calize d mark and
a p ers i stent ro ot or i s pre s ent in a p ointer eld of an
sweep p erforms a traversal f rom S and identi e s all
ob ject in the databas e or i s in the trans ient memory
ob jects reachable f rom S and colours them re d Let
program var iable s or regi sters of an active transac
us denote the ab ove s et by R It then colours green
tion that read the value f rom an ob ject in the databas e
every ob ject in R that has a reference f rom an ob ject
Note that thi s preclude s transactions f rom pass ing oids
outs ide R detecte d us ing reference counts It also
to other transactions and f rom stor ing oids in exter nal
colours green all ob jects reachable f rom any green ob
p ers i stent storage
ject Dur ing thi s green marking phas e some p ointer
Our algor ithms can b e us e d in centralize d as well
strengths are up date d to ensure that every ob ject has
as client s erver s ettings Let us cons ider rst the cent
at least one strong p ointer to it We will de scr ib e thi s
ralize d s etting
p ointer strength up date in detail in the context of our
transactional cyclic reference counting algor ithm At As sumption In the centralized setting we as
the end all ob jects in R not marke d green are garbage sume that transactions fol low str ict WAL that is
they log both the undo and the redo value before actu The TCRC algor ithm also maintains a p ers i stent
al ly performing the update 2 table the Weak Reference Table WRT which con
tains oids for the ob jects which have a zero SRefC i e
Our algor ithms also work in a data shipping client
no strong p ointers incident on them The p ers i stent
s erver environment under the following assumptions
ro ot i s never put into the WRT
All the ab ove information can b e constructe d f rom
As sumption In the client server setting we as
the ob ject graph and therefore it could b e made tran
sume that clients fol low
s ient However we would then have to reconstruct the
str ict WAL with respect to the server That is
information after a system crash by scanning the entire
before any data is received by the server the undo
databas e which would b e exp ens ive Hence we make
as wel l as redo information for the data must have
it p ers i stent Up date s to SRefC and WRefC up date
already been received by the server
of the strength bit of an ob ject or of a p ointer and the
ins ert or delete of entr ie s f rom the WRT are logge d as
force with respect to the server That is be
part of the transaction whos e p ointer up date caus e d
fore the transaction commits al l the updated data
the information to b e up date d ins erte d delete d
must have been received by the server 2
There i s also a non p ers i stent table which i s us e d
dur ing garbage collection the Red Reference Table
The s e assumptions make the client transaction b e
RRT thi s table asso ciate s with some ob jects a
have as f ar as the s erver i s concer ne d just like a lo cal
strong red reference count SRe dRefC a weak red ref
transaction that follows str ict WAL
erence count WRe dRefC and a bit that indicate s
Our technique s are not a ecte d by the unit of data
whether the colour of the ob ject i s re d or green Thi s
shipping such as page or ob ject and whether or not
table i s store d on di sk s ince the s ize of thi s table could
data i s cache d at the client The clients can retain
b e large in the worst cas e but up date s to thi s table are
copie s of up date d data after it has b een s ent to the
not logge d
s erver
Most of the assumptions ab ove are sati s e d by typ Finally s imilar to AFG TCRC maintains an
non p ers i stent in memory table calle d the Temporary
ical storage managers for ob ject or iente d databas e s
Reference Table TRT which contains all thos e oids
Our client s erver assumptions are also very s imilar to
such that a reference to the ob ject was adde d or de
thos e of AFG
lete d by an active transaction or the ob ject was cre
ate d by the transaction Such an oid may b e store d in
Transactional Cyclic Reference
the trans ient memory of an active transaction although
Counting
the ob ject may not b e reference d by any other ob ject
We will now de scr ib e the Transactional Cyclic Refer
in the databas e An ob ject whos e oid i s in TRT may
ence Counting TCRC algor ithm We rst de scr ib e
not b e garbage even if it i s unreachable f rom any other
the data structure s nee de d by the transactional cyclic
ob ject s ince the transaction may store a reference to
reference counting algor ithm
the ob ject back in the databas e Up date s to TRT are
also not logge d The TRT also provide s a s imple way
Data Structure s
of handling the p ers i stent ro ot its oid i s entere d in
the TRT at system start up and i s never remove d
Asso ciate d with each ob ject we p ers i stently maintain
Thi s prevents the garbage collector f rom collecting the
a strong reference count SRefC giving the numb er of
p ers i stent ro ot
strong p ointers p ointing to the ob ject a weak refer
ence count WRefC giving the numb er of weak p oint
The Algor ithm
ers p ointing to the ob ject and a strength bit for the
ob ject Each p ointer also has a strength bit Both
TCRC cons i sts of two di stinct algor ithms run by
strength bits are p ers i stent The p ointer i s strong if
di erent pro ce ss e s The rst i s the log analyzer al
the strength bit in the p ointer and the strength bit in
gor ithm The s econd algor ithm i s the actual garbage
the ob ject p ointe d to have the same value otherwi s e
col lection algor ithm We de scr ib e them b elow
the p ointer i s weak Thi s repre s entation of strength
us ing two bits i s an imp ortant implementation tr ick
Log analyzer
f rom Brownbr idge Bro Bro It make s very e
cient the op eration of ipping the strength of all p oint The log analyzer algor ithm analyze s log records gener
ers to an ob ject that i s making all strong p ointers to ate d by the transaction and p erforms var ious actions
the ob ject weak and all weak p ointers to the ob ject bas e d on the log records As part of its actions it may
strong All that nee d b e done i s to ip the value of the also ins ert records into the log We shall assume it i s
strength bit in the ob ject run as part of the transaction its elf i s invoke d each
time a log record i s app ende d to the system log tail
and i s atomic with re sp ect to the app ending of the log
record Pro ce dure CollectGarbage f
acquire gcLatch
In the actual implementation it i s p oss ible to run
RRT fg
the log analyzer as a s eparate thread and when a
S for each oid in WRT that i s not in TRT
transaction app ends a log record to the system log it
Re dTravers e oid
actually only delivers it to the log analyzer which then
S for each oid RRT
app ends the log record to the system log In particu
latch the reference count entry of oid
lar in the client s erver implementation the log analyzer
if S Ref C W Ref C
pro ce ss i s run at the s erver end not at the client
oid oid
S RedRef C W RedRef C
The log analyzer make s us e of the following pro ce d
oid oid
mark oid as green
ure s Pro ce dure DeletePointer decrements the WRefC
unlatch reference count entry of oid
or SRefC for an ob ject when a p ointer to the ob ject
for each oid RRT that i s marke d green
i s delete d If the SRefC f alls to zero after the decre
if S Ref C S RedRef C
ment then the ob ject s oid i s put into WRT Pro ce dure
oid oid
all exter nal p ointers
AddPointer by def ault s ets the strength of the p ointer
to the object are weak
to b e weak and increments the WRefC of the ob ject
if S Ref C oid i s in WRT
p ointe d to The strength i s s et to weak so that cycle s
oid
remove oid f rom WRT
of strong e dge s are not create d however we will s ee
ip the strength of all p ointers to oid
in Section that we may b e able to make some new
swap S Ref C and W Ref C
p ointers strong
oid oid
GreenTravers e oid
The pro ce dure LogAnalyzer works as follows First
done FALSE
analyzer latch which i s also acquire d it obtains the log
S while done FALSE
by the garbage collection thread to e stabli sh a con
done TRUE
s i stent p oint in the log The latch i s obtaine d for the
analyzer latch acquire log
duration of the pro ce dure The log i s analyze d by the
S for each oid RRT that i s marke d re d
log analyzer and dep ending on the typ e of the log re
if oid TRT
cord var ious actions as outline d b elow are taken For
analyzer latch releas e log
undo re do log records caus e d by p ointer up date s the
GreenTravers e oid
reference counts for the a ecte d ob jects are up date d
done FALSE
Thi s i s done by DeletePointer in cas e of undo logs and
acquire log analyzer latch
AddPointer in cas e of re do logs For log records cor
releas e log analyzer latch
re sp onding to the allo cation of ob jects the reference
S for each oid RRT that i s marke d re d
counts for the new ob ject are initialize d to zero and
Collect oid
the oid of the ob ject i s ins erte d into the WRT In all
releas e gcLatch
the ab ove cas e s i e for p ointer up date s and ob ject al
remove all agge d entr ie s f rom TRT
lo cation the oid of the a ecte d ob ject i s ins erte d into
g
the TRT with the tid of the transaction that generate d
the record
Pro ce dure GreenTravers e oid f
For end of transaction commit or ab ort log re
starting with oid as the ro ot do a
cords the algor ithm rst tr ie s to get the gcLatch If the
depth rst traversal re str icte d to
latch i s obtaine d imme diately then garbage collection
the objects marke d re d in RRT
i s not in progre ss and all the oid entr ie s for the termin
when vi s iting an object dur ing the traversal
ating transaction f rom the TRT are remove d and the
mark the object green
gcLatch releas e d thereafter However if the gcLatch
make strong all p ointers f rom the object
cannot b e obtaine d imme diately then a garbage col
to any re d object not yet vi s ite d
lection i s in progre ss concurrently In thi s cas e the
make weak all p ointer f rom the object to
oid entr ie s for the terminating transaction are not re
any green object already vi s ite d
move d but instead agge d for later removal by the
g
garbage collector
All op erations on p ointer strengths and reference
counts are protecte d by a latch on the ob ject p oin
te d to although not explicitly mentione d in our al
Figure Ps eudo Co de for Garbage Collector
gor ithms Acce ss to WRT and TRT are also protecte d
by latche s
Garbage Collector analyzer latch for the last time in the while lo op the log
at step S as T Thi s guarantee s that all ob jects in
The garbage collection algor ithm i s activate d p er io dic
RRT that are marke d re d at step S are not in TRT
ally p oss ibly dep ending on availability of f ree space
according to log at T
The algor ithm make s us e of the following supp ort func
tions Pro ce dure Collect actually delete s an ob ject
Supp ort for Logical Undo by the Recov
b efore doing so it delete s all p ointers out of the ob
ery Manager
ject up dating the store d reference counts of the ob
The TCRC algor ithm nee ds some supp ort f rom the re
jects p ointe d to It also delete s the ob ject f rom RRT
covery manger in the form of supp orting logical undos
and WRT
to ensure correctne s s There are some actions whos e
Pro ce dure Re dTravers e p erforms a reachability scan
undos have to b e p erforme d logically and not phys
f rom the sp eci e d ob ject following only strong p oint
ically We di scuss them b elow and di scuss what the
ers and marks all reachable ob jects re d and puts
logical undo should do in each cas e
them in RRT Re dTravers e also maintains for each
Pointer Deletion and Strength Up date Undo
ob ject pre s ent in RRT two counts S RedRef C and
of a p ointer deletion or strength up date if p erforme d
W RedRef C giving re sp ectively the numb er of strong
naively may intro duce strong cycle s in the graph
and weak p ointers to the ob ject f rom all other ob jects
which can a ect the correctne ss of the algor ithm The
pre s ent in RRT The s e counts are maintaine d on the
r ight way to undo a p ointer deletion i s to re ins ert the
y dur ing the traversal in order to do so Re dTravers e
p ointer with the strength s et to b e weak even if it
also maintains the s e counts for ob jects that are reach
was strong earlier Similarly the undo of a p ointer
able by a s ingle weak e dge f rom ob jects in RRT s ince
strength up date done in cas e of system crash dur ing
such ob jects may b e adde d to RRT later in the scan
the garbage collection phas e i s to s et the strength
The garbage collection algor ithm i s implemente d by
of the p ointer as weak irre sp ective of the or iginal
Pro ce dure CollectGarbage shown in Figure Initially
strength
all no de s reachable f rom ob jects in WRT us ing only the
Reference Counts Up date The reference counts
strong p ointers are coloure d re d and put in RRT by
of an ob ject O can b e concurrently up date d by multiple
calling Re dTravers e Thi s function p erforms a fuzzy
transactions including the garbage collector through
lo calize d traversal of the ob ject graph dur ing which
di erent ob jects which are lo cke d by the transactions
no lo cks are obtaine d on the ob jects b e ing travers e d
The ob ject O its elf nee d not b e lo cke d s ince only a ref
Short term latche s may b e obtaine d on ob jects or page s
erence to it i s b e ing up date d Only short term latche s
to ensure phys ical cons i stency
are nece ssary for maintaining phys ical cons i stency If a
After thi s in Step S some no de s are marke d green
transaction that up date d the reference count of an ob
bas e d on the value s of the ir WRefC SRefC and WRe
ject ab orts it should b e logically undone the undo of
dRefC SRe dRefC WRe dRefC i s the numb er of weak
a reference count increment i s a decrement of the same
p ointers p ointing to an ob ject amongst p ointers f rom
reference count while the undo of a reference count
ob jects in RRT Similarly SRe dRefC i s the numb er of
decrement i s always an increment of WRefC s ince a
strong p ointers p ointing to an ob ject amongst p oint
re ins erte d p ointer i s always weak
ers f rom ob jects in RRT The expre ss ion WRe dRefC
SRe dRefC counts how many p ointers to a no de s
Correctne s s
are f rom no de s in RRT If thi s count i s le ss than the
Theorem The TCRC algorithm
total numb er of p ointers to no de s there must b e an
exter nal to ob jects in RRT p ointer to s and s i s
eventual ly col lects any object that is garbage
not garbage Such ob jects are marke d green in Step
S The Pro ce dure GreenTravers e calle d in Pro ce dure
does not incorrectly reclaim live objects as
CollectGarbage can b e found in Figure
garbage 2
Next in Step S any ob jects in RRT that are in
TRT are also marke d green s ince the ir reference s may The ab ove theorem e stabli she s the correctne ss of the
+
still b e store d in an ongoing transaction and store d TCRC algor ithm a pro of i s pre s ente d in ARS
back in the databas e Ob jects that are reachable f rom The theorem holds in the pre s ence of concurrent trans
actions and system f ailure s
the ab ove ob jects are also marke d green by invoking
GreenTravers e The reason for p erforming Step S re An intere sting p oint to note i s that Re dTravers e fol
p eate dly in the while lo op at Step S i s to e stabli sh lows only strong p ointers and not weak p ointers in
a cons i stent p oint in the log at which no ob ject in the contrast to Mark and Sweep Our pro of of correctne ss
RRT i s in TRT thi s helps s implify the pro of of correct shows that every garbage ob ject i s e ither in WRT or
ne ss Let us denote the time instant when we acquire i s reachable by a s equence of strong e dge s f rom an
ob ject in WRT and thus Re dTravers e nds all garbage ject manager calle d Brahm a develop e d at I IT Bom
ob jects We also show that all non garbage ob jects col bay Brahm a supp orts concurrent transactions us ing
oure d re d are later coloure d green by a call on Green two phas e lo cking and a complete implementation of
Travers e even though GreenTravers e only follows e dge s the ARIES recovery algor ithm It provide s extend
+
through re d ob jects ible hash indice s as well as B tree indice s as addi
Another intere sting p oint i s that although our tional acce ss mechani sms
traversals b oth Re dTravers e and GreenTravers e are
The WRT i s implemente d as a p ers i stent extendible
fuzzy that i s they do not acquire any long term lo cks
hash table indexe d on the oid while the TRT i s an
the algor ithms are still correct The TRT also us e d
in memory hash table indexe d s eparately on the oid
by AFG plays an imp ortant role here s ince any
and the transaction id to allow easy deletion of all
p ointers that are adde d or delete d dur ing the traversal
entr ie s of a transaction The reference counts SRefC
are ins erte d into the TRT Ob jects reachable f rom
and WRefC are store d with the ob ject its elf The
TRT are not garbage collecte d
only p ers i stent structure s require d by PMS are one
A badly de s igne d garbage collection algor ithm could
Incoming Reference List IRL p er partition which i s
+
create in nite work for its elf by leaving oids in WRT
maintaine d as a p ers i stent B tree
which will b e travers e d by another garbage collection
Our p erformance study in thi s s ection i s bas e d on
phas e which in tur n leave s oids in WRT ad in nitum
the standard OO b enchmark CDN In particular
We now state a theorem which guarantee s that thi s
we worke d on the standard smal l datas et in OO
do e s not happ en that i s in the abs ence of up date s
which was also us e d in YNY for the ir s imulation
the system eventually reache s a state where garbage
study The OO parameters and the ir value s for thi s
collection thread do e s no more work
datas et are given in Table and are explaine d b elow
The OO datas et i s comp os e d of a numb er of mod
Theorem If there are no updates from the begin
ules sp eci e d by NUMMODULES Each mo dule con
ning of one garbage col lection phase to the end of the
s i sts of a tree of ob jects calle d ass emblie s The tree
next garbage col lection phase no object wil l be in WRT
i s a complete tree with a f anout of NUMASSMPER
at the end of the second garbage col lection phase 2
ASSM and has NUMASSMLEVELS levels The last
+
level of the tree i s calle d a bas e ass embly while the
The pro of i s pre s ente d in ARS
upp er levels are calle d complex ass emblie s In addi
tion each mo dule cons i sts of NUMCOMPPERMOD
Us ing the Schema Graph
ULE comp os ite ob jects The bas e ass emblie s p oint
We now s ee how to us e information f rom the data
to NUMCOMPPERASSM of the s e comp os ite ob jects
bas e schema to optimize TCRC The schema graph i s
Many bas e ass emblie s may share a comp os ite ob ject
a directe d graph in which the the no de s are the class e s
Each comp os ite ob ject p oints to a a pr ivate s et of
in the schema An e dge f rom no de i to no de j in the
NUMATOMICPERCOMP atomic objects b a di s
schema graph denote s that Class i has an attr ibute that
tingui she d atomic ob ject calle d the composite root
i s a reference to Class j The p ointers in the schema
and c a document ob ject An atomic ob ject has a
graph thus form a template for the p ointers b etween
xe d numb er of connections sp eci e d by NUMCON
the actual instance s of the ob jects If an e dge E in
NPERATOMIC out of it to other atomic ob jects in
a schema graph i s not involve d in a cycle then ne ither
the same s et A connection i s its elf mo dele d as an
can an e dge e in the ob ject graph for which E i s the
ob ject calle d a connection object p ointe d to by the
template
source of the connection and in tur n p oints to the de s
We lab el e dge s which are not part of a cycle in the
tination of the connection The connections connect
schema graph as acyclic and the others as cyclic When
the atomic ob jects into a cycle with chords We will
adding an e dge e to the ob ject graph if its corre sp ond
call a comp os ite ob ject along with its pr ivate s et of
ing template e dge in the schema graph i s acyclic the
atomic ob jects connection ob jects and the do cument
strength of e i s s et to b e strong Dur ing garbage col
ob ject together as an object composite All ob ject ref
lection in Re dTravers e we do not follow strong e dge s
erence s in the b enchmark have invers e s and we always
whos e template e dge i s acyclic In the extreme cas e
ins ert or delete reference s in pairs the reference and
where the schema graph i s acyclic no e dge s are tra
its invers e
vers e d and TCRC b ehave s just like reference counting
The datas et cons i ste d of ob jects o ccupying
re ducing the cost s igni cantly
megabyte s of space Each ob ject comp os ite con
s i ste d of ob jects and had a s ize of byte s Dur
Performance Evaluation
ing the cours e of exp er iments the s ize was maintaine d
We implemente d the TCRC algor ithm and the Parti constant by adding and deleting the same amount of
tione d Mark and Sweep PMS algor ithm on an ob data The ob ject manager us e d a bu er p o ol cons i sting
Parameter Value
PMS for thi s workload Three f actors contr ibute to
the overall p erformance the f requency of invo cation
NUMMODULES
of the garbage collector the overhead dur ing a garbage
NUMCOMPPERMODULE
collection pass and the overhead due to normal pro
NUMCONNPERATOMIC
ce ss ing We study the s e three f actors in detail now
NUMATOMICPERCOMP
NUMCOMPPERASSM
NUMASSMPERASSM
Invo cation Frequency
NUMASSMLEVELS
We checke d the databas e s ize at the end of every up date
pass and invoke d the garbage collector if the databas e
Table Parameters for the OO b enchmark
of KB page s The I O cost i s measure d in terms
s ize excee de d MB TCRC collects all garbage and
of the numb er of KB page s read f rom or wr itten to
therefore the amount of garbage which i s generate d at
the di sk All the complex and bas e ass emblie s form
the rate of byte s p er up date pass excee de d
ing the tree structure were clustere d together We also
MB and thus the total databas e s ize excee de d MB
clustere d together all the ob jects create d for a comp os
after s even up date pass e s Thus garbage collection in
ite
cas e of TCRC i s cons i stently invoke d after every s even
up date pass e s
For PMS the data was divide d into partitions
each partition ts in memory The inter partition ref
The patter n i s more intere sting in the cas e of PMS
erence s were kept very small All the complex and
Approximately one out of fty comp os ite s spanne d par
bas e ass emblie s forming the tree structure were put in
titions such a comp os ite which i s cyclic i s never col
the same partition Approximately one out of every
lecte d Thi s caus e d the databas e s ize to increas e with
comp os ite s spanne d partitions
time Since the thre shold remaine d xe d at MB thi s
caus e d the garbage collection to b e invoke d more f re
We conducte d two s ets of exp er iments the rst was
quently as time progre ss e d Dur ing the cours e of the
bas e d on structure mo di cations sugge ste d in the OO
up date pass e s TCRC garbage collector was invoke d
b enchmark while the s econd mo di e s complex ass em
time s while PMS was invoke d time s Initially the
blie s We di scuss each in tur n
PMS collector was invoke d every s even up date pass e s
then every s ix up date pass e s and by the end of the
Structure Mo di cations
up date pass e s every ve up date pass e s By the end of
The workload in thi s exp er iment cons i ste d of re
the up date pass e s there were byte s of uncol
p eate dly ins erting ve ob ject comp os ite s and attaching
lecte d garbage for PMS
each comp os ite to a di stinct bas e ass embly ob ject and
then pruning the newly create d reference s to the same
Overhe ad of a Garbage Collection Pas s
ve ob ject comp os ite s we call thi s whole s et of in
s erts and delete s an up date pass Thi s corre sp onds
The table b elow give s the average I O overhead and
to the structure mo di cation op erations of the OO
the amount of logs generate d by TCRC and PMS for
b enchmark Thi s workload repre s ents the cas e when
an invo cation of the collector To get the total cost the
an application create s a numb er of temp orary ob jects
gure s have to b e multiplie d by the numb er of invo ca
dur ing execution and di sp os e s them at the end of the
tions which i s for PMS and for TCRC
execution The re sults pre s ente d are over up date
pass e s intersp ers e d with garbage collection garbage
Metr ic TCRC PMS
collection i s invoke d when the databas e s ize cross e s
Logs MB
MB recall the steady state databas e s ize i s MB
I O Read Wr ite
We rst pre s ent the cumulative overheads cost dur
ing dur ing normal pro ce ss ing as well as the overhead
Since garbage collection was invoke d r ight after the
due to the garbage collection thread for thi s workload
ins ertions TCRC found all the ob jects that it had to
travers e in the cache and incurre d no reads PMS
Metr ic TCRC PMS
nee de d to make a reachability scan f rom the ro ot and
Logs MB
therefore had to vi s it all of the ob jects in the
I O Read Wr ite
datas et Thi s accounts for the exce ss ive reads incurre d
by PMS The logs generate d by TCRC i s however big
Although the amount of logs generate d by the ger than PMS s ince i the s ize of an ob ject i s bigger
TCRC algor ithm i s more than that of the PMS al due to the pre s ence of reference counts and therefore
gor ithm the overall I O p erformance including the the logs corre sp onding to the deletion of garbage ob
I O s for logs of TCRC i s ab out b etter than jects are larger and ii the garbage ob jects are delete d
f rom WRT and the s e deletions have to b e logge d re of ob jects TCRC had to travers e In thi s exp er iment
call that all newly create d ob jects will b e in WRT s ince we rep ort only on the overheads of the garbage collec
all new p ointers are weak tion pass The normal pro ce ss ing overheads are very
s imilar to the previous exp er iment s ince we are creat
ing some numb er of ob jects and pruning reference s to
Normal Pro ce s s ing Overhe ads
others like the previous exp er iment The cost of the
The following table shows the amount of I O p erforme d
garbage collection phas e for TCRC i s tabulate d b elow
and the amount of logs generate d dur ing normal pro
ce ss ing when the collector i s not running over the
Metr ic Level of Ro ot of Subtree
cours e of the up date pass e s
Logs MB
Metr ic TCRC PMS
I O Read
Logs MB
I O Wr ite
I O Read Wr ite
The cost of the garbage collection phas e for PMS i s
The algor ithms have to maintain the p ers i stent data
tabulate d b elow
structure s cons i stent with the data dur ing normal pro
ce ss ing In the cas e of PMS the only p ers i stent data
Metr ic Level of Ro ot of Subtree
structure i s the IRL which i s up date d quite rarely On
the other hand in the cas e of TCRC the reference
Logs MB
counts as well as the WRT may b e up date d The
I O Read
amounts of log generate d show the additional logging
I O Wr ite
that has to b e p erforme d by TCRC for maintaining
the s e p ers i stent structure s The additional logs ac
The re sults show that numb er of reads by TCRC i s
count for ab out extra wr ite s for TCRC The re st
smaller than the numb er of reads by PMS for mo di ca
of the extra wr ite s p erforme d by TCRC ab out
tions at the lower levels but degrade s for mo di cations
are due to wr iting parts of WRT back as a re sult of
higher up the hierarchy Thi s i s exp ecte d s ince TCRC
normal cache replacement The amount of reads p er
p erforms a lo cal traversal The numb er of reads for
forme d by TCRC i s s igni cantly smaller that PMS b e
PMS i s the same for mo di cations at all levels No
caus e the cache i s not di sturb e d much by the garbage
tice however that even though PMS travers e s the en
collection thread in the cas e of TCRC In the cas e of
tire graph the cost of TCRC i s s igni cantly higher
PMS at the end of the collection pass the cache could
than PMS for mo di cations higher up the hierarchy
contain many ob jects f rom the ass embly tree which are
There are two reasons for thi s The rst i s that TCRC
not require d dur ing normal pro ce ss ing
reads all ob jects as it encounters the ir reference s dur
ing the traversals unlike PMS which follows only intra
Up dating Complex As s emblies
partition reference s Thi s re sults in exce ss ive read
overhead s ince there i s a lot of cache con icts for ob
In thi s s et of exp er iments we up date d the ass embly
jects on di erent page s Secondly the RRT i s di sk re s
hierarchy tree by replacing a subtree ro ote d at a com
ident and as its s ize grows there i s extra I O overhead
plex ass embly by a di erent one The lowe st level bas e
for acce ss ing RRT In contrast our implementation of
ass emblie s in the new hierarchy tree p ointe d to the
PMS assume s information ab out which ob jects in a
same comp os ite ob jects In thi s exp er iment we mo di
partition have b een marke d dur ing the mark phas e can
e d the OO b enchmark by removing the back p ointers
b e maintaine d in memory its elf
to the bas e ass embly ob jects f rom the comp os ite ob
jects Thi s provide s acyclic data which enable s us to
The amount of logs generate d by TCRC a for
te st our schema graph optimization It also limits the
the amount of logs generate d indicate s that the amount
of logs generate d i s le ss than KB grows in compar traversal of TCRC
i son to the logs generate d by PMS as the level numb er We var ie d the level of the ro ot of the the subtree
grows s ince GreenTravers e up date s p ointer strengths that we were replacing The level was var ie d f rom two
th
of ob jects which are also logge d The more the ob to s ix level n corre sp onds to the level which i s the n
jects travers e d the more the numb er of p ointers whos e level upwards f rom the bas e ass emblie s Notice that
strengths get change d In f act most of the informa the subtree that was replace d i s garbage after thi s up
tion in the logs generate d by the TCRC i s very small date After such a up date we invoke d the garbage col
e ither a p ointer strength up date an up date to WRT lector The higher the level of the ro ot of the subtree
or an up date to the reference count However each b e ing replace d the more the numb er of ob ject com
of the s e logs has a s igni cant log header overhead in p os ite s reachable and therefore the more the numb er
the Brahm a system In a system which can club all Acknowle dgments
the s e logs under a s ingle log header along with the log
We thank Je Naughton and Jie bing Yu for giving
for the actual p ointer up date the overheads will come
us a vers ion of the ir garbage collection co de which
down drastically We are currently mo difying the log
provide d us ins ight into garbage collection implement
subsystem in Brahm a to do thi s
ation We also thank Sandhya Jain for br inging the
The TCRC algor ithm can b e optimize d by us ing s e
work by Brownbr idge to our notice
mantics available f rom the schema graph Notice that
the template for the p ointer f rom a complex ass embly
Reference s
to a bas e ass embly i s acyclic and therefore nee d not
AFG L Amsaleg M Franklin and O Grub er Ef
b e travers e d by the Re dTravers e algor ithm thus pre
cient Incremental Garbage Collection for Client
venting TCRC f rom unnece ssar ily travers ing the ob
Server Ob ject Databas e Systems In Procs of the In
ject comp os ite s The cost of the TCRC garbage collec
ternational Conf on Very Large Databases Septem
tion pass when the exp er iment was rep eate d with thi s
b er
schema bas e d optimization are tabulate d b elow It can
+
ARS S Ashwin Prasan Roy S Se shadr i Avi Silb er
b e s een that TCRC with the optimization outp erforms
schatz and S Sudarshan Garbage Collection in Ob
the bas ic TCRC as well as the PMS algor ithm
ject Or iente d Databas e s Us ing Transactional Cyclic
Reference Counting Technical rep ort Indian Insti
Metr ic Level of Ro ot of Subtree
tute of Technology Mumbai India June
Bro D R Brownbr idge Recursive Structures in Com
Logs MB
puter Systems PhD the s i s Univers ity of Newcastle
I O Read
up on Tyne Unite d Kingdom Septemb er
I O Wr ite
Bro D R Brownbr idge Cyclic Reference Counting for
Combinator Machine s In Jean Pierre Jouannaud
Conclus ions and Future Work
e ditor ACM Conf on Functional Programming Lan
guages and Computer Architecture page s
We have pre s ente d a garbage collection algor ithm
Spr inger Verlag
calle d TCRC bas e d on cyclic reference counting and
CDN M Carey D DeWitt and J Naughton The
prove d it correct in the f ace of concurrent up date s and
OO Benchmark In Proc of the ACM SIGMOD
system f ailure s We have implemente d and te ste d the
Int Conf Washington D C May
algor ithm
CWZ J Co ok A Wolf and B Zor n Partition Selec
Our p erformance re sults indicate that TCRC can
tion Policie s in Ob ject Databas e Garbage Collection
b e much cheap er at least in certain cas e s than par
In Procs of the ACM SIGMOD Conf on Manage
titione d mark and sweep s ince it can concentrate on
ment of Data page s May
lo cal cycle s of garbage We b elieve our algor ithm will
JL Richard E Jone s and Raf ael D Lins Cyclic
lay the foundation for cyclic reference counting in data
we ighte d reference counting Technical rep ort
bas e systems
Univers ity of Kent Canterbury Unite d Kingdom
We plan to explore s everal optimizations of the
Decemb er
TCRC algor ithm in the future For instance we
Lin Raf ael D Lins Cyclic reference counting with lazy
have obs erve d that just after creation of the datas ets
mark scan Technical rep ort Univers ity of Kent
garbage collection has to p erform extra work to convert
Canterbury Unite d Kingdom June
weak p ointers into strong p ointers However once the
MWL A D Martinez R Wachenchauzer and Ra
convers ion has b een p erforme d a go o d s et of strong
f ael D Lins Cyclic reference counting with lo cal
p ointers i s e stabli she d and the further cost of garbage
mark scan Information Processing Letters
collection i s quite low It would b e intere sting to de
velop bulk loading technique s for re ducing the cost of
PvEP E J H Pep els M C J D van Eekelen and M J
s etting up p ointer strengths
Plasme ijer A cyclic reference counting algor ithm and
We plan to optimize Re dTravers e by only following
its pro of Inter nal Rep ort Univers ity of Nijme
a strong p ointer into an ob ject if all other strong p oint
gen Nijmegen
ers into that ob ject have b een already encountere d
YNY V Yong J Naughton and J Yu Storage Re
Thi s will greatly re duce the numb er of ob jects tra
clamation and Reorganization in Client Server Per
vers e d and may lead to s igni cant p erformance b e
s i stent Ob ject Store s In Proc of the Data Engineer
ne ts Finally another intere sting extens ion of the
ing Int Conf page s February
TCRC algor ithm would b e to develop a partitione d
TCRC algor ithm in which dur ing a lo cal mark and
sweep only intra partition e dge s are travers e d