Combining Associative and Navigational Access in Persistent Object Stores

Transcription

1 Combiig Associative ad Navigatioal Access i Persistet Object Stores Markus Kirchberg, Weea Nusdi, Alexei Tretiakov Iformatio Sciece Research Cetre, Departmet of Iformatio Systems, Massey Uiversity, Private Bag 222, Palmersto North 530, New Zealad {m.kirchberg,a.tretiakov}@massey.ac.z Abstract. We itroduce a approach allowig to support queries ivolvig both avigatio alog refereces (i.e. avigatioal access) ad impositio of coditios o object data (i.e. associative access) i Persistet Object Stores (POS). Our approach does ot directly rely o the kowledge of the database schema ad of the queries to be supported, ad thus ca be used to support ad-hoc queryig of semistructured data. The basic access structures it uses (i.e. selector metaobjects represetig sets of values coected via refereces to database objects ad refereces) are stable with respect to chages i database data i a sese that chages i the value of oe object do ot ecessitate chages of the elemets of the support structure facilitatig access to other objects. I additio, we propose a extesio of the matrix idex approach to support avigatioal access such that mai memory space usage is decreased. Also, we demostrate how matrix idex codig ca be ehaced further to support the combied avigatioal ad associative access by providig guaratees for ecoded object sequeces by referecig selector metaobjects.. Itroductio The area of providig access to stored data is oe of the importat research topics of database systems. It relates to several fuctios of a database maagemet system (DBMS) such as query laguages (QLs) ad secodary storage maagemet. [] defies that a QL is, 'a otatio for expressig queries, coupled with a mechaism for assigig meaig to the expressio'. I other words, a QL eables users to pose questios about data i a database. For object-orieted data models (OODMs) there have bee a umber of query laguages proposed, icludig algebraic, calculus, logic programmig orieted ad SQL-like approaches []. I relatio to the secodary storage maagemet of a object-orieted database system (OODBS), which affects the efficiecy of retrieval of requested data from a database, there are several issues cocered. Such issues iclude the eed to build auxiliary data structures (i.e. idices) that speed up the search for requested data. Efficiet data access approaches reduce the umber of I/O operatios eeded ad the time spet durig the search for requested data i secodary (or tertiary) storage devices. The criteria used to evaluate the performace of idices are for example the cost to search for requested data usig idices ad the storage size required to store idices [3, 8, 0, 23]. The cost performace of idices ca be estimated i terms of the umber of I/O operatios required to perform idex-based data lookup. I particular, if

2 the size of idices is small eough for them to fit ito the mai memory, the lookup time is dramatically improved. Therefore, miimizig the idex size is of prime importace. As commoly agreed, queries i a OODBS are supported by three types of data access icludig direct, avigatioal ad associative access [8, 9, 0, 23]: Direct access is retrieval of a set of objects via their explicitly give object idetifiers (OIDs). Navigatioal access is retrieval of a set of OIDs based o avigatio alog refereces betwee objects begiig from ay give object. Associative access is retrieval of a set of OIDs that meet coditios specified o object values. Associative access i a OODBS ofte icludes avigatioal access to refereced or referecig objects of the object beig accessed [8]. It was foud that the existig approaches proposed for associative access are tied to specific paths i the objectorieted schema, ad do ot perform well i case of ad-hoc queries or semi-structured or close to semi-structured data [5]. Our research addresses these problems. I this paper, we study how associative access ca be supported i a persistet object store (POS) regardless of paths or iheritace hierarchies ivolved with a query. We propose extesios to a model of a POS such that approaches that are proposed for avigatioal access ca be used to support associative access i the exteded POS. The extesios iclude:. clusterig storage objects i a POS o their classes or values of attributes; 2. clusterig refereces i a POS o classes or values of attributes of objects they coect; 3. providig guaratees for groups of refereces, ad for objects they coect. The rest of the article is orgaized as follows. Sectio 2 discusses the related work o idexig OODBMS ad XML data. Sectios 3 ad 4 itroduce a geeric POSlevel data model ad the query laguage used i this paper. Sectios 5 ad 6 describe a approach to miimize access to permaet storage via clusterig objects ad refereces by usig selector metaobjects. Sectio 7 exteds the matrix-idex codig approach to POS avigatio, ad demostrates how the exteded approach ca be used to provide guaratees for groups of objects ad refereces that ca be used i query optimizatio. Sectio 8 discusses further optimizatios achieved by replacig refereces to metaobjects by flags. Fially, sectios 9 ad 0 discuss a proof of cocept implemetatio, ad list coclusios. 2. Related Work There has bee a umber of data access approaches proposed for OODBSs. For direct access - that is the simplest type of data access - [23] suggests that it may be implemeted by associative access approaches used i RDBSs such as B-tree or hashig idices. This is because the direct access ca be compared with associative access to data records i a RDBS via search key values.

3 Examples of the approaches that have bee proposed to support avigatioal access i a OODBS are avigatio idex [23], rig ad spider data structures [8], object skeletos [5], joi idex hierarchies [4, 22], triple-ode hierarchies [2], ad Matrix-Idex Codig (MIC) [0]. The joi idex hierarchies ad triple-ode hierarchies are modificatios of joi idices used i a RDBS. Object skeletos maitai etworks of object IDs as structures to support avigatio amog objects. I the rig ad spider data structures, a object stores referece poiters that idicate refereced or referecig objects of the object. The avigatio idex ad MIC employ i-memory calculatio techiques by appedig codes with IDs of objects. The code of a object ca be expaded to a set of object IDs of refereced or referecig objects of the object. Amog the approaches proposed to support avigatioal access, MIC employs relatively simple ad efficiet cocepts compared with others. The MIC works like joi idices but allows to retrieve a sequece of object IDs, rather tha a sigle object ID i sigle idex access by applyig a ecodig techique based o simple cotiuous fractios [0]. [9] suggests that the origial cocept of the avigatio idex ad MIC ca be geeralized by makig the avigatio idex ad MIC idepedet from a codig techique used, i.e. ay appropriate codig techique ca be selected to guaratee optimal performace i differet circumstaces. Especially, data compressio techiques should be cosidered as alterative codig techiques because they ca reduce the storage size of the avigatio idex ad MIC. The approaches that have bee proposed to support associative access i a OODBS are for example Sigle-Class (SC) ad Class-Hierarchy (CH) idices [8], H- tree [], hierarchy class Chai (hcc) tree [7], Class-Divisio (CD) idex [6], ested, path ad multi idices [3], access support relatios [7], ad Nested-Iherited idex (NIX) [2]. These approaches are modificatios of approaches used i a RDBS such as B+ tree ad joi idices. I these approaches, a class is regarded as a relatio ad a logical object, which is a object defied i a data model, is regarded as a tuple over a relatio. A UID, which is a system-defied uique idetifier for a tuple, is regarded as a OID of a logical object. Ufortuately, these approaches caot perform well whe associative access icludes avigatioal access ivolved with multiple paths over attribute/iheritace hierarchies [5]. Recetly, the related problem of idexig XML documets received a lot of attetio (see e.g. [20, 2, 24, 4, 25] for some recet publicatios, ad [3] for a recet review). Most of the existig approaches to XML idexig take advatage of the tree structure of XML documets, ad support queries relyig o that structure. O the other had, if refereces are cosidered, XML ca also be viewed as a geeral graph, resultig thus i a situatio similar to the oe i OODBSs. [5] is the first publicatio o XML idexig that takes that view; it offers a approach based o idexig all possible paths (to support ad-hoc queries of semi-structured data). The cosequece is that the resultig idex is extremely large. [9] ad [6] improved the approach applied by [5] by restrictig the paths to be idexed, resultig i smaller idices, but made little progress ito aother problem associated with idexig paths: the resultig idex structures are highly ustable with respect to updates of the uderlyig data: a update at a sigle locatio i the data graph may affect how other locatios reachable from it

4 via idexed paths are represeted i the access structure, leadig to the ecessity to rebuild a large part of it. I this article, we offer a approach based o clusterig object IDs, refereces, ad joi idex etries i exteded matrix-idex codig (which we itroduce). The access structures we propose do ot directly rely o the kowledge of the uderlyig schema or queries they are to support, ad thus support ad-hoc queryig of semistructured data while still offerig a possibility of tuig for specific data ad access patters, ad are stable with respect to chages i the data, amely, small data updates ever ecessitate dramatic restructurig of idices. 3. Data Model The POS level data model is defied as follows. Objects are pairs ( OID, value ), where OID is a uique idetifier (which ca appear i o more tha oe such pair), ad value is the object's data, which from the poit of view of POS has o structure. Refereces are ordered pairs of object ID's ( OID, OID 2). Object IDs used i refereces should be valid objects (ad thus, preset as ( OID, value ) pairs). Thus, from the poit of view of POS, the database is structured as a labeled directed graph with objects actig as vertices, values - as labels, ad refereces - as edges. We ote that to simplify treatmet we do ot label refereces, ad assume that ay refereces with attached data are reified to objects. Defied attributes: dom( class) = OODBSchemaClass dom( umber) = Iteger dom( ame) = Strig { } value : :, :57367 class paper umber value :{ :, : } 2 class studet ame Brow value :{ :, : } 3 class studet ame Smith Figure. A istace of the POS data model. Attributes are strigs with associated domais. We require that all of the employed domais have partial or total orders defied o them (if o atural partial order exists for a domai, we will use a partial order i which each elemet ca oly be compared, ad is equal, to itself.) For each value, there is a mappig defied assigig to each attribute from a fiite set of attributes costat values from their respective domais, resultig i a tuple represetig the object's state. For a give value, we will say that the attributes formig the domai of such a mappig are "defied" for the value. For a give value, attributes that are ot defied are referred to as "udefied". For a OID, defied ad udefied attributes are the attributes defied or (respectively)

5 udefied for its value. Attributes represetig a object do ot ecessarily assume a uique set of values: differet objects may result i the same represetig tuple. 4. Query Laguage Approaches to object clusterig itroduced i this article is geeral eough to support a variety of query laguages. To verify its viability, we demostrate its applicatio i case of a simple query laguage based o path expressios. We assume that the service provided by POS is limited to returig subgraphs of the data graph, so we cosider a laguage that does ot create ew objects ad refereces. (Certaily, POS would also offer a iterface allowig to modify data. However, we assume that views of the data graph offered by queries are limited to its subgraphs.) This implies that jois ca be realized via avigatio, amely, objects that may eed to be joied i queries are already coected via refereces. I the query laguage, a select query is comprised of two sequeces: a avigatio sequece ad a filter sequece. The avigatio sequece is a sequece i the form ( O, R,2, O 2, R 2,3, O 3,, Rm, m, O m ), where O i are object avigatio selectors give as expressios i the form attr ( Oi ) sset ( Oi ), where attr ( O i ) is a set of attributes ad sset ( O i ) is a subset of the Cartesia product of these attributes' domais. Ri, i are referece avigatio selectors give as expressios i the form disjoit attr ( Ri, i) attr2 ( Ri, i) sset ( Ri, i), where attr( R i, i) ad attr2( R i, i) are sets of attributes, while sset ( R i, i) is a subset of the Cartesia product of these attributes' domais. A object avigatio selector O i evaluates to true o a give OID if all attr O are defied for the OID, ad the tuple they form oce they are attributes i ( i ) assiged values (o the value for this OID ) is a elemet of ( i ) (, 2) sset O. A referece avigatio selector R i evaluates to true o a give referece OID OID if attributes i attr( R i, i) ad ( 2 i, i) OID ad OID 2, attr R are defied o respectively, ad the tuple formed by cocateatig their values is a member of ( i, i) sset R. A filter sequece should be of the same legth as the avigatio sequece. The sytax for filter sequeces is defied similarly to avigatio sequeces. I the followig, we ofte use the term "selector set" to refer to a set of tuples o some attribute set. A selector set may be ifiite, ad it does ot eed to be defied by explicitly listig all tuples it cotais. Select queries are evaluated as follows. The avigatio sequece is matched to all possible paths i the graph. It matches if all selectors for object IDs ad for refereces coectig them match. For each matched path, the filter sequece is applied, ad objects ad refereces for which selectors i the filter sequece match are icluded i the result of the query. However, for a give match of a path via the avigatio sequece, refereces for which some of the objects they coect are ot

6 icluded after applyig the filter sequece are also ot icluded. We observe that selectors o refereces may be regarded as realizig joi coditios. Let us cosider some examples. Let objects represetig papers be coected by refereces to objects represetig studets erolled. The a query returig studets erolled i paper umber ca be formulated as follows. The avigatio sequece cosists of three selectors. The first selector would select objects belogig to the class paper, with umber (attribute set is { class, umber }, ad selector set is {{ class : paper, umber :57367}}). The secod avigatio selector is a trivial selector evaluatig to true o all refereces. The third avigatio selector would evaluate to true o all objects of class studet. Now, the filter sequece would iclude two selectors that always evaluate to false to get rid of the paper ad the refereces, ad the last selector that always evaluates to true to iclude all studets matched by the avigatio sequece. As a variatio, oe could choose ot to filter aythig out i the filter sequece, with the query returig the paper, the studets, ad the refereces coectig the paper to the studets (which, perhaps, at the layer usig the POS services could be assembled ito a higher level object represetig the paper ad ecapsulatig the refereces to studets as part of the object, ad ito a umber of separate higher level objects represetig the studets.) Fially, if we were to request a umber of papers, with studets erolled, rather tha a sigle paper, the query would effectively realize a kid of a joi, ad the result would be a directed graph with some of the studets possibly shared by more tha oe paper. As a secod example, cosider a database i which objects represet cities, ad refereces represet flights. Cosider the followig query: retur all cities i Russia that ca be visited if oe flies from Lodo to Tokyo with 2 stopovers, such that the time differece betwee ay of the subsequet stops is less tha 6 hours. To formalize this query, oe eeds selectors for avigatio sequece that would evaluate to true o refereces if objects they coect have attribute values for attribute diffgmt (differece from GMT) close eough (coditio that is easy to represet as set membership). I additio, selectors for the filter sequece should esure that oly cities i Russia are retured, with objects correspodig to other cities ad refereces represetig the flight coectios left out. It is easy to exted the select queries to allow ifiite or boud umber of repetitios, as i XML XPath ad i regular expressios. However, as far as object ad referece clusterig is cocered, such extesios do ot itroduce ew issues, so we limit ourselves to the relatively restricted defiitio of select queries give above. For the same reaso, although it is easy to itroduce queries ivolvig set operatios o results of select queries, ad queries ivolvig semi-jois for vertices ot coected via refereces, we omit these details. 5. Selector Sets ad Selector Metaobjects Let us require that sets used i selectors are such that membership ad set iclusio tests are relatively iexpesive. This would be the case if selector sets are hypercubes formed as Cartesia products of itervals [ low, high ], with low ad high costats take from domais of attributes used i the selector (oe iterval for each attribute). We

7 require that low high, which implies that i case of partially ordered domais (such as class hierarchy) low ad high should be comparable. We observe, that a cojuctio of equalities ca be represeted as a selector with a hypercube selector set for which o all attributes high = low. I additio, for a set of attributes with domais (combied) formig a Euclidea space, we may form selector sets by delimitig areas with hyperplaes. Fially, we allow selector sets formed by explicitly eumeratig a small umber of poits, selector sets obtaied as uios of a small umber of selector sets (formed for the same set of attributes), ad selector sets obtaied as Cartesia products of selector sets (formed for disjoit sets of attributes). While object IDs are relatively small, we expect that the value part of a POS object may be rather large. Therefore, we assume that POS object values are stored o permaet storage. Geerally, to retrieve attribute values for a object value (to evaluate query selectors), oe eeds to retrieve the value from permaet storage, which is computatioally very expesive. Therefore, there is a eed to maitai i the mai memory some auxiliary structures that would allow oe to miimize the umber of objects for which the value has to be retrieved. Such auxiliary structures should determie the smallest possible superset of objects that eed to be retrieved from permaet storage (with the ideal auxiliary structure allowig to retrieve oly the objects that eed to be retured by the query). I fact, as it should have bee clear from the itroductio, the focus of this article is o defiig such structures. To defie auxiliary structures, we rely o metaobjects represetig selector sets, which we call selector objects. The value of such a POS object would ecode the defiitio of a selector set. We do ot dwell o how such ecodig could be achieved, as it is quite easy to defie (e.g., for a selector which is a hypercube, oe could store a flag idicatig that this is a hypercube, ad for each attribute store attribute ame ad domai together with high ad low values). Selector objects ca be retrieved by the query compiler, which ca the take advatage of various guaratees provided via refereces to ad from a selector object OID. We observe here, that while POS is uaware of the structure of values for objects ecapsulatig database data, it has to be aware of the structure of selector metaobjects, hece, for POS, selector metaobjects should be distiguishable from objects ecapsulatig database data. 6. Clusterig Objects ad Refereces To facilitate the executio of queries ivolvig evaluatio of selectors, we add refereces betwee objects ad selector metaobjects. We will refer to refereces to a selector metaobject as upstream refereces, ad to refereces from a selector metaobject as dowstream refereces. I this sectio, we assume that refereces are maitaied as joi idices: sequeces of object IDs pairs ( OID, OID 2) sorted by OID, with two joi idices provided: oe for refereces betwee objects ecapsulatig database data, ad aother oe for refereces to ad from metaobjects. I additio, we maitai a joi idex allowig to associate selector metaobjects with refereces as a sequece of object triplets ( OID, OID2, MOID ), where ( OID, OID 2) is the referece, ad MOID is the ID of the associated metaobject. I the followig sectio we will exted our cosideratio to a more geeral access structure based o matrix-idex codig.

8 Let us cosider how selector metaobjects ca be applied to support select queries (see Figure 2). To match the first selector i avigatio sequece, the query compiler would fid a selector metaobject for which the selector set cotais the first selector set i the avigatio sequece of the query, while beig as close to it as possible. For attribute sets formig Euclidea spaces, closeess ca be judged by comparig eclosig volumes. For some attribute domais, closeess ca be difficult or impossible to defie, the, a radom choice ca be made. For the chose metaobject, dowstream refereces are followed, resultig i a superset of object IDs matchig the first selector i avigatio sequece. For all of these objects, upstream refereces are followed to determie if there is a metaobject for the curret object with a selector set cotaied by the selector set from the avigatio sequece of the query, which provides a guaratee that the object ID matches the query selector ad should be retaied for further processig. For the rest of the objects i the superset, values are retrieved from permaet storage, attribute values are matched agaist the selector set from the query, ad oly object IDs actually matchig the selector are retaied for further processig of the query. We ote that if selector metaobject suitable for assemblig the iitial superset were ot available, the query egie would have to retrieve values of all objects i the database, which from performace poit of view is clearly ot acceptable. Figure 2. Matchig a path ivolvig two objects ad a referece by usig selector metaobjects. See the descriptio i the text. The rest of the query is executed by acceptig or rejectig objects ad refereces o paths of the graph accordig to avigatio ad filter sequeces by followig upstream refereces ad verifyig if there is a metaobject cotaiig the selector set (for a referece or for a object) with the selector set cotaied by the selector set from the query. If such a metaobject is available, it provides a guaratee that the referece (or the object) matches the selectio criteria. Otherwise, object values are retrieved ad attribute values are matched agaist the selectors directly. Object values already retrieved may be cached. If a object with a cached value is available, upstream refereces are ot followed, ad determiatio is made based o matchig attribute values agaist the selectors directly. This approach is applied for the rest of the avigatio sequece (apart from the first match), ad for the whole of the filter sequece (which is applied oly if all of the avigatio sequece has matched). The use of selector metaobjects allows miimizig the ecessity to retrieve values from permaet storage. It is the job of the query optimizer to geerate suitable

9 metaobjects for objects ad refereces. Providig a algorithm for achievig it is beyod the scope of this article ad remais a topic for further research. The cost of employig selector metaobjects i terms of mai memory space ca be estimated as ( 2N + 2N + 3N ) sizeof ( OID) () DOREF UOREF URREF where N DOREF is the umber of dowstream refereces to objects, N UOREF is the umber of upstream refereces from objects, ad N URREF is the umber of upstream refereces to metaobjects from refereces betwee database objects. The cost of matchig a avigatio sequece i terms of executio time ca be estimated as ( + ) + ( + ) lpath uom tom lpath urm trm tom + (2) 2 where t om is the time required to access the joi idex that matches database objects to selector metaobjects, t rm is the time required to access the table matchig refereces betwee database objects to selector metaobjects, l path is the legth of the sequece, uom is the umber of upstream refereces from objects i the sequece, ad urm is the umber of upstream refereces from refereces i the sequece. If a object is added, removed or updated, upstream ad dowstream refereces from ad to this object are added or removed as eeded, but (ulike i approaches ivolvig idexig paths) it does ot directly affect how other objects are reflected i the access structure. Also, additio or removal of a referece betwee database objects affects oly upstream refereces to metaobjects from that referece. Hece, the access structure based o usig selector metaobjects is relatively stable with respect to chages i database data. O the other had, to maitai the itegrity of the access structure, it is essetial that selector metaobjects with dowstream refereces are referecig all of the objects they match. Therefore, i case of value updates or object additio, updates to the access structure ca ot be deferred. 7. Exteded Matrix-Idex Codig Approach ad Navigatio Guaratees Matrix-idex codig approach [9, 0] allows to speed up avigatio by replacig the secod object ID i a joi idex ( OID, OID 2) by a compressed sequece of object IDs: ( OID, ecode( OID2, OID3,, OID )). The sequece is formed as follows: for a object with two or more outgoig refereces (the so-called brachig object) the object IDs of referece eds are ecoded i arbitrary order. For a object OID with a sigle outgoig referece, followed (alog this referece) by a umber of similar objects, the sequece of object IDs is ecoded i the order they are ecoutered whe movig from OID to the ext brachig object whose ID is placed as the last ID i the ecoded sequece. To distiguish etries correspodig to brachig objects from etries correspodig to objects with a sigle outgoig referece, a flag is attached to each joi idex etry. Matrix-idex codig allows to retrieve several refereces via a sigle access to the joi idex (refereces are recostructed from the decoded sequece).

10 Here, to beefit from guaratees provided via selector metaobjects, we geeralize the matrix-idex codig techique to make it more flexible. While i its origial defiitio, the matrix-idex approach suggests that ecodig is applied i all cases whe it is applicable (so that a OID appears i the left colum of the resultig joi idex oly oce), we relax this requiremet. For example, i case of OID coected directly to OID 2, OID 3, OID 4 ad OID 5 (case of a brachig object), we would allow the situatio where OID eters the joi idex twice: oce as ( OID, ecode( OID2, OID 3) ), ad aother time - as ( OID, ecode( OID4, OID 5) ). The advatage of such a approach is that the query optimizer ca apply the ecodig as eeded for fastest operatio. For example, for a log sequece of o-brachig object IDs that is ofte avigated through startig from the first object ID, the whole sequece ca be ecoded oly oce ad stored with the object used to retrieve it. There is o eed to ecode partial sequeces may times, with the etire object IDs i the sequece, thus savig sigificat amout of memory space. The cost for such flexibility is that eve if a object ID eters the joi idex oly oce, to retrieve all refereces startig from that object ID two accesses to the joi idex are ecessary (the secod oe to cofirm that there are o further etries). However, as the joi idex is sorted by the object ID by which it is accessed such additioal costs are likely to be very miimal. Aother sigificat beefit of the more flexible approach to matrix-idex codig is the ability to provide avigatio guaratees via selector objects. With each etry of the joi idex we associate a umber of object IDs of selector metaobjects, so that each joi idex etry ow appears as ( OID, ecode ( OID2, OID3,, OID),{ MOID, MOID2,, MOIDm} ) (we expect that would ormally be much greater tha m ). We require that all object IDs uder ecode should match all of the selector metaobjects i the same joi idex etry. (This approach ca be easily exteded to allow providig guaratees for all refereces i a joi idex etry.) Figure 3. Exteded matrix-idex codig: Usig selector metaobjects to provide guaratees for objects ecoded i joi idex etries. As a example, cosider agai a database i which objects represetig papers are coected via refereces to objects represetig studets, with some of the studets ot erolled i ay papers. Cosider a query that would retrieve all female studets erolled i papers (it is easy to see that such a query ca be expressed by usig the query laguage itroduced above). To support queries of this kid, the query optimizer would create two joi idex etries for each paper, oe for male studets, ad aother oe for female studets, ad add object IDs of the appropriate metaobjects to the joi idex etries. The, whe executig the query the system would ot avigate alog the etries for which a guaratee is provided that all of the objects i them are i a wrog category (i our case, male).

11 8. Further Optimizatio by Usig Flags Istead of Refereces To check if a object has a upstream referece to a certai selector metaobject, access to the joi idex coectig objects to metaobjects is required. Further optimizatio ca be achieved by addig oe more level of idirectio: selector metaobject IDs are matched to flags, which are stored with object IDs. We require that sizes of such flags would be smaller or equal to the size of a object ID. (Ideally, flags should be much smaller tha object IDs. It is trivial to itroduce flags equal i size to object IDs, as IDs of metaobjects themselves ca be used as flags.) This way, the availability of a upstream referece to a metaobject ca be verified every time the OID is available without ay further accesses to auxiliary structures. The drawback of such a approach is that for a sigle object participatig i may refereces the OID ca eter the joi idex may times, so that compared to usig upstream refereces the approach usig flags may tur out to be more expesive i terms of mai memory space. However, both approaches could be used simultaeously. The query optimizer could the choose the curretly most efficiet approach based o the umber of refereces, usage patters etc. We ote that flags ca also be used i cojuctio with the joi idex to provide guaratees for refereces ad for joi idex etries (with flags attached to "target" object IDs i joi idex etries, ad to joi idex etries themselves). I case of refereces, redudacy is possible if matrix-idex ecodig is applied (as the, the same referece ca be reflected i the idex may times). O the other had, for simple joi idices each referece eters the idex oly oce, so that the overhead associated with usig flags is miimal. For joi idex etries, usig flags ever leads to redudacy, ad sice i that case flags are replacig metaobject IDs that are larger tha the flags, usig flags is likely to be advatageous i most cases. 9. Proof of Cocept Implemetatio A limited versio of the approach outlied above (ivolvig the use of selector metaobjects for object IDs oly without the selectio of refereces) was implemeted as a C++ program, ad proved to be effective i executig a variety of queries ivolvig both avigatio ad coditios o object attributes without accessig object data. 0. Coclusios We itroduced a approach allowig to support queries ivolvig both avigatio alog refereces (avigatioal access) ad imposig coditios o object data (associative access) at the level of Persistet Object Stores (POS). Our approach does ot directly rely o the kowledge of the database schema ad of the queries to be supported, ad thus ca be used to support ad-hoc queryig of semistructured data. The basic access structures it uses (selector metaobjects represetig sets of values coected via refereces to database objects ad refereces) are stable with respect to chages i database data i a sese that chages i the value of oe object do ot ecessitate chages of the elemets of the support structure facilitatig access to other objects. I additio, we proposed a extesio of the matrix idex approach to avigatioal access allowig to save mai memory space, ad demostrated how matrix idex codig ca be ehaced to support the combied avigatioal ad associative

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