1. Data Integration and Physical Storage Zachary G. Ives University of Pennsylvania CIS 550 – Database & Information Systems November 15, 2005

2. 2 Mappings between Schemas LSD provides attribute correspondences, but not complete mappings Mappings generally are posed as views: define relations in one schema (typically either the mediated schema or the source schema), given data in the other schema  This allows us to “restructure” or “recompose + decompose” our data in a new way We can also define mappings between values in a view  We use an intermediate table defining correspondences – a “concordance table”  It can be filled in using some type of code, and corrected by hand

3. 3 A Few Mapping Examples  Movie(Title, Year, Director, Editor, Star1, Star2)  PieceOfArt(ID, Artist, Subject, Title, TypeOfArt)  MotionPicture(ID, Title, Year) Participant(ID, Name, Role) CustIDCustName 1234Smith, J. PennIDEmpName 46732John Smith PieceOfArt(I, A, S, T, “Movie”) :- Movie(T, Y, A, _, S1, S2), ID = T || Y, S = S1 || S2 Movie(T, Y, D, E, S1, S2) :- MotionPicture(I, T, Y), Participant(I, D, “Dir”), Participant(I, E, “Editor”), Participant(I, S1, “Star1”), Participant(I, S2, “Star2”) T1 T2 Need a concordance table from CustIDs to PennIDs

4. 4 Two Important Approaches  TSIMMIS [Garcia-Molina+97] – Stanford  Focus: semistructured data (OEM), OQL-based language (Lorel)  Creates a mediated schema as a view over the sources  Spawned a UCSD project called MIX, which led to a company now owned by BEA Systems  Other important systems of this vein: Kleisli/K2 @ Penn  Information Manifold [Levy+96] – AT&T Research  Focus: local-as-view mappings, relational model  Sources defined as views over mediated schema  Requires a special  Led to peer-to-peer integration approaches (Piazza, etc.)  Focus: Web-based queriable sources

5. 5 TSIMMIS  One of the first systems to support semi-structured data, which predated XML by several years: “OEM”  An instance of a “global-as-view” mediation system  We define our global schema as views over the sources

6. 6 XML vs. Object Exchange Model Bernstein Newcomer Principles of TP Chamberlin DB2 UDB O1: book { O2: author { Bernstein } O3: author { Newcomer } O4: title { Principles of TP } } O5: book { O6: author { Chamberlin } O7: title { DB2 UDB } }

7. 7 Queries in TSIMMIS Specified in OQL-style language called Lorel  OQL was an object-oriented query language that looks like SQL  Lorel is, in many ways, a predecessor to XQuery Based on path expressions over OEM structures: select book where book.title = “DB2 UDB” and book.author = “Chamberlin” This is basically like XQuery, which we’ll use in place of Lorel and the MSL template language. Previous query restated = for $b in AllData()/book where $b/title/text() = “DB2 UDB” and $b/author/text() = “Chamberlin” return $b

8. 8 Query Answering in TSIMMIS Basically, it’s view unfolding, i.e., composing a query with a view  The query is the one being asked  The views are the MSL templates for the wrappers  Some of the views may actually require parameters, e.g., an author name, before they’ll return answers  Common for web forms (see Amazon, Google, …)  XQuery functions (XQuery’s version of views) support parameters as well, so we’ll see these in action

9. 9 A Wrapper Definition in MSL Wrappers have templates and binding patterns ($X) in MSL: B :- B: }> // $$ = “select * from book where author=“ $X //  This reformats a SQL query over Book(author, year, title) In XQuery, this might look like: define function GetBook($x AS xsd:string) as book { for $b in sql(“Amazon.DB”, “select * from book where author=‘” + $x +”’”) return {$b/title} $x } book title author … … … The union of GetBook’s results is unioned with others to form the view Mediator()

10. 10 How to Answer the Query Given our query: for $b in Mediator()/book where $b/title/text() = “DB2 UDB” and $b/author/text() = “Chamberlin” return $b Find all wrapper definitions that:  Contain output enough “structure” to match the conditions of the query  Or have already tested the conditions for us!

11. 11 Query Composition with Views We find all views that define book with author and title, and we compose the query with each: define function GetBook($x AS xsd:string) as book { for $b in sql(“Amazon.DB”, “select * from book where author=‘” + $x + “’”) return {$b/title} {$x} } for $b in Mediator()/book where $b/title/text() = “DB2 UDB” and $b/author/text() = “Chamberlin” return $b book title author … …

12. 12 Matching View Output to Our Query’s Conditions  Determine that $b/book/author/text()  $x by matching the pattern on the function’s output: define function GetBook($x AS xsd:string) as book { for $b in sql(“Amazon.DB”, “select * from book where author=‘” + $x + “’”) return { $b/title } {$x} } let $x := “Chamberlin” for $b in GetBook($x)/book where $b/title/text() = “DB2 UDB” return $b book title author … …

13. 13 The Final Step: Unfolding let $x := “Chamberlin” for $b in ( for $b’ in sql(“Amazon.com”, “select * from book where author=‘” + $x + “’”) return { $b/title } {$x} )/book where $b/title/text() = “DB2 UDB” return $b  How do we simplify further to get to here? for $b in sql(“Amazon.com”, “select * from book where author=‘Chamberlin’”) where $b/title/text() = “DB2 UDB” return $b

14. 14 Virtues of TSIMMIS  Early adopter of semistructured data, greatly predating XML  Can support data from many different kinds of sources  Obviously, doesn’t fully solve heterogeneity problem  Presents a mediated schema that is the union of multiple views  Query answering based on view unfolding  Easily composed in a hierarchy of mediators

15. 15 Limitations of TSIMMIS’ Approach Some data sources may contain data with certain ranges or properties  “Books by Aho”, “Students at UPenn”, …  If we ask a query for students at Columbia, don’t want to bother querying students at Penn…  How do we express these? Mediated schema is basically the union of the various MSL templates – as they change, so may the mediated schema

16. 16 An Alternate Approach: The Information Manifold (Levy et al.) When you integrate something, you have some conceptual model of the integrated domain  Define that as a basic frame of reference, everything else as a view over it  “Local as View” May have overlapping/incomplete sources  Define each source as the subset of a query over the mediated schema  We can use selection or join predicates to specify that a source contains a range of values: ComputerBooks(…)  Books(Title, …, Subj), Subj = “Computers”

17. 17 The Local-as-View Model The basic model is the following:  “Local” sources are views over the mediated schema  Sources have the data – mediated schema is virtual  Sources may not have all the data from the domain – “open-world assumption” The system must use the sources (views) to answer queries over the mediated schema

18. 18 Query Answering Assumption: conjunctive queries, set semantics Suppose we have a mediated schema: author(aID, isbn, year), book(isbn, title, publisher) Suppose we have the query: q(a, t) :- author(a, i, _), book(i, t, p), t = “DB2 UDB” and sources: s1(a,t)  author(a, i, _), book(i, t, p), t = “123” … s5(a, t, p)  author(a, i, _), book(i,t), p = “SAMS” We want to compose the query with the source mappings – but they’re in the wrong direction!  Yet: everything in s1, s5 is an answer to the query!

19. 19 Answering Queries Using Views Numerous recently-developed algorithms for these  Inverse rules [Duschka et al.]  Bucket algorithm [Levy et al.]  MiniCon [Pottinger & Halevy]  Also related: “chase and backchase” [Popa, Tannen, Deutsch] Requires conjunctive queries

20. 20 Summary of Data Integration Local-as-view integration has replaced global-as-view as the standard  More robust way of defining mediated schemas and sources  Mediated schema is clearly defined, less likely to change  Sources can be more accurately described Methods exist for query reformulation, including inverse rules Integration requires standardization on a single schema  Can be hard to get consensus  Today we have peer-to-peer data integration, e.g., Piazza [Halevy et al.], Orchestra [Ives et al.], Hyperion [Miller et al.] Some other aspects of integration were addressed in related papers  Overlap between sources; coverage of data at sources  Semi-automated creation of mappings and wrappers Data integration capabilities in commercial products: BEA’s Liquid Data, IBM’s DB2 Information Integrator, numerous packages from middleware companies

21. 21 Performance: What Governs It?  Speed of the machine – of course!  But also many software-controlled factors that we must understand:  Caching and buffer management  How the data is stored – physical layout, partitioning  Auxiliary structures – indices  Locking and concurrency control (we’ll talk about this later)  Different algorithms for operations – query execution  Different orderings for execution – query optimization  Reuse of materialized views, merging of query subexpressions – answering queries using views; multi-query optimization

22. 22 Our General Emphasis  Goal: cover basic principles that are applied throughout database system design  Use the appropriate strategy in the appropriate place Every (reasonable) algorithm is good somewhere  … And a corollary: database people reinvent a lot of things and add minor tweaks…

23. 23 What’s the “Base” in “Database”?  Could just be a file with random access  What are the advantages and disadvantages?  DBs generally require “raw” disk access  Need to know when a page is actually written to disk, vs. queued by the OS  Predictable performance, less fragmentation  May want to exploit striping or contiguous regions  Typically divided into “extents” and pages

24. 24 Buffer Management  Could keep DB in RAM  “Main-memory DBs” like TimesTen  But many DBs are still too big; we read & replace pages  May need to force to disk or pin in buffer  Policies for page replacement, prefetching  LRU, as in Operating Systems (not as good as you might think – why not?)  MRU (one-time sequential scans)  Clock, etc.  DBMIN (min # pages, local policy) Buffer Mgr Tuple Reads/Writes

25. 25 Storing Tuples in Pages Tuples  Many possible layouts  Dynamic vs. fixed lengths  Ptrs, lengths vs. slots  Tuples grow down, directories grow up  Identity and relocation Objects and XML are harder  Horizontal, path, vertical partitioning  Generally no algorithmic way of deciding Generally want to leave some space for insertions t1 t2t3

26. Alternatives for Organizing Files Many alternatives, each ideal for some situation, and poor for others:  Heap files: for full file scans or frequent updates  Data unordered  Write new data at end  Sorted Files: if retrieved in sort order or want range  Need external sort or an index to keep sorted  Hashed Files: if selection on equality  Collection of buckets with primary & overflow pages  Hashing function over search key attributes

27. Model for Analyzing Access Costs We ignore CPU costs, for simplicity:  p(T): The number of data pages in table T  r(T): Number of records in table T  D: (Average) time to read or write disk page  Measuring number of page I/O’s ignores gains of pre- fetching blocks of pages; thus, I/O cost is only approximated.  Average-case analysis; based on several simplistic assumptions.  Good enough to show the overall trends!

28. Assumptions in Our Analysis  Single record insert and delete  Heap files:  Equality selection on key; exactly one match  Insert always at end of file  Sorted files:  Files compacted after deletions  Selections on sort field(s)  Hashed files:  No overflow buckets, 80% page occupancy

29. 29  Several assumptions underlie these (rough) estimates! Heap FileSorted FileHashed File Scan all recsp(T) D 1.25 p(T) D Equality Searchp(T) D / 2D log 2 p(T)D Range Searchp(T) DD log 2 p(T) + (# pages with matches) 1.25 p(T) D Insert2DSearch + p(T) D2D DeleteSearch + DSearch + p(T) D2D Cost of Operations

30. 30 Speeding Operations over Data  Three general data organization techniques:  Indexing  Sorting  Hashing

31. Technique I: Indexing  An index on a file speeds up selections on the search key attributes for the index (trade space for speed).  Any subset of the fields of a relation can be the search key for an index on the relation.  Search key is not the same as key (minimal set of fields that uniquely identify a record in a relation).  An index contains a collection of data entries, and supports efficient retrieval of all data entries k* with a given key value k.

32. Alternatives for Data Entry k* in Index  Three alternatives: 1. Data record with key value k Clustered  fast lookup  Index is large; only 1 can exist 2., OR 3. Can have secondary indices Smaller index may mean faster lookup  Often not clustered  more expensive to use  Choice of alternative for data entries is orthogonal to the indexing technique used to locate data entries with a given key value k.

33. Classes of Indices  Primary vs. secondary: primary has primary key  Clustered vs. unclustered: order of records and index approximately same  Alternative 1 implies clustered, but not vice-versa  A file can be clustered on at most one search key  Dense vs. Sparse: dense has index entry per data value; sparse may “skip” some  Alternative 1 always leads to dense index  Every sparse index is clustered!  Sparse indexes are smaller; however, some useful optimizations are based on dense indexes

34. Clustered vs. Unclustered Index Suppose Index Alternative (2) used, records are stored in Heap file  Perhaps initially sort data file, leave some gaps  Inserts may require overflow pages Index entries Data entries direct search for (Index File) (Data file) Data Records data entries Data entries Data Records CLUSTERED UNCLUSTERED

35. B+ Tree: The DB World’s Favorite Index  Insert/delete at log F N cost  (F = fanout, N = # leaf pages)  Keep tree height-balanced  Minimum 50% occupancy (except for root).  Each node contains d <= m <= 2d entries. d is called the order of the tree.  Supports equality and range searches efficiently. Index Entries Data Entries ("Sequence set") (Direct search)

36. Example B+ Tree  Search begins at root, and key comparisons direct it to a leaf.  Search for 5*, 15*, all data entries >= 24*...  Based on the search for 15*, we know it is not in the tree! Root 17 24 30 2* 3*5* 7*14*16* 19*20* 22*24*27* 29*33*34* 38* 39* 13

37. B+ Trees in Practice  Typical order: 100. Typical fill-factor: 67%.  average fanout = 133  Typical capacities:  Height 4: 1334 = 312,900,700 records  Height 3: 1333 = 2,352,637 records  Can often hold top levels in buffer pool:  Level 1 = 1 page = 8 Kbytes  Level 2 = 133 pages = 1 Mbyte  Level 3 = 17,689 pages = 133 MBytes

38. Inserting Data into a B+ Tree  Find correct leaf L.  Put data entry onto L.  If L has enough space, done!  Else, must split L (into L and a new node L2)  Redistribute entries evenly, copy up middle key.  Insert index entry pointing to L2 into parent of L.  This can happen recursively  To split index node, redistribute entries evenly, but push up middle key. (Contrast with leaf splits.)  Splits “grow” tree; root split increases height.  Tree growth: gets wider or one level taller at top.

39. Inserting 8* into Example B+ Tree  Observe how minimum occupancy is guaranteed in both leaf and index pg splits.  Recall that all data items are in leaves, and partition values for keys are in intermediate nodes Note difference between copy-up and push-up.

40. 40 Inserting 8* Example: Copy up Root 17 24 30 2* 3*5* 7*14*16* 19*20* 22*24*27* 29*33*34* 38* 39* 13 Want to insert here; no room, so split & copy up: 2* 3* 5* 7* 8* 5 Entry to be inserted in parent node. (Note that 5 is copied up and continues to appear in the leaf.) 8*

41. 41 Inserting 8* Example: Push up Root 17 24 30 2* 3* 14*16* 19*20* 22*24*27* 29*33*34* 38* 39* 13 5* 7* 8* 5 Need to split node & push up 5 2430 17 13 Entry to be inserted in parent node. (Note that 17 is pushed up and only appears once in the index. Contrast this with a leaf split.)

42. Deleting Data from a B+ Tree  Start at root, find leaf L where entry belongs.  Remove the entry.  If L is at least half-full, done!  If L has only d-1 entries,  Try to re-distribute, borrowing from sibling (adjacent node with same parent as L).  If re-distribution fails, merge L and sibling.  If merge occurred, must delete entry (pointing to L or sibling) from parent of L.  Merge could propagate to root, decreasing height.

43. B+ Tree Summary B+ tree and other indices ideal for range searches, good for equality searches.  Inserts/deletes leave tree height-balanced; log F N cost.  High fanout (F) means depth rarely more than 3 or 4.  Almost always better than maintaining a sorted file.  Typically, 67% occupancy on average.  Note: Order (d) concept replaced by physical space criterion in practice (“at least half-full”).  Records may be variable sized  Index pages typically hold more entries than leaves

44. 44 Other Kinds of Indices  Multidimensional indices  R-trees, kD-trees, …  Text indices  Inverted indices  Structural indices  Object indices: access support relations, path indices  XML and graph indices: dataguides, 1-indices, d(k) indices  Describe parent-child, path relationships