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  • 1. Data Integration, Concluded Physical Data Storage Zachary G. Ives University of Pennsylvania CIS 550 – Database & Information Systems June 21, 2010
  • 2. 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”
  • 3. 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
  • 4. 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 = “DB2 UDB”
          • 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!
  • 5. 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
  • 6. Inverse Rules
    • Reverse the implication in each rule:
          • author(a, i 1 (a,t) , _) :- s1(a,t)
          • book( i 1 (a,t) , t, p 1 (a,t) ) :- s1(a,t), t = “DB2 UDB”
          • author(a, i 5 (a,t,p) , _) :- s5(a, t, p)
          • book( i 5 (a,t,p) , t) :- s5(a, t, p), p = “SAMS”
    • Then unfold:
        • q(a, t) :- author(a, i, _), book(i, t, p), t = “DB2 UDB”
        • q(a, t) :- s1(a, x), i = i 1 (a,x), s1(a,t), t=“DB2 UDB”, i = i 1 (a,t), p=p 1 (a,t), t=“DB2 UDB”
        • q(a, t) :- author(a, i, _), book(i, t, p), t = “DB2 UDB”
        • q(a, t) :- s5(a, x, y), i = i 1 (a,x,y), s5(a,t,p), i = i 1 (a,t,p), p=“SAMS”, t=“DB2 UDB”
  • 7. 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: Oracle Fusion, IBM’s WebSphere Information Integrator, numerous packages from middleware companies; MS BizTalk Mapper, IBM Rational Data Architect
  • 8. 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
  • 9. 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…
  • 10. 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 t2 t3
  • 11. 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
  • 12. 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!
  • 13. Approximate Cost of Operations
    • Several assumptions underlie these (rough) estimates!
    * * No overflow buckets, 80% page occupancy Heap File Sorted File Hashed File Scan all recs p(T) D p(T) D 1.25 p(T) D Equality Search p(T) D / 2 D log 2 p(T) D Range Search p(T) D D log 2 p(T) + (# pages with matches) 1.25 p(T) D Insert 2D Search + p(T) D 2D Delete Search + D Search + p(T) D 2D
  • 14. Speeding Operations over Data
    • Recall that we’re interested in how to get good performance in answering queries
    • The first consideration is how the data is made accessible to the DBMS
      • We saw different arrangements of the tables: Heap (unsorted) files, sorted files, and hashed files
    • Today we look further at 3 core concepts that are used to efficiently support sort- and hash-based access to data:
      • Indexing
      • Sorting
      • Hashing
  • 15. 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 .
    • Generally the entries of an index are some form of node in a tree – but should the index contain the data, or pointers to the data?
  • 16. Alternatives for Data Entry k* in Index
    • Three alternatives for where to put the data:
      • Data record wherever key value k appears
        • Clustered  fast lookup
        • Index is large; only 1 can exist
      • < k , rid of data record with search key value k > , OR
      • < k , list of rids of data records with search key k >
        • 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
    rid = row id, conceptually a pointer
  • 17. Classes of Indices
    • Primary vs. secondary : primary has the primary key
      • Most DBMSs automatically generate a primary index when you define a primary key
    • Clustered vs. unclustered : order of records and index are approximately the 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 [Why?]
      • Every sparse index is clustered!
      • Sparse indexes are smaller; however, some useful optimizations are based on dense indexes
  • 18. Clustered vs. Unclustered Index
    • Suppose Index Alternative (2) used, with pointers to records stored in a heap file
      • Perhaps initially sort data file, leave some gaps
      • Inserts may require overflow pages
    • Consider how these strategies affect disk caching and access
    Index entries Data entries direct search for (Index File) (Data file) Data Records data entries Data entries Data Records CLUSTERED UNCLUSTERED
  • 19. 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 <= 2 d entries. d is called the order of the tree.
    • Supports equality and range searches efficiently.
    Index Entries Data Entries (&quot;Sequence set&quot;) (Direct search)
  • 20. 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
  • 21. 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 of tree in buffer pool:
      • Level 1 = 1 page = 8 KB
      • Level 2 = 133 pages = 1 MB
      • Level 3 = 17,689 pages = 133 MB
      • Level 4 = 2,352,637 pages = 18 GB
      • “ Nearly O(1)” access time to data – for equality or range queries!
  • 22. 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 .
  • 23. 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*
  • 24. 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 24 30 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.)
  • 25. 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.
  • 26. 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