Data Integration, ConcludedPhysical Data Storage

Zachary G. IvesUniversity of Pennsylvania

CIS 550 – Database & Information Systems

April 21, 2023

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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”

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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

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Query Answering

Assumption: conjunctive queries, set semanticsSuppose 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!

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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

Inverse Rules

Reverse the implication in each rule:author(a, i1(a,t), _) :- s1(a,t)book(i1(a,t), t, p1(a,t)) :- s1(a,t), t = “DB2 UDB”…author(a, i5(a,t,p), _) :- s5(a, t, p)book(i5(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 = i1(a,x), s1(a,t), t=“DB2 UDB”, i = i1(a,t),

p=p1(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 = i1(a,x,y), s5(a,t,p), i = i1(a,t,p),

p=“SAMS”, t=“DB2 UDB”

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Summary of Data IntegrationLocal-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 rulesIntegration 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

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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

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Our General Emphasis

Goal: cover basic principles that are applied throughout database system design

Use the appropriate strategy in the appropriate placeEvery (reasonable) algorithm is good somewhere

… And a corollary: database people reinvent a lot of things and add minor tweaks…

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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

t1t2 t3

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

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!

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Several assumptions underlie these (rough) estimates!

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 log2 p(T) D

Range Search

p(T) D D log2 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

Approximate Cost of Operations

*

* No overflow buckets, 80% page occupancy

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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

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?

Alternatives for Data Entry k* in Index

Three alternatives for where to put the data:1. Data record wherever key value k appears

Clustered fast lookup Index is large; only 1 can exist

2. <k, rid of data record with search key value k>, OR

3. <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

Classes of Indices

Primary vs. secondary: primary has the primary key Most DBMSs automatically generate a primary index when

you define a primary keyClustered 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

Clustered vs. Unclustered IndexSuppose 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

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)

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*

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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!

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.

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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*

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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 andcontinues to appear in the leaf.)

8*

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Inserting 8* Example: Push up

Root

17 24 30

2* 3* 14* 16* 19* 20* 22* 24* 27* 29* 33* 34* 38* 39*

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5* 7* 8*

5

Need to split node & push up

5 24 30

17

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Entry to be inserted in parent node.(Note that 17 is pushed up and onlyappears once in the index. Contrastthis with a leaf split.)

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.

B+ Tree Summary

B+ tree and other indices ideal for range searches, good for equality searches. Inserts/deletes leave tree height-balanced; logF 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