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Information Retrieval and Data Mining (AT71.07) Comp. Sc. and Inf. Mgmt. Asian Institute of Technology

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Title: Information Retrieval and Data Mining (AT71.07) Comp. Sc. and Inf. Mgmt. Asian Institute of Technology


1
Information Retrieval and Data Mining
(AT71.07)Comp. Sc. and Inf. Mgmt.Asian
Institute of Technology
  • Instructor Dr. Sumanta Guha
  • Slide Sources Introduction to Information
    Retrieval book slides from Stanford University,
    adapted and supplemented
  • Chapter 4 Index construction

2
  • CS276 Information Retrieval and Web Search
  • Christopher Manning and Prabhakar Raghavan
  • Lecture 4 Index construction

3
Index construction
Ch. 4
  • How do we construct an index?
  • What strategies can we use with limited main
    memory?

4
Hardware basics
Sec. 4.1
  • Many design decisions in information retrieval
    are based on the characteristics of hardware
  • We begin by reviewing hardware basics

5
Hardware basics
Sec. 4.1
  • Access to data in memory is much faster than
    access to data on disk.
  • Disk seeks No data is transferred from disk
    while the disk head is being positioned.
  • Therefore Transferring one large chunk of data
    from disk to memory is faster than transferring
    many small chunks.
  • Disk I/O is block-based Reading and writing of
    entire blocks (as opposed to smaller chunks).
  • Block sizes 8KB to 256 KB.

6
Hardware basics
Sec. 4.1
  • Servers used in IR systems now typically have
    several GB of main memory, sometimes tens of GB.
  • Available disk space is several (23) orders of
    magnitude larger.
  • Fault tolerance is very expensive Its much
    cheaper to use many regular machines rather than
    one fault tolerant machine.

7
Hardware assumptions
Sec. 4.1
  • symbol statistic value
  • s average seek time 5 ms 5 x 10-3 s
  • b transfer time per byte 0.02 µs 2 x 10-8 s
  • processors clock rate 1 ns 10-9
    s
  • transfer time/byte in main 5 ns
    5 x 10-9 s
  • p low-level operation 10 ns 10-8 s
  • (e.g., compare swap a word)
  • size of main memory several GB
  • size of disk space 1 TB or more

8
RCV1 Our collection for this lecture
Sec. 4.2
  • Shakespeares collected works definitely arent
    large enough for demonstrating many of the points
    in this course.
  • The collection well use isnt really large
    enough either, but its publicly available and is
    at least a more plausible example.
  • As an example for applying scalable index
    construction algorithms, we will use the Reuters
    RCV1 collection.
  • This is one year of Reuters newswire (part of
    1995 and 1996)

9
A Reuters RCV1 document
Sec. 4.2
10
Reuters RCV1 statistics
Sec. 4.2
  • symbol statistic value
  • N documents 800,000
  • L avg. tokens per doc 200
  • M terms ( word types) 400,000
  • avg. bytes per token 6
  • (incl. spaces/punct.)
  • avg. bytes per token 4.5
  • (without spaces/punct.)
  • avg. bytes per term 7.5
  • non-positional
    postings 100,000,000

4.5 bytes per word token vs. 7.5 bytes per term
Why? Many tokens of small size, while there is
only 1 term for identical tokens.
11
Recall IIR Ch. 1 index construction
Sec. 4.2
  • Documents are parsed to extract words and these
    are saved with the Document ID.

Doc 1
Doc 2
I did enact Julius Caesar I was killed i' the
Capitol Brutus killed me.
So let it be with Caesar. The noble Brutus hath
told you Caesar was ambitious
12
Key step
Sec. 4.2
  • After all documents have been parsed, the
    inverted file is sorted by terms.

We focus on this sort step. We have 100M items to
sort.
13
Scaling index construction
Sec. 4.2
  • In-memory index construction does not scale.
  • How can we construct an index for very large
    collections?
  • Taking into account the hardware constraints we
    just learned about . . .
  • Memory, disk, speed, etc.

14
Sort-based index construction
Sec. 4.2
  • As we build the index, we parse docs one at a
    time.
  • While building the index, we cannot easily
    exploit compression tricks (you can, but much
    more complex)
  • The final postings for any term are incomplete
    until the end.
  • At 12 bytes per non-positional postings entry
    (termID 4 bytes docID 4 bytes freq 4 bytes),
    demands a lot of space for large collections.
  • Total 100,000,000 in the case of RCV1
  • So we can do this in memory in 2009, but
    typical collections are much larger. E.g. the
    New York Times provides an index of gt150 years of
    newswire
  • Thus We need to store intermediate results on
    disk.

15
Use the same algorithm for disk?
Sec. 4.2
  • Can we use the same index construction algorithm
    for larger collections, but by using disk instead
    of memory?
  • No Sorting T 100,000,000 records on disk is
    too slow too many disk seeks.
  • We need an external sorting algorithm.

16
Bottleneck
Sec. 4.2
  • Parse and build postings entries one doc at a
    time
  • Now sort postings entries by term (then by doc
    within each term)
  • Doing this with random disk seeks would be too
    slow must sort T100M records

If every comparison took 2 disk seeks, and N
items could be sorted with N log2N comparisons,
how long would this take?
17
BSBI Blocked sort-based Indexing (Sorting with
fewer disk seeks)
Sec. 4.2
  • 12-byte (444) records (termID, doc, freq).
  • These are generated as we parse docs.
  • Must now sort 100M such 12-byte records by term.
  • Define a Block 10M such records
  • Can fit comfortably into memory for in-place
    sorting (e.g., quicksort).
  • Will have 10 such blocks to start with.
  • Basic idea of algorithm
  • Accumulate postings for each block, sort, write
    to disk.
  • Then merge the blocks into one long sorted order.

Total 100M records
The term -gt termID mapping ( dictionary) must
already be available built from a first pass.
18
Postings lists to be merged
Merged postings lists
brutus d1, 3 d3, 2 caesar d1, 2 d2, 1 d4,
4 noble d5, 2 with d1, 2 d3, 1 d5, 2
brutus d6, 1 d8, 3 caesar d6, 4 julius d10,
1 killed d6, 4 d7, 3
brutus d1, 3 d3, 2 d6, 1 d8, 3 caesar d1, 2
d2, 1 d4, 4 d6, 4 julius d10, 1 killed d6, 4
d7, 3 noble d5, 2 with d1, 2 d3, 1 d5, 2

disk
19
Sorting 10 blocks of 10M records
Sec. 4.2
  • First, read each block, sort in main, write back
    to disk
  • Quicksort takes 2N ln N expected steps
  • In our case 2 x (10M ln 10M) steps
  • Exercise estimate total time to read each block
    from disk and and quicksort it.
  • 10 times this estimate gives us 10 sorted runs
    of 10M records each on disk. Now, need to merge
    all!
  • Done straightforwardly, merge needs 2 copies of
    data on disk (one for the lists to be merged, one
    for the merged output)
  • But we can optimize this

20
Sec. 4.2
21
How to merge the sorted runs?(Source Wikipedia)
Sec. 4.2
Use a 9-element priority queue repeatedly
deleting its smallest element and adding to it
from the buffer to which the smallest belonged.
  • External mergesort
  • One-pass
  • One example of external sorting is the external
    mergesort algorithm. For example, for sorting 900
    megabytes of data using only 100 megabytes of
    RAM
  • Read 100 MB of the data in main memory and sort
    by some conventional method, like quicksort.
  • Write the sorted data to disk.
  • Repeat steps 1 and 2 until all of the data is in
    sorted 100 MB chunks, which now need to be merged
    into one single output file.
  • Read the first 10 MB of each sorted chunk into
    input buffers in main memory and allocate the
    remaining 10 MB for an output buffer. (In
    practice, it might provide better performance to
    make the output buffer larger and the input
    buffers slightly smaller.)
  • Perform a 9-way merge and store the result in the
    output buffer. If the output buffer is full,
    write it to the final sorted file. If any of the
    9 input buffers gets empty, fill it with the next
    10 MB of its associated 100 MB sorted chunk until
    no more data from the chunk is available.

22
How to merge the sorted runs?(Source Wikipedia)
Sec. 4.2
  • External mergesort
  • Mutliple-passes
  • Previous example shows a one-pass sort.
  • For sorting, say, 50 GB in 100 MB of RAM, a
    one-pass sort wouldn't be efficient the disk
    seeks required to fill the input buffers with
    data from each chunk would take up most of the
    sort time.
  • Multi-pass sorting solves the problem. For
    example, to avoid doing a 500-way merge for the
    preceding example, a program could
  • Run a first pass merging 25 chunks at a time,
    resulting in 500/2520 larger sorted chunks.
  • Run a second pass to merge the 20 larger sorted
    chunks.

23
Remaining problem with sort-based algorithm
Sec. 4.3
  • Our assumption was we can keep the dictionary in
    memory.
  • We need the dictionary (which grows dynamically)
    in order to implement a term to termID mapping.
  • Actually, we could work with term,docID postings
    instead of termID,docID postings . . .
  • . . . but then intermediate files become very
    large. (We would end up with a scalable, but very
    slow index construction method.)

24
SPIMI Single-pass in-memory indexing
Sec. 4.3
  • Key idea 1 Generate separate dictionaries for
    each block no need to maintain term-termID
    mapping across blocks.
  • In other words, sub-dictionaries are generated
    on the fly.
  • Key idea 2 Dont sort. Accumulate postings in
    postings lists as they occur.
  • With these two ideas we can generate a complete
    inverted index for each block.
  • These separate indexes can then be merged into
    one big index.

25
SPIMI-Invert
Sec. 4.3
Dictionary term generated on the fly!
  • Merging of blocks is analogous to BSBI.

26
BSBI vs. SPIMI
Block 2
Block 4
Dictionary
Block 2
Block 1
Inverted Index
Block 1
Block 3
Block 5
Main
Pass 1
Pass 2
Merge
Phase
Disk
BSBI
27
BSBI vs. SPIMI
Sub-dictionary
Block 3
Sub-dictionary
Block 1
Sub-dictionary
Sub-dictionary
Block 1
Block 2
Inverted Index
Sub-dictionary
Main
Block 2
Single Pass
Merge
Phase
Disk
SPIMI
28
SPIMI Compression (From IIR Ch. 5)
Sec. 4.3
  • Compression makes SPIMI even more efficient.
  • Compression of terms
  • Compression of postings
  • Instead of storing successive docIDs, store
    successive offsets, e.g., instead of lt1001, 1010,
    1052, gt store lt1001, 9, 42, gt. This gives rise
    to smaller numbers if the term occurs in many
    docs.
  • Store the offset values as a variable-size prefix
    code so that they can be stored one after another
    in a bit array, without having to reserve a fixed
    bit length (e.g., 32) for each. Examples of such
    codes include the Elias gamma and delta codes.

29
Elias gamma coding
  • Elias gamma code is a prefix code for positive
    integers developed by Peter Elias.
  • To code a number
  • Write it in binary.
  • Subtract 1 from the number of bits written in
    step 1 and prepend that many zeros.
  • An equivalent way to express the same process
  • Separate the integer into the highest power of 2
    it contains (2N) and the remaining N binary
    digits of the integer.
  • Encode N in unary that is, as N zeroes followed
    by a one.
  • Append the remaining N binary digits to this
    representation of N.
  • Examples
  • 1 ?1, 2 ? 010, 3 ?011, 4 ? 00100, 5 ? 00101, 6 ?
    ?, 7 ? ?, 8 ? ?, 27 ? ?, 33 ? ?
  • The sequence 12345 ? 10100110010000101 decode
    ?

30
Elias delta coding
  • Elias delta code is a prefix code for positive
    integers developed by Peter Elias.
  • To code a number
  • Separate the integer into the highest power of 2
    it contains (2N' ) and the remaining N' binary
    digits of the integer.
  • Encode N N' 1 with Elias gamma coding.
  • Append the remaining N' binary digits to this
    representation of N.
  • Examples
  • 1 ?1, 2 ? 0100, 3 ?0101, 4 ? 01100, 5 ? 01101, 6
    ? 01110, 7 ? ?, 8 ? ?, 27 ? ?, 33 ? ?

31
Distributed indexing
Sec. 4.4
  • For web-scale indexing (dont try this at home!)
  • must use a distributed computing cluster
  • Individual machines are fault-prone
  • Can unpredictably slow down or fail
  • How do we exploit such a pool of machines?

32
Google data centers
Sec. 4.4
  • Google data centers mainly contain commodity
    machines.
  • Data centers are distributed around the world.
  • Estimate a total of 1 million servers, 3 million
    processors/cores (Gartner 2007)
  • Estimate Google installs 100,000 servers each
    quarter.
  • Based on expenditures of 200250 million dollars
    per year
  • This would be 10 of the computing capacity of
    the world!?!

33
Google data centers
Sec. 4.4
  • If in a non-fault-tolerant system with 1000
    nodes, each node has 99.9 uptime, what is the
    uptime of the system?
  • Answer 63 (99.9)1000

34
Distributed indexing
Sec. 4.4
  • Maintain a master machine directing the indexing
    job considered safe.
  • Break up indexing into sets of (parallel) tasks.
  • Master machine assigns each task to an idle
    machine from a pool.

35
Parallel tasks
Sec. 4.4
  • We will use two sets of parallel tasks
  • Parsers
  • Inverters
  • Break the input document collection into splits
  • Each split is a subset of documents
    (corresponding to blocks in BSBI/SPIMI)

36
Parsers
Sec. 4.4
  • Master assigns a split to an idle parser machine
  • Parser reads a document at a time and emits
    (term, doc) pairs
  • Parser writes pairs into j partitions
  • Each partition is for a range of terms first
    letters
  • (e.g., a-f, g-p, q-z) here j 3.
  • Now to complete the index inversion

37
Inverters
Sec. 4.4
  • An inverter collects all (term,doc) pairs (
    postings) for one term-partition.
  • Sorts and writes to postings lists

38
Data flow
Sec. 4.4
Master
assign
assign
Postings
Parser
Inverter
a-f
g-p
q-z
a-f
Parser
a-f
g-p
q-z
Inverter
g-p
Inverter
splits
q-z
Parser
a-f
g-p
q-z
Map phase
Reduce phase
Segment files
39
MapReduce
Sec. 4.4
  • The index construction algorithm we just
    described is an instance of MapReduce.
  • MapReduce (Dean and Ghemawat 2004) is a robust
    and conceptually simple framework for distributed
    computing
  • without having to write code for the
    distribution part.
  • They describe the Google indexing system (ca.
    2002) as consisting of a number of phases, each
    implemented in MapReduce.

40
Dynamic indexing
Sec. 4.5
  • Up to now, we have assumed that collections are
    static.
  • They rarely are
  • Documents come in over time and need to be
    inserted.
  • Documents are deleted and modified.
  • This means that the dictionary and postings lists
    have to be modified
  • Postings updates for terms already in dictionary
  • New terms added to dictionary

41
Simplest approach
Sec. 4.5
  • Maintain big main index
  • New docs go into small auxiliary index
  • Search across both, merge results
  • Deletions
  • Invalidation bit-vector for deleted docs
  • Filter docs output on a search result by this
    invalidation bit-vector
  • Periodically, re-index into one main index

42
Issues with main and auxiliary indexes
Sec. 4.5
  • Problem of frequent merges you touch stuff a
    lot
  • Poor performance during merge
  • Actually
  • Merging of the auxiliary index into the main
    index is efficient if we keep a separate file for
    each postings list.
  • Merge is the same as a simple append.
  • But then we would need a lot of files
    inefficient for O/S.
  • Assumption for the rest of the lecture The index
    is one big file.
  • In reality Use a scheme somewhere in between
    (e.g., split very large postings lists, collect
    postings lists of length 1 in one file etc.)

43
Dynamic/Positional indexing at search engines
Sec. 4.5
  • All the large search engines now do dynamic
    indexing
  • Their indices have frequent incremental changes
  • News items, blogs, new topical web pages
  • Sarah Palin,
  • But (sometimes/typically) they also periodically
    reconstruct the index from scratch
  • Query processing is then switched to the new
    index, and the old index is then deleted
  • Positional indexes
  • Same sort of sorting problem just larger

Why?
44
Sec. 4.5
45
Resources for todays lecture
Ch. 4
  • Chapter 4 of IIR
  • MG Chapter 5
  • Original publication on MapReduce Dean and
    Ghemawat (2004)
  • Original publication on SPIMI Heinz and Zobel
    (2003)
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