COMP6714: Information Retrieval & Web Search
Introduction to
Information Retrieval
Lecture 4: Index Construction
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COMP6714: Information Retrieval & Web Search
Plan
▪ Last lecture:
▪ Dictionary data structures
▪ Tolerant retrieval ▪ Wildcards
▪ Spell correction ▪ Soundex
▪ This time:
▪ Index construction
a-hu hy-mn-z
$m
mace
madden
mo
among
amortize
on
abandon
among
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COMP6714: Information Retrieval & Web Search
Ch. 4
Index construction
▪ How do we construct an index?
▪ What strategies can we use with limited main memory?
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COMP6714: Information Retrieval & Web Search
Sec. 4.1
Hardware basics
▪ Many design decisions in information retrieval are based on the characteristics of hardware
▪ We begin by reviewing hardware basics
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COMP6714: Information Retrieval & Web Search
Sec. 4.1
Hardware basics
▪ 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.
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COMP6714: Information Retrieval & Web Search
Sec. 4.1
Hardware basics
▪ Servers used in IR systems now typically have several GB of main memory, sometimes tens of GB.
▪ Available disk space is several (2–3) orders of magnitude larger.
▪ Fault tolerance is very expensive: It’s much cheaper to use many regular machines rather than one fault tolerant machine.
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COMP6714: Information Retrieval & Web Search
Sec. 4.1
Hardware assumptions
▪ symbol statistic
value
5 ms = 5 x 10−3 s 0.02 μs = 2 x 10−8 s 109 s−1
0.01 μs = 10−8 s
several GB
1 TB or more
▪ s ▪ b ▪ ▪ p
▪ ▪
average seek time
transfer time per byte
processor’s clock rate
low-level operation (e.g., compare & swap a word)
size of main memory size of disk space
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COMP6714: Information Retrieval & Web Search
Sec. 4.2
RCV1: Our collection for this lecture
▪ Shakespeare’s collected works definitely aren’t large enough for demonstrating many of the points in this course.
▪ The collection we’ll use isn’t really large enough either, but it’s 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)
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COMP6714: Information Retrieval & Web Search
Sec. 4.2
A Reuters RCV1 document
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COMP6714: Information Retrieval & Web Search
Sec. 4.2
Reuters RCV1 statistics
▪ symbol ▪ N
▪ L
▪ M
▪
▪
▪ ▪
statistic value
documents 800,000 avg. # tokens per doc 200 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
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COMP6714: Information Retrieval & Web Search
Sec. 4.2
Term
Doc #
I
1
did
1
enact
1
julius
1
cae sar
1
I
1
was
1
kille d
1
i’
1
the
1
capitol
1
brutus
1
kille d
1
me
1
so
2
let
2
it
2
be
2
with
2
cae sar
2
the
2
noble
2
brutus
2
hath
2
told
2
you
2
cae sar
2
was
2
ambitious
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2
Recall IIR 1 index construction
▪ 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
COMP6714: Information Retrieval & Web Search
Sec. 4.2
Key step
▪ 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.
Term
Doc #
Term
I
did
enact
capitol
brutus
kille d
1
ambitious
1
be
1
brutus
julius
1
brutus
cae sar
1
capitol
I
was
kille d
1
cae sar
1
cae sar
1
cae sar
i’
1
did
the
1
enact
1
hath
1
I
1
I
me
1
i’
so
2
it
let
it
be
2
julius
Doc #
2
2
1
2
1
1
2
2
1
1
1
1
1
1
2
1
2
kille d
1
2
kille d
with
2
let
cae sar
2
me
the
noble
brutus
2
noble
2
so
2
the
hath
2
the
told
2
told
you
cae sar
was
2
you
2
was
2
was
ambitious
2
with
1
2
1
2
2
1
2
2
2
1
2
2
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COMP6714: Information Retrieval & Web Search
Sec. 4.2
Hash based in-memory index construction
▪ Another in-memory index construction method is to use hash-tables
▪ Append (docid, pos) to the existing (partial) postings list of the token; create a new postings list if necessary
▪ Generally, faster than sorting-based method ▪ Further optimizations
▪ Dealing with collision: insert-at-back and move-to-front heuristics
▪ Saving space and time: use ArrayList to implement postings lists
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COMP6714: Information Retrieval & Web Search
Sec. 4.2
Scaling index construction
▪ 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.
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COMP6714: Information Retrieval & Web Search
Sec. 4.2
Sort-based index construction
▪ 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 (term, doc,
freq), demands a lot of space for large collections.
▪ T = 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 >150 years of newswire
▪ Thus: We need to store intermediate results on disk.
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COMP6714: Information Retrieval & Web Search
Sec. 4.2
Use the same algorithm for disk?
▪ 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.
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COMP6714: Information Retrieval & Web Search
Sec. 4.2
Bottleneck
▪ 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 T=100M records
If every comparison took 2 disk seeks, and N items could be sorted with N log2N comparisons, how long would this take?
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COMP6714: Information Retrieval & Web Search
Sec. 4.2
BSBI: Blocked sort-based Indexing (Sorting with fewer disk seeks)
▪ 12-byte (4+4+4) records (term, doc, freq).
▪ These are generated as we parse docs.
▪ Must now sort 100M such 12-byte records by term.
▪ Define a Block such records ▪ Can easily fit a couple into memory.
▪ 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.
~ 10M
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COMP6714: Information Retrieval & Web Search
Sec. 4.2
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COMP6714: Information Retrieval & Web Search
Sec. 4.2
Sorting 10 blocks of 10M records
▪ First, read each block and sort within: ▪ Quicksort takes 2N ln N expected steps
▪ In our case 2 x (10M ln 10M) steps
▪
▪ 10 times this estimate – gives us 10 sorted runs of 10M records each.
▪ Done straightforwardly, need 2 copies of data on disk ▪ But can optimize this
Exercise: estimate total time to read each block from disk and and quicksort it.
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COMP6714: Information Retrieval & Web Search
Sec. 4.2
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COMP6714: Information Retrieval & Web Search
Example
▪ Settings
▪B: Block/pagesize
▪ M: Size of main memory in pages (e.g., = 10 blocks)
▪ N: Number of documents (e.g., = 10000)
▪ R: Size of the (term, docID) pairs one document emits.
▪ Simplifying assumptions:
▪ R: the same for all documents
▪ B = c*R, for some integer c (e.g., c = 5) ▪ All I/Os have the same cost
COMP6714: Information Retrieval & Web Search
External Merge-Sort: Phase I
▪ Phase I: load the (term, docID) pairs from (M*B)/R documents (at a time) into M buffer pages; sort
▪ Result: (initial) runs of length M pages ▪ # of runs = 200
.. .
Disk
. . .
Disk
(this, 1), (is, 1), … (I, 2), (am, 2), … …
(today, c*M), …
M page of main memory
sort
COMP6714: Information Retrieval & Web Search
Phase II /1
▪ Recursively merge (up to) M – 1 runs into a new run
▪ Result: runs of length M (M – 1) pages
Input Buffer 1 Input Buffer 2
Input Buffer M-1
. . . . . . . …
Output Buffer
Disk
M bytes of main memory
Disk
(M-1)-way Merge
COMP6714: Information Retrieval & Web Search
Phase II /2
▪ Recursively merge (up to) M – 1 runs into a new run
▪ Result: runs of length M (M – 1)2 pages
Input Buffer 1 Input Buffer 2
Input Buffer M-1
.. .
Output Buffer
Disk
… .
M bytes of main memory
Disk
(M-1)-way Merge
COMP6714: Information Retrieval & Web Search
Phase II /3
▪ Recursively merge (up to) M – 1 runs into a new run
▪ Result: a single run
Input Buffer 1 Input Buffer 2
Input Buffer M-1
Output Buffer
Disk
… .
M bytes of main memory
Disk
(M-1)-way Merge
COMP6714: Information Retrieval & Web Search
Cost of External Merge Sort
▪ Number of passes: 1 + Total I/O cost: 2 ⋅ 𝑁𝑅 ⋅
𝐵
log𝑀−1
𝑁𝑅 𝑀𝐵
1 +
log 𝑁𝑅 𝑀−1 𝑀𝐵
blocks/pages
▪ How much data can we sort with 10MB RAM? ▪ Assume B = 4KB
▪ 1 pass 10MB “data”
▪ 2 passes ≈25GB “data” (M-1 = 2559) ▪ 3 passes ?
Another Example
▪ Can sort most reasonable inputs in 2 or 3 passes !
COMP6714: Information Retrieval & Web Search
Example: 2-Way Merge for 20 Runs
R1 R2 R3 R4 R5 R6 R7 R8 R9 R10R11 R12 R13R14 R15 R16R17R18R19 R20
S1 S2 S3 S4 S5 S6
T1 T2 T3
S7 S8
T4
S9
S10
T5
U1
U2
U3
V2
V1
Number of passes = 5
W1
COMP6714: Information Retrieval & Web Search
Example: 5-Way Merge for 20 Runs
R1 R2 R3 R4 R5 R6 R7 R8 R9 R10R11 R12 R13R14 R15 R16R17R18R19 R20
S1 S2 S3 S4
Number of passes = 2
T1
COMP6714: Information Retrieval & Web Search
adapted from https://karticks.wordpress.com/2009/07/29/the-mapreduce-design-pattern-demystified/
K-way Merge: Using a min-heap
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COMP6714: Information Retrieval & Web Search
Sec. 4.3
Remaining problem with sort-based algorithm
▪ 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.)
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COMP6714: Information Retrieval & Web Search
Sec. 4.3
SPIMI:
Single-pass in-memory indexing
▪ Key idea 1: Generate separate dictionaries for each block – no need to maintain term-termID mapping across blocks.
▪ Key idea 2: Don’t 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.
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COMP6714: Information Retrieval & Web Search
Sec. 4.3
SPIMI-Invert
▪ Merging of blocks is analogous to BSBI.
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COMP6714: Information Retrieval & Web Search
Sec. 4.3
SPIMI: Compression
▪ Compression makes SPIMI even more efficient. ▪ Compression of terms
▪ Compression of postings
▪ See next lecture
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COMP6714: Information Retrieval & Web Search
Sec. 4.4
Distributed indexing
▪ For web-scale indexing (don’t 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?
For those interested in the topic, read the textbook for distributed indexing using the Map-Reduce paradigm.
Also check out: http://terrier.org/docs/v3.5/hadoop_indexing.html
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COMP6714: Information Retrieval & Web Search
Sec. 4.5
Dynamic indexing
▪ 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
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COMP6714: Information Retrieval & Web Search
Sec. 4.5
Simplest approach – Immediate Merge ▪ Maintain “big” main index
▪ New docs go into “small” auxiliary index
▪ Merge immediately with the big main index when memory
is full
▪ 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
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COMP6714: Information Retrieval & Web Search
Sec. 4.5
Issues with main and auxiliary indexes
▪ 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.)
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COMP6714: Information Retrieval & Web Search
Sec. 4.5
Another Extreme – No Merge
▪ Whenever memory is full, write the sub-index to the disk
▪ Never merge sub-indexes ▪ Pros:
▪ High indexing performance ▪ Cons:
▪ Slow query performance
▪ Require Ω(|C|/M) seeks to fetch the inverted list for a term
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COMP6714: Information Retrieval & Web Search
Sec. 4.5
Compromise – Logarithmic merge ▪ Comprise of the previous two extremes
▪ Generation of a sub-index
▪ The one directly created from in-memory index has
generation = 0
▪ Merge of multiple sub-index with max generation = g gives a new index with generation = g+1
▪ Invariant: no two sub-indexes can have the same generation
▪ When memory is full, create I0
▪ If we have two sub-indexes of generation g, merge them to form a single sub-index of generation g+1
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COMP6714: Information Retrieval & Web Search
Sec. 4.5
Illustration
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COMP6714: Information Retrieval & Web Search
Sec. 4.5
Algorithm
▪ Maintain a series of indexes, each twice as large as the previous one.
▪ Keep smallest (Z0) in memory
▪ Larger ones (I0, I1, …) on disk
▪ If Z0 gets too big (> n), write to disk as I0
▪ or merge with I0 (if I0 already exists) as Z1
▪ Either write merge Z1 to disk as I1 (if no I1)
▪ or merge with I1 to form Z2
▪ etc.
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COMP6714: Information Retrieval & Web Search
Sec. 4.5
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COMP6714: Information Retrieval & Web Search
Sec. 4.5
Logarithmic merge
▪ Auxiliary and main index: index construction time is O(C2/M) as each posting is touched in each merge.
▪ C = Collection Size, and M = memory size
▪ Logarithmic merge: Each posting is merged
O(log C/M) times, so complexity is O(C log (C/M))
▪ So logarithmic merge is much more efficient for index construction
▪ But query processing now requires the merging of O(log T) indexes
▪ Whereas it is O(1) if you just have a main and auxiliary index
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COMP6714: Information Retrieval & Web Search
Lucene
▪ Mergefactor:
▪ http://lucene.sourceforge.net/talks/inktomi/ ▪ In animation:
▪ http://blog.mikemccandless.com/2011/02/visualizing- lucenes-segment-merges.html
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COMP6714: Information Retrieval & Web Search
Sec. 4.5
Further issues with multiple indexes ▪ Collection-wide statistics are hard to maintain
▪ E.g., when we spoke of spell-correction: which of several corrected alternatives do we present to the user?
▪ We said, pick the one with the most hits
▪ How do we maintain the top ones with multiple
indexes and invalidation bit vectors?
▪ One possibility: ignore everything but the main index for such ordering
▪ Will see more such statistics used in results ranking
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COMP6714: Information Retrieval & Web Search
Sec. 4.5
Dynamic indexing at search engines
▪ 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
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COMP6714: Information Retrieval & Web Search
Sec. 4.5
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COMP6714: Information Retrieval & Web Search
Sec. 4.5
Other sorts of indexes ▪ Positional indexes
▪ Same sort of sorting problem … just larger
▪ Building character n-gram indexes:
▪ As text is parsed, enumerate n-grams.
Why?
▪ For each n-gram, need pointers to all dictionary terms containing it – the “postings”.
▪ Note that the same “postings entry” will arise repeatedly in parsing the docs – need efficient hashing to keep track of this.
▪ E.g., that the trigram uou occurs in the term deciduous will be discovered on each text occurrence of deciduous
▪ Only need to process each term once
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COMP6714: Information Retrieval & Web Search
Ch. 4
Resources for today’s lecture
▪ 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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