Query processing:
optimizations
Paolo Ferragina
Dipartimento di Informatica Università di Pisa
Reading 2.3
Augment postings with skip pointers (at indexing time)
How do we deploy them ?
Where do we place them ?
128
2 4 8 41 48 64
31
1 2 3 8 11 17 21
11 31
41 128
Sec. 2.3
Using skips
128
2 4 8 41 48 64
31
1 2 3 8 11 17 21
11 31
41 128
Suppose we’ ve stepped through the lists until we process 8 on each list. We match it and advance.
We then have 41 and 11 on the lower. 11 is smaller.
But the skip successor of 11 on the lower list is 31, so we can skip ahead past the intervening postings.
Sec. 2.3
Placing skips
Tradeoff:
More skips shorter spans more likely to skip. But lots of comparisons to skip
pointers.
Fewer skips longer spans few
successful skips. Less pointer comparisons.
Sec. 2.3
Placing skips
Simple heuristic for postings of length L
use L evenly-spaced skip pointers.
This ignores the distribution of query terms.
Easy if the index is relatively static.
This definitely useful for in-memory index
The I/O cost of loading a bigger list can outweigh the gains!
Sec. 2.3
Placing skips, contd
What if it is known a distribution of access pk to the k-th element of the inverted list?
w(i,j) = sumk=i..j pk
L^0(i,j) = average cost of accessing an item in the sublist from i to j = sumk=i..j pk * (k-i+1)
L^1(1,n) = 1 (first skip cmp) + (cost to access the right list)
minu>1w(1,u-1) * L^0(1,u-1) + w(u,n) * L^1(u,n)
L^0(i,j) can be tabulated in O(n^2) time
Computing L^1(i,n) takes O(n), given L^1(j,n), for j>i
Computing the total L^1(1,n) takes O(n^2) time
Sec. 2.3
You can solve it by Shortest Path
Placing skips, contd
What if it is also fixed the number of p skip- pointers that can be allocated?
Same as before but we add as parameter p
L^1_p(1,n) = 1 + min_{u>1} w(1,u-1) * L^0(1,u- 1) +
w(u,n) * L^1_{p-1}(u,n)
L^1_0(i,j) = L^0(i,j), i.e. no pointers left then scan
L^i(j,n) takes O(n) time [min calculation] if are available the values for L^{i-1}(h,n) with h > j
So L^p(1,n) takes O(pn^2) time
Sec. 2.3
Faster query = caching?
Two opposite approaches:
I. Cache the query results (exploits query locality)
II. Cache pages of posting lists (exploits term locality)
Query processing:
phrase queries and positional indexes
Paolo Ferragina
Dipartimento di Informatica Università di Pisa
Reading 2.4
Phrase queries
Want to be able to answer queries such as
“ stanford university” – as a phrase
Thus the sentence “ I went at Stanford my university” is not a match.
Sec. 2.4
Solution #1: Biword indexes
For example the text “ Friends, Romans, Countrymen” would generate the biwords
friends romans
romans countrymen
Each of these biwords is now an entry in the dictionary
Two-word phrase query-processing is immediate.
Sec. 2.4.1
Longer phrase queries
Longer phrases are processed by reducing them to bi-word queries in AND
stanford university palo alto can be broken into the Boolean query on biwords, such as
stanford university AND university palo AND palo alto
Need the docs to verify +
They are combined with other solutions
Can have false positives!
Index blows up
Sec. 2.4.1
Solution #2: Positional indexes
In the postings, store for each term and document the position(s) in which that term occurs:
<term, number of docs containing term;
doc1: position1, position2 … ; doc2: position1, position2 … ; etc.>
Sec. 2.4.2
Processing a phrase query
“ to be or not to be” .
to:
2:1,17,74,222,551; 4:8,16,190,429,433;
7:13,23,191; ...
be:
1:17,19; 4:17,191,291,430,434;
5:14,19,101; ...
Same general method for proximity searches
Sec. 2.4.2
Query term proximity
Free text queries: just a set of terms typed into the query box – common on the web
Users prefer docs in which query terms occur within close proximity of each other
Would like scoring function to take this into account – how?
Sec. 7.2.2
Positional index size
You can compress position values/offsets
Nevertheless, a positional index expands postings storage by a factor 2-4 in English
Nevertheless, a positional index is now
commonly used because of the power and usefulness of phrase and proximity queries
… whether used explicitly or implicitly in a ranking retrieval system.
Sec. 2.4.2
Combination schemes
BiWord + Positional index is a profitable combination
Biword is particularly useful for particular phrases (“ Michael Jackson” , “ Britney Spears” )
More complicated mixing strategies do exist!
Sec. 2.4.3
Soft-AND
E.g. query rising interest rates
Run the query as a phrase query
If <K docs contain the phrase rising interest rates, run the two phrase queries rising
interest and interest rates
If we still have <K docs, run the “ vector space query” rising interest rates (…see next…)
“Rank” the matching docs (…see next…)
Sec. 7.2.3
Query processing:
other sophisticated queries
Paolo Ferragina
Dipartimento di Informatica Università di Pisa
Reading 3.2 and 3.3
Wild-card queries: *
mon*: find all docs containing words beginning with “ mon” .
Use a Prefix-search data structure
*mon: find words ending in “ mon”
Maintain a prefix-search data structure for reverse terms.
How can we solve the wild-card query pro*cent ?
Sec. 3.2
What about * in the middle?
co*tion
We could look up co* AND *tion and intersect the two lists
Expensive
se*ate AND fil*er
This may result in many Boolean AND queries.
The solution: transform wild-card queries so that the *’ s occur at the end
This gives rise to the Permuterm Index.
Sec. 3.2
Permuterm index
For term hello, index under:
hello$, ello$h, llo$he, lo$hel, o$hell,
$hello
where $ is a special symbol.
Queries:
X lookup on X$
X* lookup on $X*
*X lookup on X$*
*X* lookup on X*
X*Y lookup on Y$X*
X*Y*Z ??? Exercise!
Sec. 3.2.1
Permuterm query processing
Rotate query wild-card to the right
P*Q Q$P*
Now use prefix-search data structure
Permuterm problem: ≈ 4x lexicon size
Empirical observation for English.
Sec. 3.2.1
K-gram indexes
The k-gram index finds terms based on a query consisting of k-grams (here k=2).
mo on
among
$m mace
among
amortize madden
arond
Sec. 3.2.2
K-gram for wild-cards queries
Query mon* can now be run as
$m AND mo AND on
Gets terms that match AND version of our wildcard query.
Must post-filter these terms against query.
Sec. 3.2.2
Isolated word correction
Given a lexicon and a character sequence Q, return the words in the lexicon closest to Q
What’ s “ closest” ?
Edit distance (Levenshtein distance)
Weighted edit distance
n-gram overlap
Useful in query-mispellings
Sec. 3.3.2
Edit distance
Given two strings S1 and S2, the minimum number of operations to convert one to the other
Operations are typically character-level
Insert, Delete, Replace, (Transposition)
E.g., the edit distance from dof to dog is 1
From cat to act is 2 (Just 1 with transpose.)
from cat to dog is 3.
Generally found by dynamic programming.
Sec. 3.3.3
Let E(i,j) = edit distance between T1,j and P1,i.
DynProg for Edit Distance
E(i,0)=E(0,i)=i
E(i, j) = E(i–1, j–1) if P
i=T
jE(i, j) = min{E(i, j–1), E(i–1, j),
E(i–1, j–1)}+1 if P
iT
jExample
T
0 1 2 3 4 5 6
p t t a p a
P
0
0 1 2 3 4 5 6
1
p 1 0 1 2 3 4 5
2
a 2 1 1 2 2 3 4
3
t 3 2 1 1 2 3 4
4
t 4 3 2 1 2 3 4
Weighted edit distance
As above, but the weight of an operation depends on the character(s) involved
Meant to capture OCR or keyboard errors, e.g. m more likely to be mis-typed as n than as q
Therefore, replacing m by n is a smaller edit distance than by q
Requires weight matrix as input
Modify dynamic programming to handle weights
Sec. 3.3.3
k-gram overlap for Edit Distance
Enumerate all the k-grams in the query string as well as in the lexicon
Use the k-gram index (recall wild-card search) to retrieve all lexicon terms matching any of the query k-grams
Threshold by number of matching k-grams
If the term is L chars long
If E is the number of allowed errors (E*k, k-grams are killed)
At least (L-k+1) – E*k of the query k-grams must match a dictionary term to be a candidate answer.
Sec. 3.3.4
Context-sensitive spell correction
Text: I flew from Heathrow to Narita.
Consider the phrase query “ flew form Heathrow”
We’ d like to respond
Did you mean “ flew from Heathro w ” ?
because no docs matched the query phrase.
Sec. 3.3.5
Zone indexes
Paolo Ferragina
Dipartimento di Informatica Università di Pisa
Reading 6.1
Parametric and zone indexes
Thus far, a doc has been a term sequence
But documents have multiple parts:
Author
Title
Date of publication
Language
Format
etc.
These are the metadata about a document
Sec. 6.1
Zone
A zone is a region of the doc that can contain an arbitrary amount of text e.g.,
Title
Abstract
References …
Build inverted indexes on fields AND zones to permit querying
E.g., “ find docs with merchant in the title zone and matching the query gentle rain”
Sec. 6.1
Example zone indexes
Encode zones in dictionary vs. postings.
Sec. 6.1
Tiered indexes
Break postings up into a hierarchy of lists
Most important
…
Least important
Inverted index thus broken up into tiers of decreasing importance
At query time use top tier unless it fails to yield K docs
If so drop to lower tiers
Sec. 7.2.1
Example tiered index
Sec. 7.2.1
