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 two lists)
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 the 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, so 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
