index construction: sorting
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Index Construction: sorting. Paolo Ferragina Dipartimento di Informatica Università di Pisa. Reading Chap 4. Indexer steps. Dictionary & postings: How do we construct them? Scan the texts Find the proper tokens-list Append to the proper tokens-list the docID. How do we: - PowerPoint PPT PresentationTRANSCRIPT
Index Construction:sorting
Paolo FerraginaDipartimento di Informatica
Università di Pisa
Reading Chap 4
Indexer steps
Dictionary & postings: How do we construct them? Scan the texts Find the proper tokens-list Append to the proper
tokens-list the docID
How do we:• Find ? …time issue…• Append ? …space issues …• Postings’ size?• Dictionary size ? … in-memory issues …
Indexer steps: create token
Sequence of pairs: < Modified token, Document ID >
What about var-length strings?
I did enact JuliusCaesar I was killed
i' the Capitol; Brutus killed me.
Doc 1
So let it be withCaesar. The noble
Brutus hath told youCaesar was ambitious
Doc 2
Indexer steps: Sort
Sort by Term Then sort by DocID
Core indexing step
Indexer steps: Dictionary & Postings
Multiple term entries in a single document are merged.
Split into Dictionary and Postings
Doc. frequency information is added.
Sec. 1.2
Some key issues…
6Pointers
Terms and
counts Now:• How do we sort?• How much storage is needed ?
Sec. 1.2
Lists of docIDs
Keep attention on disk...
If sorting needs to manage strings
Key observations:
Array A is an “array of pointers to objects”
For each object-to-object comparison A[i] vs A[j]: 2 random accesses to 2 memory locations A[i] and A[j] (n log n) random memory accesses (I/Os ??)
Memory containing the strings
A
Again chaching helps,But how much ?
You sort ANot the strings
Binary Merge-Sort
Merge-Sort(A,i,j)01 if (i < j) then02 m = (i+j)/2; 03 Merge-Sort(A,i,m);04 Merge-Sort(A,m+1,j);05 Merge(A,i,m,j)
Merge-Sort(A,i,j)01 if (i < j) then02 m = (i+j)/2; 03 Merge-Sort(A,i,m);04 Merge-Sort(A,m+1,j);05 Merge(A,i,m,j)
DivideConquer
Combine
1 2 8 10 7 9 13 19
1 2 7
Merge is linear in the
#items to be merged
Few key observations
Items = (short) strings = atomic...
On english wikipedia, about 109 tokens to sort (n log n) memory accesses (I/Os ??)
[5ms] * n log2 n ≈ 3 years
In practice it is a “faster”, why?
SPIMI: Single-pass in-memory indexing
Key idea #1: Generate separate dictionaries for each block (No need for term termID)
Key idea #2: Don’t sort. Accumulate postings in postings lists as they occur (in internal memory).
Generate an inverted index for each block. More space for postings available Compression is possible
Merge indexes into one big index. Easy append with 1 file per posting (docID are
increasing within a block), otherwise multi-merge like
SPIMI-Invert
Use the same algorithm for disk?
multi-way merge-sortaka BSBI: Blocked sort-based Indexing
Mapping term termID to be kept in memory for constructing the
pairs Consumes memory to pairs’ creation Needs two passes, unless you use hashing
and thus some probability of collision.
Recursion
10 2
10 2
5 1
5 1
13 19
13 19
9 7
9 7
15 4
15 4
8 3
8 3
12 17
12 17
6 11
6 11
10 2 5 1 13 19 9 7 15 4 8 3 12 17 6 11
10 2 5 1 13 19 9 7 15 4 8 3 12 17 6 11
10 2 5 1 13 19 9 7 15 4 8 3 12 17 6 11
log2 N
Implicit Caching…
10 2
2 10
5 1
1 5
13 19
13 19
9 7
7 9
15 4
4 15
8 3
3 8
12 17
12 17
6 11
6 11
1 2 5 10 7 9 13 19 3 4 8 15 6 11 12 17
1 2 5 7 9 10 13 19 3 4 6 8 11 12 15 17
1 2 3 4 5 6 7 8 9 10 11 12 13 15 17 19
log2 N
MN/M runs, each sorted in internal memory (no I/Os)
2 passes (one Read/one Write) = 2 * (N/B)
I/Os
— I/O-cost for binary merge-sort is ≈ 2 (N/B) log2 (N/M)
Log
2 (
N/M
)
2 passes
(R/W)
2 passes
(R/W)
B
A key inefficiency
1 2 4 7 9 10 13 19 3 5 6 8 11 12 15 17
B
After few steps, every run is longer than B !!!
B
We are using only 3 pagesBut memory contains M/B pages ≈ 230/215 = 215
B
OutputBuffer Disk
1, 2, 3
1, 2, 3
OutputRun
4, ...
Multi-way Merge-Sort
Sort N items with main-memory M and disk-pages B:
Pass 1: Produce (N/M) sorted runs. Pass i: merge X = M/B-1 runs logX N/M passes
Main memory buffers of B items
Pg for run1
Pg for run X
Out Pg
DiskDisk
Pg for run 2
. . . . . .
. . .
How it works
1 2 5 10 7 9 13 19
1 2 5 7….
1 2 3 4 5 6 7 8 9 10 11 12 13 15 17 19
MN/M runs, each sorted in internal memory = 2 (N/B) I/Os
2 passes (one Read/one Write) = 2 * (N/B)
I/Os
— I/O-cost for X-way merge is ≈ 2 (N/B) I/Os per level
Log
X (
N/M
)
M
X
X
Cost of Multi-way Merge-Sort
Number of passes = logX N/M logM/B (N/M)
Total I/O-cost is ( (N/B) logM/B N/M ) I/Os
Large fan-out (M/B) decreases #passes
In practice
M/B ≈ 105 #passes =1 few mins
Tuning dependson disk features
Compression would decrease the cost of a pass!
Distributed indexing
For web-scale indexing: must use a distributed computing cluster of PCs
Individual machines are fault-prone
Can unpredictably slow down or fail
How do we exploit such a pool of machines?
Distributed indexing
Maintain a master machine directing the indexing job – considered “safe”.
Break up indexing into sets of (parallel) tasks.
Master machine assigns tasks to idle machines
Other machines can play many roles during the computation
Parallel tasks
We will use two sets of parallel tasks Parsers and Inverters
Break the document collection in two ways:
• Term-based partitionone machine handles a subrange of terms
• Doc-based partitionone machine handles a subrange of documents
• Term-based partitionone machine handles a subrange of terms
• Doc-based partitionone machine handles a subrange of documents
Data flow: doc-based partitioning
splits
Parser
Parser
Parser
Master
Inverter
Inverter
Inverter
Postings
IL1
assign assign
IL2
ILk
Set1
Set2
Setk
Each query-term goes to many machines
Data flow: term-based partitioning
splits
Parser
Parser
Parser
Master
a-f g-p q-z
a-f g-p q-z
a-f g-p q-z
Inverter
Inverter
Inverter
Postings
a-f
g-p
q-z
assign assign
Set1
Set2
Setk
Each query-term goes to one machine
MapReduce
This is a robust and conceptually simple framework
for distributed computing … without having to write code for the
distribution part.
Google indexing system (ca. 2002) consists of a number of phases, each implemented in MapReduce.
Data flow: term-based partitioning
splits
Parser
Parser
Parser
Master
a-f g-p q-z
a-f g-p q-z
a-f g-p q-z
Inverter
Inverter
Inverter
Postings
a-f
g-p
q-z
assign assign
Mapphase
Reducephase
Segmentfiles
(local disks)
16Mb -64Mb
Guarantee fitting in
one machine ?
Guarantee fitting in
one machine ?
Guarantee fitting in
one machine ?
Guarantee fitting in
one machine ?
Dynamic indexing
Up to now, we have assumed static collections.
Now more frequently occurs that: Documents come in over time Documents are deleted and modified
And this induces: Postings updates for terms already in dictionary New terms added/deleted to/from dictionary
Simplest approach
Maintain “big” main index New docs go into “small” auxiliary index Search across both, and merge the results
Deletions Invalidation bit-vector for deleted docs Filter search results (i.e. docs) by the
invalidation bit-vector
Periodically, re-index into one main index
Issues with 2 indexes
Poor performance 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 [new docIDs are greater].
But this needs a lot of files – inefficient for O/S.
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.)
Logarithmic merge
Maintain a series of indexes, each twice as large as the previous one: 20 M, 21 M , 22 M , 23
M , … Keep a small index (Z) in memory (of size 20 M) Store I0, I1, … on disk (sizes 20 M , 21 M , …)
If Z gets too big (> M), write to disk as I0
or merge with I0 (if I0 already exists) Either write merge Z to disk as I1 (if no I1)
or merge with I1 to form a larger Z etc. # indexes = logarithmic# indexes = logarithmic
Some analysis (T = #postings = #tokens)
Auxiliary and main index: index construction time is O(T2) as each posting is touched in each merge.
Logarithmic merge: Each posting is merged O(log (T/M) ) times, so complexity is O( T log
(T/M) )
Logarithmic merge is more efficient for index construction, but its query processing requires the merging of O( log (T/M) ) lists of results
Web search engines
Most search engines now support dynamic indexing News items, blogs, new topical web pages
But (sometimes/typically) they also periodically reconstruct the index Query processing is then switched to the
new index, and the old index is then deleted