CS276: Information Retrieval and Web Search
Pandu Nayak and Prabhakar Raghavan
Lecture 4: Index Construction
How do we construct an index?
What strategies can we use with limited main memory?
Many design decisions in information retrieval are based on the characteristics of hardware
We begin by reviewing 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.
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.
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
processor’s clock rate 109 s−1
p low-level operation 0.01 μs = 10−8 s
(e.g., compare & swap a word)
size of main memory several GB
size of disk space 1 TB or more
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)
symbol statistic value
N documents 800,000
L avg. # tokens per doc 200
M terms (= word types) 400,000
avg. # bytes per token 6
avg. # bytes per token 4.5
avg. # bytes per term 7.5
non-positional postings 100,000,000
4.5 bytes per word token vs. 7.5 bytes per word type: why?
Documents are parsed to extract words and these are saved with the Document ID.
|We focus on this sort step.We have 100M items to sort.|
Can’t stuff entire collection into memory, sort, then write back
How can we construct an index for very large collections?
Taking into account the hardware constraints we just learned about . . .
Memory, disk, speed, etc.
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.
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.
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
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 ~ 10M 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.
First, read each block and sort within:
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.
Done straightforwardly, need 2 copies of data on disk
But can optimize this
Can do binary merges, with a merge tree of log210 = 4 layers.
During each layer, read into memory runs in blocks of 10M, merge, write back.
But it is more efficient to do a multi-way merge, where you are reading from all blocks simultaneously
Providing you read decent-sized chunks of each block into memory and then write out a decent-sized output chunk, then you’re not killed by disk seeks.
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.)
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.
Merging of blocks is analogous to BSBI.
Compression makes SPIMI even more efficient.
Compression of terms
Compression of postings
See next lecture
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?
Web search data centers (Google, Bing, Baidu) mainly contain commodity machines.
Data centers are distributed around the world.
Estimate: Google ~1 million servers, 3 million processors/cores (Gartner 2007)
If in a non-fault-tolerant system with 1000 nodes, each node has 99.9% uptime, what is the uptime of the system?
Exercise: Calculate the number of servers failing per minute for an installation of 1 million servers.
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.
We will use two sets of parallel tasks
Break the input document collection into splits
Each split is a subset of documents (corresponding to blocks in BSBI/SPIMI)
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
An inverter collects all (term,doc) pairs (= postings) for one term-partition.
Sorts and writes to postings lists
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.
Index construction was just one phase.
Another phase: transforming a term-partitioned index into a document-partitioned index.
Term-partitioned: one machine handles a subrange of terms
Document-partitioned: one machine handles a subrange of documents
As we’ll discuss in the web part of the course, most search engines use a document-partitioned index … better load balancing, etc.
Schema of map and reduce functions
map: input → list(k, v) reduce: (k,list(v)) → output
Instantiation of the schema for index construction
map: collection → list(termID, docID)
d1 : C came, C c’ed.
d2 : C died. →
→ <C,(d1:2,d2:1)>, <died,(d2:1)>, <came, (d1:1)>, <c'ed,(d1:1)>)
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
Maintain “big” main index
New docs go into “small” auxiliary index
Search across both, merge results
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
Problem of frequent merges – you touch stuff a lot
Poor performance during merge
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 OS.
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.)
Maintain a series of indexes, each twice as large as the previous one
At any time, some of these powers of 2 are instantiated
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
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) times, so complexity is O(T log T)
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
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
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 deleted
Same sort of sorting problem … just larger ← WHY?
Building character n-gram indexes:
As text is parsed, enumerate n-grams.
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
Chapter 4 of IIR
MG Chapter 5
Original publication on MapReduce: Dean and Ghemawat (2004)
Original publication on SPIMI: Heinz and Zobel (2003)