Posting Lists

On Monday, we began looking at index constrction in detail.
We discussed an ADT and some data structure implementations suitable for dictionaries.
We now look at posting lists.
As opposed to dictionaries, posting lists contain the majority of the information stored in an inverted index and tend to be too large to store in memory.
Lists are transferred into memory on an as need basis.
To make the transfer of postings from disk to memory as efficient as possible, each term's posting list should be stored in a contiguous region of the hard-drive.
For single term queries one typically accesses a posting list in a sequential fashion.
On the other hand, for conjunctive queries we want to do things like galloping and binary search.

Random Accesses of Posting Lists

Binary search of a posting list of 50 million items, might take `|~ log_2(5 times 10^7)~| = 26` many random list accesses.
On a disk, that many accesses (each require a nonsequential page lookup) would be prohibitively slow, on the order of hundreds of milliseconds.
Alternatively one can try to read the whole posting list into memory, and then do in memory binary search.
50 million postings, each of 8 bytes, on a reasonably new hard drive would take about 4 seconds to read into memory.
So we need to do something different... one common idea is to use a per-term index.
A per-term index is a disk-based data structure that is part of the header of a posting list. It contains a copy of a subset of the postings in the posting list -- for example, every 5000th posting -- and the location in the posting list for these items.
When accessing the posting list, this structure is read into memory.
Searches are first done on the per-term posting list, then the relevant block of 5000 postings is read into memory.
Elements of the per-term-index are sometimes called synchronization points, and the whole per-term index method is sometimes called self-indexing.
Sometimes people consider using B-trees rather than per-term indexes, but in practice an at most two-tier per-term index suffices for even postings lists with billions of postings.

Prefix Queries

We already said that for prefix queries one needs to take a sorted approach to the dictionary.
This also holds for where the postings lists are stored on disk.
For example, if one does a search on "inform*" in GOV2, there are 4,365 different terms with that stem and 67million postings corresponding to them.
By storing posting lists in lex order, we are ensuring that each of these posting lists will be close to each other on disk and hence reduce our seek times.
If we had to do both a disk seek and rotational latency wait for each of the different terms, because they were stored on the disk in some random order, it would take a minute to access all the terms, not counting the times to do any operations on them.
If the postings lists were contiguous, on the other hand, this could be done in about 2 seconds.

Interleaving Dictionary and Posting Lists

An example of the dictionary interleaving strategy

The dictionary for the GOV2 collection consists in about 49 million distinct terms -- and this is small compared to Clue Web or say Google.
To hold all these entries together with pointers to the appropriate posting lists take about 1GB of memory -- doable, but it shows that even for large collections the dictionary itself might not fit into memory, even if compression is used.
If term bigrams are used the dictionary even gets larger.
Storing the entire dictionary on disk, however, is slow, it would require at least one more disk seek per term.
One solution to this problem is to dictionary interleaving: All entries are stored on disk, each entry right before the respective posting list. This allows the terms and posting list to be read with one read operation. In addition to this some dictionary entries are keep in memory. Lookup of nearest two entries is done in memory, then binary search between the pointers is used to find the correct posting list.
Usually, a block size of between 4 and 16KB between in memory dictionary entries suffices to reduce the in memory dictionary size to be easily storable in RAM.

In-Class Exercise

Suppose we have documents 1, 2, 3. In the whole corpus we have twenty-five terms A,B,C,D,E,AA,BB,CC,DD,EE,..., AAAAA,BBBBB,CCCCC,DDDDD,EEEEE. Document i contains a term if:

(len(term) + (alphabet_pos(term))) mod 3 = i mod 3.

Here alphabet_pos(term) is 0 if the term uses the letter A, 1 if the term uses B, etc.

Let's assume A and C occur in all documents.

(1) Suppose we have a per-term index where we have a synchronization entry every second posting. Using ascii draw what the auxiliary index and posting list look like.

(2) Draw what an interleaved index might look like for the above corpus.

Post your answer to the Oct 10 Thread.

Dropping the distinction between terms and postings

One can take the dictionary interleaving strategy further, by viewing index data as a sequence of pairs (term, posting).
The on-disk index could be divided into 64KB index blocks.
All postings are stored on-disk in alphabetical-order of their terms. Postings for the same term are stored in order of increasing posting offset.
The in-memory data structure used to access this on-disk index is a simple array, containing for each index block a pair of the form (term, posting) for the first term in the given block.
This approach unifies the self-indexing and interleaving methods we have described into a single thing to do.
Unfortunately, this approach tends to have higher memory requirements.