1. Hao Yan, Shuai Ding, Torsten Suel
Inverted Index Compression and Query Processing with Optimized Document Ordering
Hao Yan, Shuai Ding, Torsten Suel
Department of Computer Science and Engineering, Polytechnic Institute of New York University, Brooklyn, NY 11201
Yahoo! Research

2. What are the best compression methods for compressing
indexes of search engines?
In particular, what if given a particular ordering of documents?

3. Outline
• Motivation & Background
• Our Methods
• Conclusion

4. Search Engines – Performance Challenge
• Performance challenges in large web search engines:
- A large amount of data (>1,000,000,000 pages)
- Fast! (>1,000 queries/second)

5. Many ways to improve performances
• Caching
• Early termination
• Parallel processing
• Data compression (inverted index compression)

6. the required size of memory
Using Compression is Better
Before
After
disk traffic!
the required size of memory

7. What are Inverted Indexes?
• Storing information about where a word (term) occurs in the collection
• Each word has an inverted list that is a sequence of integers (called docIDs),
each of which uniquely identify a document in the collection
• Inverted Indexes = a set of such inverted lists
madrid , 777, 11437,….
museum , 1234, 4356, 12457,….
spain , 19, 29, 98, 143, 777, ...
barcelona , 457, 777, 789, ...
mall , 777, 2134, 3970, ...
university , 256, 372, 511, 777, 1000, ...

8. DocID + Frequency • madrid: 345, 777, 11437,….
• Inverted list :
<docID1, freq1>, <docID2, freq2>, <docID3, freq3>, …
• Normal layout for better compression:
store docIDs and frequencies separately
madrid docID : 345, 777, 1437, …
freq: 7, , , ...

9. D-gaps (Differences Between DocIDs)
madrid: 345, 777, 11437, …
• D-gaps
madrid: 345, 432, 10660, …
• Frequences (Freqs):
madrid: 7, 4, 11, Not in sorted order! No gaps!

10. Partitioned into blocks
Blocks of Inverted Lists (d-gaps)
• madrid : 345, 111, 1, …, 2, 14, …, , 423, ..
Partitioned into blocks
• madrid: 345, 111, 1, …, , 14, …, , 423, ..
block1
block2
block3 …

11. Indexes – In Summary block1 block2 block3 …
• D-gaps: 345, 111, 1, …, , 14, …, , 423, …, …..
• Freqs: 4, 3, 7, …, , 8, …, , 3, …, …..
block1
block2
block3 …

12. Query Processing 777 disk memory Index Index madrid 345, 777, 11437,….
museum , 1234, 4356, 12457,….
disk
memory

13. How to Judge Compression Techniques
• Small compressed index size
• Fast decompression (frequently called)
• Compression can be slower (seldom called)

14. Existing Research on Compressing
• DocID
Many existing techniques
• Frequency
Few techniques

15. Related Research – Reordering
• Given a collection of N documents, we need to first assign them document IDs
• DocIDs can be assigned randomly, or simply in the order documents are crawled
• However, researchers have found that
special assignment strategies may result in better compression

16. Related Research – Reordering
R. Blanco and A. Barreiro. Document identifier reassignment through dimensionality reduction. ECIR’05.
D. Blandford and G. Blelloch. Index compression through document reordering. DCC’02
W. Shieh, T. Chen, J. Shann, and C. Chung. Inverted file compression through document identifier reassignment. Inf. Processing and Management, 2003.
F. Silvestri. Sorting out the document identifier assignment problem. ECIR’07.
F. Silvestri, S. Orlando, and R. Perego. Assigning identifiers to documents to enhance the clustering property of fulltext indexes. SIGIR’04

17. Related Research – Reordering
• Idea: first sort documents in a particular order such that similar documents are clustered (close to each other); then assign docIDs sequentially
• Advantage: most d-gaps are smaller and can be better compressed
• Reason: If a word occurs in a document, it is very likely it will occur in the similar
documents; if these similar documents have similar docIDs, the d-gaps
in the word’s inverted list will become much smaller
• madrid (docIDs) 345, 777, 11437, 11438, 11443, 11450, …..
• madrid (d-gaps) 345, 432, 10660, 1, 5, 7,…..
• One interesting re-ordering method:
• sorting documents by URLs
(F. Silvestri, Sorting out the document identifier reassignment problem, ECIR’07)

18. Existing Research about Compression with Reordering
• Previous work has focused on determining the best possible ordering of documents
• However, few existing techniques focusing on compressing indexes AFTER reordering
• DocID : NO
• Frequency: NO

19. Our work – the rest of the talk
Given the special reordering (sorting by URLs), we study:
• The best inverted index compression methods for
• DocID
• Frequency
• Query processing
• A hybrid approach combining different methods

20. • Extensively study most existing methods
DocID Compression - Contributions
• Extensively study most existing methods
• Propose improved PForDelta coding
• Study effects on docID compression of document re-ordering

21. Experiment Setup • Data set • Measurement Metric • Size
• TREC GOV2 , 25.2 million pages
• 1000 randomly selected queries
• Measurement Metric
• Size
• Data associated with each query: MB/query
• Data for the entire indexes: MB
• Bits/int (somewhere)
• Speed
• Million Integers/second
• Different orderings
• Original
• Random
• Sorted

22. DocID (d-gap) Compression
• Gamma coding
• Delta coding
• Variable byte coding (Var-byte)
• Golomb coding
• Rice coding
• RiceVT coding
• Simple9 (S9)
• Simple16 (S16)
• Interpolative (IPC)
• PForDelta (PFD)

23. PForDelta coding (PFD)
• S. Heman. Super-scalar database compression between RAM and CPU-cache.
MS Thesis, Centrum voor Wiskunde en Informatica, Netherlands, July 2005
• M. Zukowski, S. Heman, N. Nes, and P. Boncz. Super-scalar RAM-CPU cache
compression. In Proc. of the Int. Conf. on Data Engineering, 2006
• Decompression is extremely fast
• Compression is not the best but still good

24. PForDelta Coding (PFD, by S. Heman, etc)
• Using 2 bits to encode 128 numbers 3 42 2 3 3 1 1 … 3 3 23 1 2 11 10 11 11 01 01 … 11 11 01 10 42 23
Problem:
• We have to insert extra exceptions if two consecutive exceptions are far from
each other
a block of 128 numbers

25. First Improvement of PForDelta (NewPFD)
• Using b (e.g., 2) bits to encode 128 numbers 3 42 2 3 3 1 1 … 3 3 23 1 2 11 10 11 11 01 01 … 11 11 01 10 42 23
lower 2 bits of 23
higher bits of 23
• Offset array
• Exception array
high 10 11 … 01
low
S9, S16

26. • How to select the number of bits b for each block?
Second Improvement of PForDelta (OptPFD)
• How to select the number of bits b for each block?
• The original PFD uses a constant value for b
• A constant b is not good enough
• b , waster more bits to encode each number
• b , resulting in more exceptions
• The best b should achieve the the best tradeoff between the
compressed size and the decompresion speed
• Difficult to formulize this

27. Second Improvement of PForDelta (OptPFD)
How to select the number of bits b for each block?
• Derive a global table for
the choice of b -> tradeoff btw size and speed
• Based on the table, we can dynamically choose b
during query processing to achieve the best overall
performance (We will talk this in more detail later)

28. Global table for OptPFD
We want
• Decompression speed is above 1200 Million DocIDs/second
• Compressed size is no more than 1.5 MB/query

29. Over 1 billion docIDs/second ! Million docIDs/second
PForDelta is Extremely Fast for Decompression!
Over 1 billion docIDs/second !
Million docIDs/second

30. DocID Compression – with Re-ordering
Only 1.47 bit/docID

31. Frequency Compression – Related Work
• Few papers especially focusing on it
• Usually just choose the methods that work well for compressing small numbers, such as Gamma coding, or Rice coding
• No one has studied it for web indexes under document reordering

32. • Normally frequencies are quite small values
Frequency Compression – Unique Features
• Normally frequencies are quite small values
• Unlike docIDs, they are not in sorted order
(this has nothing to do with re-ordering)
• Re-ordering make them clustered, but we cannot directly take advantage of the clustering as docIDs since we cannot take gaps of them

33. Frequency Compression - My Algorithms
• However, we still want to take advantage of the clustering property brought by reordering
• Idea: When things are clustered but unsorted, we can use some
transform to make the frequency values smaller
• Preprocessing techniques:
• Move to front (MTF)
(Bently, burrows-wheeler compression, Comm. Of the ACM, 1986)
• Most likely next (MLN)

34. Our Preprocessing Algorithms: MTF / MLN
• Idea: Use indexes of previously occurrences to encode the current number.
• Move to front (MTF) : Keep an additional index array, and do Move-To-Front operation during encoding
• Most likely next (MLN): Keeps a small table that stores for each value which values are most likely to follow, sort values by their likelihoods, and then use indexes in the table to represent the values
• Why better?
Values of indexes of frequencies are smaller when frequencies are clustered !

35. Compressed size (MBytes/query)
Results – Compressed Size
Only 1.54 bit/freq
Compressed size (MBytes/query)

36. million frequencies/second
Results – Decompression Speed
million frequencies/second

37. Compressed Size for the Entire Indexes
• IPC, NewPFD, OptPFD
• Compressed index size (MB) on the entire GOV2 data set, containing 25.2
Million web pages and the uncompressed size of it is 500GB!!!
• IPC: 3.45GB, our optimized PFD is 3.88GB and super fast!

38. • We must decompress the entire block of docIDs
Query Processing – Skipping
decompress
skip
skip 14 23 … 43 67 77 … 89
100
123 …
150
block3 (compressed )
block1 (compressed )
block2 (compressed )
• We must decompress the entire block of docIDs
• Search 123:

39. Query Processing – Impact of Reordering
OptPFD
• Query processing is faster !
• Reason:
• After sorting by URLs, docIDs are clustered into fewer blocks!
• Therefore, fewer blocks of docIDs need to be decompressed

40. Then, How To Compress Indexes?
• Tradeoff : compressed size vs decompression speed
• Mixed Methods
• Frequently used indexes – faster decompression
e.g., PForDelta
• Non-frequently used indexes – smaller compressed size
e.g., IPC

41. One Example of Using Mixed Methods
• Goal:
• The overall index size is minimized
• While average time per query < a given time limit T
PForDelta ?
Or IPC?
madrid , 777, 11437,….
museum , 1234, 4356, 12457,….
spain , 19, 29, 98, 143, 777, ...
barcelona , 457, 777, 789, ...
mall , 777, 2134, 3970, ...
university , 256, 372, 511, 777, 1000, ...
• Solution:
• Choose the list and compression methods that gives you the smallest
increase in index size per time saved
• Note: this can be easily integrated into the normal process
of index construction, especially when indexes are built block-wise

42. Mixed Methods with OptPFD and IPC

43. Conclusions – How to Compress Web Indexes?
Previous researchers found:
• Reordering improve docID compression using standard compression methods
In our paper: Given a particular ordering – sorting by URLs
• DocID:
• We proved this (sorting by URLs is better) by testing on most existing
compression methods.
• We proposed optimized PForDelta which achieves the best performance in
terms of both compressed size and decompression speed
• Frequency
• We proposed MTF/MLN to reduce the compressed size
• Query processing (QP)
• We found that reordering improves QP since less number of docIDs/freqs need to be decoded
• Mixed Methods: We propose a hybrid method to try to achieve the best tradeoff between
• The compressed size
• Decompresion speed

44. Thank you !