Indexing

LBSC 708A/CMSC 838L

Session 7, October 23, 2001

Philip Resnik

Agenda

• Questions

• Finish up evaluation from last time

• Computational complexity

• Inverted indexes

• Question answering and predictive annotation

• Two minute paper

Supporting the Search Process

SourceSelection

Search

Query

Selection

Ranked List

Examination

Document

Delivery

Document

QueryFormulation

IR System

Indexing Index

Acquisition Collection

Some Questions for Today

• How long will it take to find a document?– Is there any work we can do in advance?

• If so, how long will that take?

• How big a computer will I need?– How much disk space? How much RAM?

• What if more documents arrive?– How much of the advance work must be repeated?

– Will searching become slower?

– How much more disk space will be needed?

A Cautionary Tale

• Searching is easy - just ask Microsoft!– “Find” can search my 1 GB disk in 30 seconds

• Well, actually it only looks at the file names...

• How long do you think find would take for– A 100 GB disk?– For the World Wide Web?

• Computers are getting faster, but…– How does AltaVista give answers in 5 seconds?

Find “complex” in the dictionary

marsupial

belligerent

complex

marsupial

belligerent

complex

arcade

astronomical

mastiff

relatively

relaxation

resplendent

Computational Complexity

• One question: how long does stuff take?

• Another: how much space do you need?

• Things you need to know:– What is the size of the input? (usu. n)

• What aspects of the input are we paying attention to?

– How is the input represented?– How is the output represented?– What are the internal data structures?– What is the algorithm?

Worst Case Complexity

0

500

1000

1500

2000

2500

3000

3500

4000

4500

10 20 30 40

10n

n^2

100n

0

20000

40000

60000

80000

100000

120000

140000

50 200 350

10n

n^2

100n

100n+25263

10n: O(n)100n: O(n)100n+25263: O(n)

n2: O(n2)n2+45662: O(n2)

Hierarchy of Complexity• Constant, i.e. O(1)

n doesn’t matter • Sublinear, e.g. O(log n)

n = 65536 log n = 16• Linear, i.e. O(n)

n = 65536 n = 65536• Polynomial, e.g. O(n3)

n = 65536 n3 = 281,474,976,710,656• Exponential, e.g. O(2n)

n = 65536 beyond astronomical

Example: matching URLshttp://goodstuff.com/eng/menu-en.htmhttp://goodstuff.com/eng/prods.htmhttp://goodstuff.com/eng/help.htm…

http://goodstuff.com/fra/menu-fr.htmhttp://goodstuff.com/fra/prods.htmhttp://goodstuff.com/fra/help.htm…

P patterns

M URLs

en fr

en fra

eng fr

eng fre

… …

N URLs

• Generate alternatives and look them up– Store French URLs in a hash table, takes O(M) time– For each English URL, substitute all possible patterns…

http://goodstuff.com/eng/menu-en.htm

http://goodstuff.com/fra/menu-en.htm

http://goodstuff.com/fra/mfru-en.htm

http://goodstuff.com/fra/menu-fr.htm

http://goodstuff.com/fra/mfru-fr.htm

…

Example, cont’d

Exponential!O(N * 2k)

Example, cont’d

• Alternative: use clever string matching– Can compare a URL e to URL f in O(L2) time,

where L is length of URLs in characters (small!)

• Requires O(N*M) comparisons of URLs– Too slow! (Sometimes N and M are 1000’s…)

• Speculation: O(M+N) algorithm if you store URLs in a trie?

One Good Trie?menu-fr2

mercredi

merci

m

e

n

u

-

f

r

r

c

r

e

d i2

i

menu-en2

en, eng

Looks promising, but theobvious solution still leadsto an exponential algorithm.

Agenda

• Questions

• Computational complexity

• Inverted indexes

• Question answering and predictive annotation

• Two minute paper

The “Inverted File” Trick

• Organize the bag of words matrix by terms– You know the terms that you are looking for

• Look up terms like you search dictionaries– For each letter, jump directly to the right spot

• For terms of reasonable length, this is very fast

– For each term, store the document identifiers• For every document that contains that term

• At query time, use the document identifiers– Consult a “postings file”

An Example

quick

brown

fox

over

lazy

dog

back

now

time

all

good

men

come

jump

aid

their

party

00110000010010110

01001001001100001

Term Doc

1

Doc

2

00110110110010100

11001001001000001

Doc

3D

oc 4

00010110010010010

01001001000101001

Doc

5D

oc 6

00110010010010010

10001001001111000

Doc

7D

oc 8

A

B

C

FD

GJLMNOPQ

T

AIALBABR

THTI

4, 82, 4, 61, 3, 7

1, 3, 5, 72, 4, 6, 8

3, 53, 5, 7

2, 4, 6, 83

1, 3, 5, 72, 4, 82, 6, 8

1, 3, 5, 7, 86, 81, 3

1, 5, 72, 4, 6

PostingsInverted File

The Finished Product

quick

brown

fox

over

lazy

dog

back

now

time

all

good

men

come

jump

aid

their

party

Term

A

B

C

FD

GJLMNOPQ

T

AIALBABR

THTI

4, 82, 4, 61, 3, 7

1, 3, 5, 72, 4, 6, 8

3, 53, 5, 7

2, 4, 6, 83

1, 3, 5, 72, 4, 82, 6, 8

1, 3, 5, 7, 86, 81, 3

1, 5, 72, 4, 6

PostingsInverted File

What Goes in a Postings File?

• Boolean retrieval– Just the document number

• Ranked Retrieval– Document number and term weight (TF*IDF, ...)

• Proximity operators– Word offsets for each occurrence of the term

• Example: Doc 3 (t17, t36), Doc 13 (t3, t45)

How Big Is the Postings File?

• Very compact for Boolean retrieval– About 10% of the size of the documents

• If an aggressive stopword list is used!

• Not much larger for ranked retrieval– Perhaps 20%

• Enormous for proximity operators– Sometimes larger than the documents!

• But access is fast - you know where to look

Building an Inverted Index• Simplest solution is a single sorted array

– Fast lookup using binary search– But sorting large files on disk is very slow– And adding one document means starting over

• Tree structures allow easy insertion– But the worst case lookup time is linear

• Balanced trees provide the best of both– Fast lookup and easy insertion– But they require 45% more disk space

Starting a B+ Tree Inverted File

now timegoodall

aaaaa now

Now is the time for all good …

Adding a New Term

now timegoodall

aaaaa now

Now is the time for all good men …

aaaaa men

men

How Big is the Inverted Index?

• Typically smaller than the postings file– Depends on number of terms, not documents

• Eventually almost all terms will be indexed– But the postings file will continue to grow

• Postings dominate asymptotic space complexity– Linear in the number of documents

• Assuming that the documents remain about the same size

Some Facts About Disks

• It takes a long time to get the first byte– A Pentium can do 1,000,000 operations in 10 ms

• But you can get 1,000 bytes just about as fast– 40 MB/sec transfer rates are typical

• So it pays to put related stuff in each “block”– M-ary trees B+ are better than binary B+ trees

• Time complexity is measured in disk blocks read– Since computing time is negligible by comparison

Indexing and Searching

• Indexing– Walk the inverted file, splitting if needed– Insert into the postings file in sorted order– Hours or days for large collections

• Query processing– Walk the inverted file– Read the postings file– Manipulate postings based on query– Seconds, even for enormous collections

Agenda

• Questions

• Computational complexity

• Inverted indexes

• Question answering and predictive annotation

• Two minute paper

Question Answering

• “In what year did Edison patent the light bulb?”– Is the user really looking for a list of documents?

• Better answer: excerpt containing the answer… after Edison’s patenting of the light bulb in 1879…

• Question words become very important!– “How much money did Clinton earn in 1999?”

QA and Predictive Annotation• Predictive annotation (Prager et al.):

– Infer possible question types within documents

– Index them along with the terms

– At search time, map question words to question types and include them in the query

• Requires– Identification of entities and their categories

– Indexing multiple items at one location

– Analysis of queries to derive question types

• Works pretty well!

Predictive Annotation, cont’d

In reality, at the time of Edison’s 1879 patent, the light bulb

had been in existence for some five decades ….

TIMEPERSON

Who patented the light bulb?When was the light bulb patented?

What did Thomas Edison patent?

patent light bulb PERSONpatent light bulb TIME

???

In what year was the light bulb patented?

Summary

• Slow indexing yields fast query processing

• We use extra disk space to save query time– Index space is in addition to document space– Time and space complexity must be balanced

• Disk block reads are the critical resource– Fast disks are more useful than fast computers

One Minute Paper

• Suppose insertions of new documents are more common than getting new queries. For example, imagine filtering news stories as they arrive, based on a small set of queries that describe long-standing topics of interest. What kind of an index should you build?

• What was the muddiest point in today’s lecture?