Transcript PowerPoint

CS 430: Information Discovery
Lecture 6
Data Structures for Information Retrieval
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Indexing Subsystem
Documents
text
assign document IDs
document
numbers
and *field
numbers
break into words
words
*Indicates
optional
operation.
from Frakes,
page 7
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documents
stoplist
non-stoplist
words
stemming*
stemmed
words
term weighting*
terms with
weights
Index
database
Organization of Inverted Files
Index file
Postings file
Term Pointer to
postings
ant
bee
cat
dog
elk
fox
gnu
hog
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Inverted
lists
Documents file
Documents File for Web Search System
Indexes are built using a web crawler, which retrieves each page
on the web (or a subset). After indexing each page is discarded,
unless stored in a cache. In addition to the usual index file
(word list) and postings files the indexing system stores:
1. List of URLs of pages indexed.
This list is used instead of the documents file.
2. Short abstract of each page (optional).
Used to describe the page when lists of hits returned to user.
3. For each page, list of URLs of pages it links to.
This data structure is used for reference pattern ranking, either
static (e.g., PageRank), or dynamic.
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Index File Structures: Linear Index
Advantages
Can be searched quickly, e.g., by binary search, O(log n)
Good for sequential processing, e.g., comp*
Convenient for batch updating
Economical use of storage
Disadvantages
Index must be rebuilt if an extra term is added
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Index File Structures: Binary Tree
Input: elk, hog, bee, fox, cat, gnu, ant, dog
elk
bee
ant
hog
cat
fox
dog
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gnu
Binary Tree
Advantages
Can be searched quickly
Convenient for batch updating
Easy to add an extra term
Economical use of storage
Disadvantages
Poor for sequential processing, e.g., comp*
Tree tends to become unbalanced
If the index is held on disk, important to optimize
the number of disk accesses
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Binary Tree
Calculation of maximum depth of tree.
Worst case: depth = n
O(n)
Ideal case: depth = log(n + 1)/log 2
O(log n)
Illustrates importance of balanced trees.
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Right Threaded Binary Tree
Threaded tree:
A binary search tree in which each node uses an
otherwise-empty left child link to refer to the node's inorder predecessor and an empty right child link to refer
to its in-order successor.
Right-threaded tree:
A variant of a threaded tree in which only the right
thread, i.e. link to the successor, of each node is
maintained.
Knuth vol 1, 2.3.1, page 325.
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Right Threaded Binary Tree
From: Robert F. Rossa
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B-trees
B-tree of order m:
A balanced, multiway search tree:
• Each node stores many keys
• Root has between 2 and 2m keys.
All other internal nodes have between m and 2m keys.
• If ki is the ith key in a given internal node
-> all keys in the (i-1)th child are smaller than ki
-> all keys in the ith child are bigger than ki
• All leaves are at the same depth
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B-trees
B-tree example (order 2)
50 65
55 59
10 19 35
36 47
1 5 8 9
12 14 18
21 24 28
70 90 98
66 68
91 95 97
72 73
Every arrow points to a node containing between 2 and 4 keys.
A node with k keys has k + 1 pointers.
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B+-tree
B+-tree:
• A B-tree is used as an index
• Data is stored in the leaves of the tree, known as buckets
50 65
10 25
... D9
55 59
D51 ... D54
70 81 90
D66...
Example: B+-tree of order 2, bucket size 4
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D81 ...
B-tree Discussion
For a discussion of B-trees, see Frake, Section 2.3.1,
pages 18-20.
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B-trees combine fast retrieval with moderately
efficient updating.
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Bottom-up updating is usual fast, but may require
recursive tree climbing to the root.
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The main weakness is poor storage utilization;
typically buckets are only 0.69 full.
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Various algorithmic improvements increase storage
utilization at the expense of updating performance.
Signature Files: Sequential Search
without Inverted File
Inexact filter: A quick test which discards many of the
non-qualifying items.
Advantages
• Much faster than full text scanning -- 1 or 2 orders
of magnitude
• Modest space overhead -- 10% to 15% of file
• Insertion is straightforward
Disadvantages
• Sequential searching no good for very large files
• Some hits are false hits
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Signature Files
Signature size. Number of bits in a signature, F.
Word signature. A bit pattern of size F with m bits set
to 1 and the others 0.
The word signature is calculated by a hash function.
Block. A sequence of text that contains D distinct
words.
Block signature. The logical OR of all the word
signatures in a block of text.
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Signature Files
Example
Word
Signature
free
text
001 000 110 010
000 010 101 001
block signature
001 010 111 011
F = 12 bits in a signature
m = 4 bits per word
D = 2 words per block
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Signature Files
A query term is processed by matching its signature
against the block signature.
(a) If the term is in the block, its word signature will
always match the block signature.
(b) A word signature may match the block signature,
but the word is not in the block. This is a false hit.
The design challenge is to minimize the false drop
probability, Fd .
Frake, Section 4.2, page 47 discussed how to minimize
Fd. The rest of this chapter discusses enhancements to
the basic algorithm.
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Search for Substring
In some information retrieval applications, any substring can
be a search term.
Tries, implemented using suffix trees, provide
lexicographical indexes for all the substrings in a document
or set of documents.
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Tries: Search for Substring
Basic concept
The text is divided into unique semi-infinite strings, or
sistrings. Each sistring has a starting position in the text,
and continues to the right until it is unique.
The sistrings are stored in (the leaves of) a tree, the suffix
tree. Common parts are stored only once.
Each sistring can be associated with a location within a
document where the sistring occurs. Subtrees below a
certain node represent all occurrences of the substring
represented by that node.
Suffix trees have a size of the same order of magnitude as
the input documents.
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Tries: Suffix Tree
Example: suffix tree for the
following words:
begin
beginning
between
bread
break
b
e
gin
_
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rea
tween
ning
d
k
Tries: Sistrings
A binary example
String:
Sistrings:
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01 100 100 010 111
1
2
3
4
5
6
7
8
01 100 100 010 111
11 001 000 101 11
10 010 001 011 1
00 100 010 111
01 000 101 11
10 001 011 1
00 010 111
00 101 11
Tries: Lexical Ordering
7
4
8
5
1
6
3
2
00 010 111
00 100 010 111
00 101 11
01 000 101 11
01 100 100 010 111
10 001 011 1
10 010 001 011 1
11 001 000 101 11
Unique string indicated in blue
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Trie: Basic Concept
1
0
0
1
1
0
2
0
1
7
0
1
5
1
0
0
0
0
4
25
6
1
8
1
3
Patricia Tree
1
0
2
0
7
0
4
2 1
1
3
0
1
10
0
5
5
00
3
4
1
1
0
2
1
6
1
8
Single-descendant nodes are eliminated.
Nodes have bit number.
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Oxford English Dictionary
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