1 CS 430: Information Discovery Lecture 4 Data Structures for Information Retrieval

2 Course Administration The Wednesday evening classes have been moved to Hollister 110. Introduction to Perl Classes will be held on Wednesday evenings, September 19 and October 3. Before the first class, look at the CS 430 web site and attempt the (optional) Assignment 0. (These classes and Assignment 0 are optional.)

3 Inverted Files: Search for Keywords Index file: Stores list of terms (keywords). Designed for rapid searching and processing range queries. May be held in memory. Postings file: Stores list of postings for each term. Designed for rapid evaluation of Boolean operators. May be stored sequentially. Document file: [Repositories for the storage of document collections are covered in CS 502.]

4 Index File Structures: Binary Tree elk cathog beedogfox ant gnu

5 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

6 Binary Tree Calculation of maximum depth of tree. Illustrates importance of balanced trees. Worst case: depth = n O(n) Ideal case: depth = log(n + 1)/log 2 O(log n)

7 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 in- order 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.

8 Right Threaded Binary Tree From: Robert F. Rossa

9 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 k i is the i th key in a given internal node -> all keys in the (i-1) th child are smaller than k i -> all keys in the i th child are bigger than k i All leaves are at the same depth

10 B + -tree B + -tree: A B-tree is used as an index Data is stored in the leaves of the tree, known as buckets D 9 D D 54 D D Example: B + -tree of order 2, bucket size 4

11 B-tree Discussion For a discussion of B-trees, see Frake, Section 2.3.1, pages B-trees combine fast retrieval with moderately efficient updating. Bottom-up updating is usual fast, but may require recursive tree climbing to the root. The main weakness is poor storage utilization; typically buckets are only 0.69 full. Various algorithmic improvements increase storage utilization at the expense of updating performance.

12 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

13 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.

14 Signature Files Example WordSignature free text block signature F = 12 bits in a signature m = 4 bits per word D = 2 words per block

15 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, F d. Frake, Section 4.2, page 47 discussed how to minimize F d. The rest of this chapter discusses enhancements to the basic algorithm.

16 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.

17 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.

18 Tries: Suffix Tree Example: suffix tree for the following words: begin beginning between bread break b e rea gin tween d k _ ning

19 Tries: Sistrings A binary example String: Sistrings:

20 Tries: Lexical Ordering Unique string indicated in blue

21 Trie: Basic Concept

22 Patricia Tree Single-descendant nodes are eliminated. Nodes have bit number.

23 Oxford English Dictionary