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### Signature Files

Information Retrieval: Data Structures and Algorithms

by W.B. Frakes and R. Baeza-Yates (Eds.) Englewood Cliffs, NJ: Prentice Hall, 1992.

(Chapters 4)

Signature Files

- Characteristics
- Word-oriented index structures based on hashing
- Low overhead (10%~20% over the text size) at the cost of forcing a sequential search over the index
- Suitable for not very large texts
- Inverted files outperform signature files for most applications

Structure

- Use superimposed coding to create signature.
- Each text is divided into logical blocks.
- A block containsn distinct non-common words.
- Each word yields “word signature”.
- A word signature is aB-bit pattern, with m 1-bit.
- Each word is divided into successive, overlapping triplets. e.g. free --> fr, fre, ree, ee
- Each such triplet is hashed to a bit position.
- The word signatures are OR’ed to form block signature.
- Block signatures are concatenated to form the document signature.

Example

- Example (n=2, B=12, m=4)word signaturefree 001 000 110 010text 000 010 101 001block signature 001 010 111 011
- Search
- Use hash function to determine the m 1-bit positions.
- Examine each block signature for 1’s bit positions that the signature of the search word has a 1.

False Drop

- false alarm (false hit, or false drop) Fdthe probability that a block signature seems to qualify, given that the block does not actually qualify.Fd = Prob{signature qualifies/block does not}
- For a given value of B, the value of m that minimizes the false drop probability is such that each row of the matrix contains “1”s with probability 0.5.Fd = 2-mm = B ln2/n

Sequential Signature File (SSF)

documents

assume documents span exactly one logical block

the size of document signature F = the size of block signature B

Classification of Signature-Based Methods

- CompressionIf the signature matrix is deliberately sparse, it can be compressed.
- Vertical partitioningStoring the signature matrix column-wise improves the response time on the expense of insertion time.
- Horizontal partitioningGrouping similar signatures together and/or providing an index on the signature matrix may result in better-than-linear search.

Classification of Signature-Based Methods

- Sequential storage of the signature matrix
- without compression sequential signature files (SSF)
- with compression bit-block compression (BC) variable bit-block compression (VBC)
- Vertical partitioning
- without compression bit-sliced signature files (BSSF, B’SSF) frame sliced (FSSF) generalized frame-sliced (GFSSF)

Classification of Signature-Based Methods(Continued)

- with compression compressed bit slices (CBS) doubly compressed bit slices (DCBS) no-false-drop method (NFD)
- Horizontal partitioning
- data independent partitioning Gustafson’s method partitioned signature files
- data dependent partitioning 2-level signature files 5-trees

Criteria

- the storage overhead
- the response time on single word queries
- the performance on insertion, as well as whether the insertion maintains the “append-only” property

Compression

- idea
- Create sparse document signatures on purpose.
- Compress them before storing them sequentially.
- Method
- Use B-bit vector, where B is large.
- Hash each word into one (or k) bit position(s).
- Use run-length encoding (McIlroy 1982).

Compression using run-length encoding

data 0000 0000 0000 0010 0000

base 0000 0001 0000 0000 0000

management 0000 1000 0000 0000 0000

system 0000 0000 0000 0000 1000

block signature 0000 1001 0000 0010 1000

L2

L3

L4

L5

L1

[L1] [L2] [L3] [L4] [L5]

where [x] is the encoded vale of x.

search: Decode the encoded lengths of all the preceding intervals

example: search “data”

(1) data ==> 0000 0000 0000 0010 0000

(2) decode [L1]=0000, decode [L2]=00, decode [L3]=000000

disadvantage: search becomes low

Data Structure:

(1) The sparse vector is divided into groups of consecutive bits

(bit-blocks).

(2) Each bit block is encoded individually.

Algorithm:

Part I. It is one bit long, and it indicates whether there are any

“1”s in the bit-block (1) or the bit -block is (0). In

the latter case, the bit-block signature stops here.

0000 1001 0000 0010 1000

0 1 0 1 1

Part II. It indicates the number s of “1”s in the bit-block. It consists

of s-1 “1” and a terminating zero.

10 0 0

Part III. It contains the offsets of the “1”s from the beginning of the

bit-block.

0011 10 00

說明：4bits，距離為0, 1, 2, 3，編碼為00, 01, 10, 11

block signature: 01011 | 10 00 | 00 11 10 00

(Continued)

Search “data”

(1) data ==> 0000 0000 0000 0010 0000

(2) check the 4th block of signature 01011 | 10 0 0 | 00 11 10 00

(4) OK, there is at least one setting in the 4th bit-block.

(5) Check furthermore. “0” tells us there is only one setting in

the 4th bit-clock. Is it the 3rd bit?

(6) Yes, “10” confirms the result.

Discussion:

(1) Bit-block compression requires less space than Sequential

Signature File for the same false drop probability.

(2) The response time of Bit-block compression is lightly less

then Sequential Signature File.

Vertical Partitioning

- ideaavoid bringing useless portions of the document signature in main memory
- methods
- store the signature file in a bit-sliced form or in a frame-sliced form
- store the signature matrix column-wise to improve the response time on the expense of insertion time

Bit-Sliced Signature Files (BSSF)

Transposed bit matrix

documents

(document signature)

transpose

documents

represent

F bit-files

search: (1) retrieve m bit-files.

e.g., the word signature of free is 001 000 110 010

the document contains “free”: 3rd, 7th, 8th, 11th bit are set

i.e., only 3rd, 7th, 8th, 11th files are examined.

(2) “and” these vectors. The 1s in the result N-bit vector

denote the qualifying logical blocks (documents).

(3) retrieve text file through pointer file.

insertion: require F disk accesses for a new logical block (document),

one for each bit-file, but no rewriting

Frame-Sliced Signature File (FSSF)

- Ideas
- random disk accesses are more expensive than sequential ones
- force each word to hash into bit positions that are closer to each other in the document signature
- these bit files are stored together and can be retrieved with a few random accesses
- Procedures
- The document signature (F bits long) is divided into k frames of s consecutive bits each.
- For each word in the document, one of the k frames will be chosen by a hash function.
- Using another hash function, the word sets m bits in that frame.

Frame-Sliced Signature File (Cont.)

documents

frames

Each frame will be kept in consecutive disk blocks.

FSSF (Continued)

- Example (n=2, B=12, s=6, f=2, m=3)Word Signature free 000000 110010 text 010110 000000 doc. signature 010110 110010
- Search
- Only one frame has to be retrieved for a single word query. I.E., only one random disk access is required.e.g., search documents that contain the word “free”->because the word signature of “free” is placed in 2nd frame,only the 2nd frame has to be examined.
- At most k frames have to be scanned for an k word query.
- Insertion
- Only f frames have to be accessed instead of F bit-slices.

Vertical Partitioning with Compression

- idea
- create a very sparse signature matrix
- store it in a bit-sliced form
- compress each bit slice by storing the position of the 1s in the slice.

Compressed Bit Slices (CBS)

- Rooms for improvements
- Searching
- Each search word requires the retrieval of m bit files.
- The search time could be improved if m was forced to be “1”.
- Insertion
- Require too many disk accesses (equal to F, which is typically 600-1000).

Compressed Bit Slices (CBS)(Continued)

documents

- Let m=1. To maintain the same false drop probability, F has to be increased.
- To compress each bit file, we store only the positions of the “1”s.
- For unpredictable number of “1”s, we store them in buckets of size Bp.

Size of a signature

Sparse bit matrix

- The directory (hash table) is sparse
- The actual word is stored nowhere
- Simple structure

Obtain the pointers to the

relevant documents from

buckets

Hash a word to

obtain bucket address

h(“base”)=30

Idea:

compress

the sparse

directory

當S變小

碰撞在一

起的的機會

變大，採用

中間buckets

為了區別

真碰撞和假

碰撞，多了

一個hash

function

Distinguish synonyms partially.

Follow the pointers of posting

buckets to retrieve the qualifying

documents.

h2(“base”)=011

h1(“base”)=30

To distinguish between synonyms completely.

Using pointer to the word

in the text file

1. Goal: group the signatures into sets, partitioning the signature

matrix horizontally.

2. Grouping criterion

documents

Partitioned Signature Files

- Using a portion of a document signature as a signature key to partition the signature file.
- All signatures with the same key will be grouped into a so-called “module”.
- When a query signature arrives,
- examine its signature key and look for the corresponding modules
- scan all the signatures within those modules that have been selected

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