SPIRE 2017

Transcript

1. PRACTICAL IMPLEMENTATION OF
   SPACE-EFFICIENT DYNAMIC
   KEYWORD DICTIONARIES
   Shunsuke Kanda, Kazuhiro Morita and Masao Fuketa
   26th–29th Sep. 2017, Palermo, ITALY
   24th International Symposium on
   String Processing and Information Retrieval
   Tokushima Univ.
   JAPAN
   

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2. Keyword Dictionaries
   2
   ¨ Associative array with string keys
   ¤ Such as std::map in C++
   ¨ Recent target data are massive [Martínez-Prieto+ 16]
   ¤ NLP, IR, Web Graph, RDF, Bioinformatics, etc.
   String
   Processing
   And
   Information
   Retrieval
   1
   2
   3
   4
   5
   Information → 4
   Keyword Value
   

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3. Keyword Dictionaries (cont.)
   3
   ¨ Research objective
   ¤ Engineering practical implementation of space-efficient
   dynamic keyword dictionaries
   libCSD
   path_decomposed_tries
   Marisa-trie
   Xcdat
   Judy
   Hat-Trie
   libart
   Cedar
   Static Dynamic
   LARGE
   SMALL
   Dictionary size
   

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4. Data structures related to our work
   Trie & Path Decomposition
   4
   

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5. Trie
   5
   ¨ Edge-labeled tree for storing a set of strings
   ¤ Search time: O(k) time where k denotes the query length
   Keyword Value
   ideal$ 1
   ideology$ 2
   tec$ 3
   technology$ 4
   tie$ 5
   trie$ 6
   t
   ide
   rie$
   ec
   hnology$
   ology$
   ie$
   6
   4
   1 2 5
   3
   al$
   $
   Search technology$
   ※ Strictly speaking, this tree is Patricia Trie
   

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6. Path Decomposition [Ferragina+ 08]
   6
   ¨ Procedure of transforming a trie to improve the cache
   efficiency by lowering the height
   ¤ Application: Static compressed dictionaries [Grossi+ 14]
   technology$
   i r $
   i
   t
   ide
   rie$
   ec
   hnology$
   ology$
   ie$
   al$
   $
   Path-Decomposed Trie (PDT)
   

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7. New implementation of space-efficient dynamic
   keyword dictionaries
   DynPDT: Dynamic Path-Decomposed Trie
   7
   

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8. Incremental Path Decomposition
   8
   ¨ Incrementally constructing a PDT
   technology$
   v1
   EX1 Add key technology$ to an empty dictionary
   

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9. Incremental Path Decomposition (cont.)
   9
   ¨ Incrementally constructing a PDT
   technology$
   v1
   (5, i)
   v2
   EX2 Add key technics$ 012345
   technics$
   cs$
   

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10. Incremental Path Decomposition (cont.)
    10
    ¨ Incrementally constructing a PDT
    technology$
    cs$
    (5, i)
    v1
    v2
    (0, q)
    v3
    EX3 Add key technique$ 012345
    technique$
    Dynamic Path-Decomposed Trie (DynPDT)
    0
    que$
    ue$
    

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11. Implementation Approaches
    11
    ¨ Tree representation (with edge labels)
    ¤ Using a compact dynamic trie, or m-Bonsai [Poyias+ 14]
    ¨ Node label management
    ¤ Separately storing the labels from the tree structure
    ¤ Pointer management is important
    technology$
    cs$
    ue$
    (5, i)
    (0, q)
    v1
    v2
    v3
    technology$
    technics$
    technique$
    

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12. Implementation Approaches
    12
    ¨ Tree representation (with edge labels)
    ¤ Using a compact dynamic trie, or m-Bonsai [Poyias+ 14]
    ¨ Node label management
    ¤ Separately storing the labels from the tree structure
    ¤ Pointer management is important
    technology$
    cs$
    ue$
    (5, i)
    (0, q)
    v1
    v2
    v3
    technology$
    technics$
    technique$
    

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13. Plain Label Management (PLAIN)
    13
    ¨ Introducing pointers to each label
    ¤ Using array P where P[v] has the pointer of node v
    ¤ GOOD: Accessing a label in constant time
    ¤ BAD: Using 64 bits for each slot (too large)
    v4
    v1
    v2
    v6
    v3
    P
    technology$ cs$ ue$
    lly$ cal$
    

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14. Compact Label Management (BITMAP)
    14
    ¨ Reducing the pointer overhead
    ¤ Grouping the node labels into ℓ labels over the IDs
    ¤ Concatenating the labels for each group
    n #pointers is divided by ℓ
    ¤ Using bit array B such that B[v] = 1 if node v has a label
    v4
    v1
    v2
    v6
    v3
    B 1 0 1 1 0 1 0 1
    P
    3lly10technology2cs 3cal2ue
    Group 1 Gourp 2
    In ℓ = 4
    

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15. Compact Label Management (BITMAP)
    15
    ¨ Access procedure
    ¤ Calculating the target label position in the group
    n Constant time using Popcnt
    ¤ Scanning the concatenated label string until the target label
    n O(ℓ) time using Skipping technique (or constant time)
    v4
    v1
    v2
    v6
    v3
    B 1 0 1 1 0 1 0 1
    P’
    3lly10technology2cs 3cal2ue
    In ℓ = 4
    Popcnt(B[v4
    ..v1
    ]) = 2
    Label of node v1
    Skipping
    

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16. Space & Time
    Experiments
    16
    

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17. Settings
    17
    ¨ Machine
    ¤ Intel Xeon E5540 @2.53 GHz CPU，32GB RAM
    ¤ Ubuntu Server 16.40 LTS
    ¨ Datasets
    ¤ Wiki: Titles from English Wikipedia
    n Size: 227MiB, Keys: 11.5M, Ave. length: 20.7 bytes
    ¤ WebBase: URLs from WebBase crawler
    n Size: 6.6GiB, Keys: 118.1M, Ave. length: 60.2 bytes
    ¤ LUBM: URIs from LUBM benchmark
    n Size: 3.1GiB, Keys: 52.6M, Ave. length: 63.7 bytes
    

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18. Settings (cont.)
    18
    ¨ Data structures
    ¤ DynPDT: PLAIN and BITMAP (ℓ = 16)
    ¤ m-Bonsai: As a naïve trie (not as a dictionary)
    ¤ Judy: Trie dictionary developed by HP-Lab.
    ¤ HAT-trie: Hybrid dictionary of trie and array hashing
    ¤ Cedar: Minimal-prefix double-array trie dictionary
    ¨ Details
    ¤ Language: C++
    ¤ Associated value type: int (4 bytes)
    ¤ Keyword order: random
    

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19. Results for Space Usage
    19
    46.6 47.5
    45.0
    18.8
    21.0
    13.8
    23.6
    29.3
    11.4
    50.5
    53.5
    33.9
    40.2
    68.9
    64.7
    41.1
    29.7
    0
    10
    20
    30
    40
    50
    60
    70
    80
    Wiki WebBase LUBM
    Bytes per keyword
    DynPDT+PLAIN DynPDT+BITMAP m-Bonsai Judy HAT-trie Cedar
    N/A
    3.3x
    4.7x
    

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20. Results for Insertion Time
    20
    1.14
    2.37
    1.65
    1.57
    2.93
    1.99
    2.22
    7.69
    4.80
    1.06
    2.94
    1.53
    1.13
    1.75
    2.58
    1.07
    2.50
    0
    1
    2
    3
    4
    5
    6
    7
    8
    9
    Wiki WebBase LUBM
    Micro sec. per keyword
    DynPDT+PLAIN DynPDT+BITMAP m-Bonsai Judy HAT-trie Cedar
    N/A
    2.6x
    

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21. Results for Search Time
    21
    1.13
    2.20
    1.12
    1.61
    2.74
    1.43
    2.06
    8.30
    3.08
    0.88
    2.42
    0.79
    0.35
    0.80
    0.51
    0.69 0.69
    0
    1
    2
    3
    4
    5
    6
    7
    8
    9
    Wiki WebBase LUBM
    Micro sec. per keyword
    DynPDT+PLAIN DynPDT+BITMAP m-Bonsai Judy HAT-trie Cedar
    N/A
    4.6x
    

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22. Summary
    22
    ¨ Proposing a new dictionary structure, or DynPDT
    ¤ GOOD: Space efficiency, BAD: Time performance
    ¤ The traversal speed of m-Bonsai is a bottleneck
    n Xorshift random number generator can solve this problem
    ¨ Future work
    ¤ To improve m-Bonsai or engineer an alternative trie
    ¤ To support more complex operations (possible in principle)
    n Invertible mapping between keywords and unique IDs
    n Prefix-based operations
    ¤ To develop and publish a useful dictionary library
    

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23. 23
    Thank you for your attention!
    My English skills are limited
    If you have any questions,
    please speak slowly and clearly :)
    My experimental implementation is available at
    https://github.com/kampersanda/dynpdt
    

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