This document discusses path decomposition techniques for trie data structures. It introduces tries, path-decomposed tries (PDTs), and dynamic path-decomposed tries (DynPDTs). It then evaluates the performance of DynPDTs with different encoding techniques (plain and bitmap) compared to other trie structures like m-Bonsai tries, Judy tries, HAT-tries, and Cedar tries on several datasets. DynPDTs with bitmap encoding outperform the other structures in most cases. The document advocates for using DynPDTs with bitmap encoding or m-Bonsai tries for path decomposition applications.

1. PATH DECOMPOSITION
2017/9/18–20 @
10th WebDB Forum or 128th IFAT

2. 2
¨
¤ C++ std::map<std::string, type>
¨ [Martínez-Prieto+ 16]
¤ NLP IR Web RDF Bioinformatics etc.
Web
Database
Forum
IFAT
IPSJ
1
2
3
4
5
IFAT → 4

3. (cont.)
3
¨
¤
libCSD
path_decomposed_tries
Marisa-trie
Xcdat
Judy
Hat-Trie
libart
Cedar
LARGESMALL

4. Trie & Path Decomposition4

5. Trie [Fredkin 60]
5
¨
¤
¤
ideal$ 1
ideology$ 2
tec$ 3
technology$ 4
tie$ 5
trie$ 6
tide
rie$ec
hnology$
ology$
ie$
6
4
1 2 5
3
al$
$
technology$
Patricia Trie

6. Path Decomposition [Ferragina+ 08]
6
¨ Trie
¤
¤ [Grossi+ 14] [Hsu+ 13]
i r $i
technology$
tide
rie$ec
hnology$
ology$
ie$
al$
$
Path-Decomposed Trie (PDT)

7. Dynamic Path-Decomposed Trie (DynPDT)
DynPDT7

8. Path Decomposition
8
¨ PDT
technology$
v1
1 technology$

9. Path Decomposition (cont.)
9
¨ PDT
technology$
v1
(5, i)
cs$
v2
2 technics$ 012345
technics$

10. Path Decomposition (cont.)
10
¨ PDT
technology$
cs$
(5, i)
v1
v2
ue$
(0, q)
v3
3 technique$ 012345
technique$
0
que$
Dynamic Path-Decomposed Trie (DynPDT)

11. DynPDT
11
¨
¤ Trie m-Bonsai [Poyias+ 14]
¨
¤
¤
technology$
cs$
ue$
(5, i)
(0, q)
v1
v2
v3
technology$
technics$
technique$

12. DynPDT
12
¨
¤ Trie m-Bonsai [Poyias+ 14]
¨
¤
¤
technology$
cs$
ue$
(5, i)
(0, q)
v1
v2
v3
technology$
technics$
technique$

13. Plain
13
¨
¤ P[v] v P
¤
¤ 64
v4 v1 v2 v6 v3
P
technology$ cs$ ue$lly$ cal$

14. Bitmap
14
¨
¤ ID ℓ
¤ P’ |#|/ℓ
¤ B
v4 v1 v2 v6 v3
B 1 0 1 1 0 1 0 1
P’
3lly10technology2cs 3cal2ue
ℓ = 4

15. Bitmap (cont.)
15
¨
¤
n popcnt
¤
n Skipping O(ℓ) or
v4 v1 v2 v6 v3
B 1 0 1 1 0 1 0 1
P’
3lly10technology2cs 3cal2ue
ℓ = 4
popcnt(B[v4..v1]) = 2
v1
skipping

16. &
16

17. 17
¨
¤ Intel Xeon E5540 @2.53 GHz CPU 32GB RAM
¤ Ubuntu Server 16.40 LTS
¨
¤ Wiki Wikipedia
n 227MiB 11.5M 20.7
¤ WebBase WebBase URL
n 6.6GiB 118.1M 60.2
¤ LUBM LUBM URI
n 3.1GiB 52.6M 63.7

18. (cont.)
18
¨
¤ DynPDT Plain Bitmap ℓ = 16
¤ m-Bonsai Trie not
¤ Judy HP Trie
¤ HAT-trie Trie Array Hash
¤ Cedar Double Array Trie
¨
¤ C++
¤ std::int32_t 4

19. 19
¨ /
Data Structure Wiki WebBase LUBM
DynPDT + Plain 46.6 (2.48x) 47.5 (2.26x) 45.0 (3.26x)
DynPDT + Bitmap 18.8 base 21.0 base 13.8 base
m-Bonsai 23.6 (1.26x) 29.3 (1.40x) 11.4 (0.83x)
Judy 50.5 (2.69x) 53.5 (2.55x) 33.9 (2.46x)
HAT-trie 40.2 (2.14x) 68.9 (3.28x) 64.7 (4.69x)
Cedar 41.1 (2.19x) N/A 29.7 (2.15x)
¨ m-Bonsai
¤ +4
¤ DynPDT + Bitmap

20. 20
¨ /
Data Structure Wiki WebBase LUBM
DynPDT + Plain 1.14 (0.73x) 2.37 (0.81x) 1.65 (0.83x)
DynPDT + Bitmap 1.57 base 2.93 base 1.99 base
m-Bonsai 2.22 (1.41x) 7.69 (2.62x) 4.80 (2.41x)
Judy 1.06 (0.68x) 2.94 (1.00x) 1.53 (0.77x)
HAT-trie 1.13 (0.72x) 1.75 (0.60x) 2.58 (1.30x)
Cedar 1.07 (0.68x) N/A 2.50 (1.26x)
¨ Path Decomposition m-Bonsai
¨

21. 21
¨ /
Data Structure Wiki WebBase LUBM
DynPDT + Plain 1.13 (0.70x) 2.20 (0.80x) 1.12 (0.78x)
DynPDT + Bitmap 1.61 base 2.74 base 1.43 base
m-Bonsai 2.06 (1.28x) 8.30 (3.03x) 3.08 (2.15x)
Judy 0.88 (0.55x) 2.42 (0.88x) 0.79 (0.55x)
HAT-trie 0.35 (0.22x) 0.80 (0.29x) 0.51 (0.36x)
Cedar 0.69 (0.43x) N/A 0.69 (0.48x)
¨ m-Bonsai
¨
¤ m-Bonsai

22. 22
¨ DynPDT
¤
¤ m-Bonsai
¨
¤ m-Bonsai or
¤
n ↔ ID [Martínez-Prieto+ 16]
n e.g. tech
¤

23. 23
https://github.com/kampersanda/dynpdt