Upgrade to Pro
— share decks privately, control downloads, hide ads and more …
Speaker Deck
Features
Speaker Deck
PRO
Sign in
Sign up for free
Search
Search
EliasFano
Search
Shunsuke Kanda
November 30, 2019
Research
1
250
EliasFano
10th StringBeginnersでの発表資料
Shunsuke Kanda
November 30, 2019
Tweet
Share
More Decks by Shunsuke Kanda
See All by Shunsuke Kanda
Leveraging LLMs for Unsupervised Dense Retriever Ranking (SIGIR 2024)
kampersanda
2
400
Lucene/Elasticsearch の Character Filter でユニコード正規化するとトークンのオフセットがズレるバグへの Workaround - Search Engineering Tech Talk 2024 Spring
kampersanda
0
1.4k
Binary and Scalar Embedding Quantization for Significantly Faster & Cheaper Retrieval
kampersanda
2
420
トライとダブル配列の基礎
kampersanda
1
1.3k
Binary search with modern processors
kampersanda
33
14k
AIP Open Seminar #6
kampersanda
0
240
ICDM2020
kampersanda
0
220
SIGSPATIAL20
kampersanda
0
200
Fast Succinct Trie
kampersanda
1
730
Other Decks in Research
See All in Research
[RSJ25] Enhancing VLA Performance in Understanding and Executing Free-form Instructions via Visual Prompt-based Paraphrasing
keio_smilab
PRO
0
140
SSII2025 [TS3] 医工連携における画像情報学研究
ssii
PRO
3
1.3k
Vision and LanguageからのEmbodied AIとAI for Science
yushiku
PRO
1
560
Learning to (Learn at Test Time): RNNs with Expressive Hidden States
kurita
1
260
能動適応的実験計画
masakat0
2
850
snlp2025_prevent_llm_spikes
takase
0
370
Hiding What from Whom? A Critical Review of the History of Programming languages for Music
tomoyanonymous
0
200
「どう育てるか」より「どう働きたいか」〜スクラムマスターの最初の一歩〜
hirakawa51
0
930
AI in Enterprises - Java and Open Source to the Rescue
ivargrimstad
0
630
大学見本市2025 JSTさきがけ事業セミナー「顔の見えないセンシング技術:多様なセンサにもとづく個人情報に配慮した人物状態推定」
miso2024
0
170
言語モデルの地図:確率分布と情報幾何による類似性の可視化
shimosan
7
1.7k
2021年度-基盤研究B-研究計画調書
trycycle
PRO
0
350
Featured
See All Featured
Imperfection Machines: The Place of Print at Facebook
scottboms
269
13k
Large-scale JavaScript Application Architecture
addyosmani
514
110k
Typedesign – Prime Four
hannesfritz
42
2.8k
The MySQL Ecosystem @ GitHub 2015
samlambert
251
13k
The Cost Of JavaScript in 2023
addyosmani
54
9k
Java REST API Framework Comparison - PWX 2021
mraible
33
8.9k
VelocityConf: Rendering Performance Case Studies
addyosmani
332
24k
Fireside Chat
paigeccino
40
3.7k
Documentation Writing (for coders)
carmenintech
75
5.1k
A Modern Web Designer's Workflow
chriscoyier
697
190k
The Psychology of Web Performance [Beyond Tellerrand 2023]
tammyeverts
49
3.1k
Automating Front-end Workflow
addyosmani
1371
200k
Transcript
EliasFano 10th StringBeginners → Kanda →
K and A → K & A → K ampersand A →
⟫ × "$& n '% S[0,n) × i.e.,
S[i-1] ≤ S[i] for each 0 < i < n ⟫ ! × Access / Predecessor / Successor ( × #( 2 0 1 2 3 4 5 6 7 S 2 7 18 28 42 43 44 59 Access(4) = 42 Predecessor(10) = 7 Successor(43) = 44
EliasFano 3 S 2 7 18 28 42 43 44
59 000 000 010 011 101 101 101 111 n = 8 u log $ log % & 010 111 010 100 010 011 100 011 2 1 3 1 1 001 100 110 0 0 0 log H = 110 0 10 10 0 1110 0 10 2 0 1 1 0 0 1 3 ( ) L = 010 111 010 100 010 011 100 011 ()
2" + " log ' ( 4 L
= 010 111 010 100 010 011 100 011 H = 110 0 10 10 0 1110 0 10 0 1 2 3 4 5 6 7 S 2 7 18 28 42 43 44 59 EliasFano log ) " " log ' ( " 2" 2 *+, ( ≈ "
2" + " log ' ( "6 ⟫
[0,u) 2 n (,/ (i.e. 4) -) #. % $*0+3 6 5 S 2 4 5 8 9 0010110011 2 45 89 n 5'& 2 u ' ( 1 5!5 3 log ' (
2" + " log ' ( 4 ⟫
[0,u) 1 n *- +& !, # "'.(2 4 6 S 2 4 4 5 8 9 0010011010001010 2 5 ')( ( / 33 (0)) 44 8 9 n 3%$1 u+n Less than half a bit per element away (Quasi-succinct) 2 log ')( ( ≈ " log ')( (
⟫ Access(i) = S[i] ⟫ Predecessor(x) = max{S[i] :
S[i] ≤ x} ⟫ Successor(x) = min{S[i] : S[i] > x} 7 O(1) O(log $ % ) 0 1 2 3 4 5 6 7 S 2 7 18 28 42 43 44 59 Access(4) = 42 Predecessor(10) = 7 Successor(43) = 44
Access&O(1) $ ⟫ &Access(4) = 42 = 101 0102 8
L = 010 111 010 100 010 011 100 011 H = 110 0 10 10 0 1110 0 10 ① !"# $ % i ! Select1 (4) – 4 = 9 – 4 = 5 = 1012 ② !"# % Select1 (i) – i H Select " o(n) Selectb (H, i)&H i ! b # %
SuccessorO(log $ % ) ⟫ Successor(43) = 44 =
101 1002 9 L = 010 111 010 100 010 011 100 011 H = 110 0 10 10 0 1110 0 10 Select0 (4) = 8 Select0 (5) = 12 log $ % = 3 3 × (Select0 (4) – 4) = 12 3 × (Select0 (5) – 5) = 21 101 0112 5 ② O(&'( ) * ) ① &'( * Select
/6 EliasFano7) ⟫ # (;+' AA ×
10%?*& × =98. " × TRIE 2! × 3<5,4!@: -> 10 10 7 5 0 1 4 8 6 9 3 a t e t a a t e c c 2 $A