erato 湊離散構造処理系プロジェクトの 主な研究成果と近況に … · fit2013...
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Proceedings of the Twenty-Sixth RAMP SymposiumHosei University, Tokyo, October 16-17, 2014
ERATO湊離散構造処理系プロジェクトの主な研究成果と近況についてPrincipal Results and Resent Activities ofERATO MINATO Discrete Structure Manipulation System Project
湊 真一1∗
Shin-ichi Minato
概要 計算機が扱う問題の多くは、離散構造の処理を基盤としている.近年,論理や集合のような基本データ構造を効率よく処理する「BDD」「ZDD」と呼ばれるデータ構造とアルゴリズムが様々な分野で活用されている.このような技法をベースとして,種々の離散構造を統合的に演算処理する技法を体系化し,分野横断的かつ大規模な実問題を高速に処理する技術基盤を構築することを目標として,「ERATO湊離散構造処理系プロジェクト」が 2009年 10月に採択された。今年度までの 5年間に,多くの興味深い研究成果が得られている.本講演では,これまでのプロジェクトの主な研究成果と最近の話題,および今後の展望について述べる.
キーワード BDD, ZDD, 二分決定グラフ, 離散構造, アルゴリズム, データ構造, 列挙索引化
1 北海道大学大学院情報科学研究科 / JST ERATO湊離散構造処理系プロジェクト,〒060-0814 札幌市北区北 14条西 9丁目Graduate School of Information Science and Technology, Hokkaido University /JST ERATO MINATO DiscreteStructure Manipulation System Project,North 14 West 9, Sapporo 060-0814, Japan
∗ E-mail address: [email protected]
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ERATOERATO
/ JST ERATO
ERATO
ELC
ERATO
CREST/
2009.10 2010.4 2010.10 2011.4
(0 ) (1 )
2011.10 2012.4
(2 )
2012.10
(3 )
2013.4
(4 )
2013.10O
2014.4
(5 )
WSWS WS WS
NIIGL FIT2010 FIT2013
WSNTT
RC
KnuthCMU ALSIP
AI
ALSIPRM2013
ALSIP2014
RC2014
2011ALSIP2012
2013
2
web
(10100 )
3
BDD/ZDD
(E i i )(E i i )(Engineering) (Engineering)(Engineering)(Engineering) (Engineering)(Engineering)
“Art”“Art”---
(Computer science / )(Computer science / )
4
BDD
1986 BDD
a 1 a0 1a 1a 1a 1 a0 1a0 1
BDD
b
c
10
01
b b
0
b
c
10
01
b
c
10
01
b
c
10
01
b b
0
b b
0Bryant (CMU)
BDDBDD AND
BDD
BDDBDD
0 1
c1
0 c c c c
0 0 01 1 1 1 10 1
c1
0
0 1
c1
0
0 1
c1
0 c c c c
0 0 01 1 1 1 1
c c c c
0 0 01 1 1 1 1
BDDBDDBDDBDD
PCBDD
2000
5
ZDD BDD
BDD [Minato1993]
xx xx
f ff f 0f ff f 0f ff fBDD ZDD
f ff fBDD ZDD
ZDD BDD
6
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0,1 ZDD
ZDDetc.
( )
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( )
--- ZDD
ZDDZDD
--
7
5RA7
GL
GL
RA
TV8
ERATO / ERATO
ERATO 5~6ERATO 1 2
40 603~4 30 40
ERATO 10 11/ 2 3/ 2 3
40 50Q&A 25 15
---
9
ERATOERATO 35 40 150
CD-ROM
10
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PNAS
23 YouTube155
12
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2012 2
1990
ERATO
13
OFF ONs1s1
s2OFFs2ON OFF ON
s3 s3 s3 s3OFF ON
s2s4
s4OFF ON
s3
NGOK
ZDD
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•ZDD
•
Takeru Inoue, Keiji Takano, Takayuki Watanabe, Jun Kawahara, Ryo Yoshinaka, Akihiro , j , y , , y ,Kishimoto, Koji Tsuda, Shin-ichi Minato, and Yasuhiro Hayashi:"Distribution Loss Minimization With Guaranteed Error Bound," IEEE Trans. Smart Grid, Vol. 5, No. 1, pp. 102-111 Jan 2014102 111, Jan. 2014.
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PNAS
23 YouTube155
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2013 8
17
LAMP (Limitless Arity Multiple testing Procedure)
OCT1
C/EBP
CTTTAAR>1
>1>1
> 11.0
EVI1
NFAT
C/EBP8-Motif
EGF0.5nM15min
>1
>1>1 0.01370.0250.050.5
GRLEF1 FOXO4
15min>1
>1>1
0.0
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LAMP
pC / mCP f( )
P f( )
k/ k
/ k < f( )/ k < f( ) max
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LCM LAMP
LCM: NII
LAMPLCM
ECML/PKDD2014LCM
LAMP
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PNAS
23 YouTube155
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YouTube
1,557,869 2014 8 17
22
“seif-avoiding walks”
( 2nCn ; )
2525 s
tt
23
ERATO 2013 12n=26
n=24 2013 2 2
TB 2 1TB 2 1
24
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2013 11
201325
Open software: “Graphillion.org”
• Toolbox for ZDD based graph enumeration.– Easy interface using Python graph library.
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Graphillion
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2014
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1 2 3 4 5G
6 7 8 9
11 12 13 14
10
15b
16 17 18 19 20
21 22 23 24 25
a
21 22 23 24 25S
Graphillionbyby
ERATO NTT
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2GraphillionGraphillion
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0,1 ZDD
ZDDetc.
( )
-
( )
---
ZDDZDD
ZDD
--
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(Sets of Sequences)
Sets of combinations:D ’t id d d d li ti f itDon’t consider order and duplication of items“abcc” and “bca” are the same.
Sets of sequences:Distinguishes all finite sequences.g q
, { }, { ab, aba, bbc }, { a, aa, aaa, aaaa }, etc.Here we exclude infinite sets such as a*.
So many real-life applications.Text search and indexingText search and indexingWeb (html/xml) data miningBio informatics
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Bio informatics
Sequence BDD (SeqBDD)
Loekito, Bailey, and Pei (2009)Same as ZDD reduction ruleSame as ZDD reduction rule.Only 0-edges keep variable ordering.1-edges has no restriction.1 edges has no restriction.Still unique representation for a given set of sequences.Each path from root to 1-terminal corresponds to a sequence.
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Suffix-DD34
:P = { | }
P 18 (= 3 6 ) P P 2
P20
15
1 11 1
35Reversible logic
Permutation Decision Diagram ( DD)
{(2,1)}
2,1
{( , )}{ e,(2,1),(1,3,2),(3,1,2),(3,2,1),(2,3,1)}
3 1{ e,(2,1,),(1,3,2),(3,1,2)}
0 1{ e,(2,1)}
3,1
3,2
{ e,( , ,),( , , ),( , , )}
{(2,1),(3,1,2),(3,2,1),(2,3,1)}
{ (2 1)}2,1
3,1{(2,1),(3,1,2)}
2,1
{ e,(2,1)}1
{ e,(2,1)}
2 1
3,2
2 1
{(2,1)}
1 1
2,1
0
2,1
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Product operation for disjoint permutations
{e,123546,123654,123564 123465 123645}
{e,123546,123654,123564 123465 123645123564,123465,123645}
6 46,4
123564,123465,123645,213456,213546,213654,213564,213465,213645,
{e,213,321,231,132,312}
6,4
6,55 4
6,5 321456,321546,321654,321564,321465,321645,231456 231546 231654
3,15,4
3,1
5,4 231456,231546,231654,231564,231465,231645,132456,132546,132654,
2 1
3,2 1 3,2
132456,132546,132654,132564,132465,132645,312456,312546312654,product
1
2,12,1 312564,312465,312645}
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2014.06.05
ERATO
ELC
ERATO
CREST/
2009.10 2010.4 2010.10 2011.4
(0 ) (1 )
2011.10 2012.4
(2 )
2012.10
(3 )
2013.4
(4 )
2013.10O
2014.4
(5 )
WSWS WS WS
NIIGL FIT2010 FIT2013
WSNTT
RC
KnuthCMU ALSIP
AI
ALSIPRM2013
ALSIP2014
RC2014
2011ALSIP2012
2013
ERATO 4/17 18 L. Simon ALSIP2014 5/13 PAKDDRC2014 7/10 11
IN 7/17 18IN 7/17 18ERATO 9/7 10
11WALCOM2015 2/26 28
publicationpublication2014 12 30
BDD/ZDD
2015 4 2016 31/4
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ERATO
BDD/ZDD
ArtZDD Knuth
ArtERATO
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