ウェーブレット行列 最速攻略 〜予告編〜 echizen_tm Sep. 16, 2012
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はじめに
今回の発表では
(Wavelet Matrix) というデータ構造の話をします
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ウェーブレット行列？
ウェーブレット行列は に対して に を
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例えばどういうこと？(1)
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例えばどういうこと？(2)
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でも普通に計算すると
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もし範囲内に データが1億件あったら
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これは困る
どんなに
に対しても に
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それ、 ウェーブレット行列でできるよ
ウェーブレット行列は に対して
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つまり ウェーブレット行列があると
2000万のユーザデータの ID1,000,000からID5,000,000の範囲で 年齢が20歳以上のユーザが何人いるかが
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ウェーブレット行列って デメリットとかないの？
定数時間で計算ってことは インデックスとか余計なデータが必要なんじゃないの？ →簡潔データ構造を使っているので
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ウェーブレット行列の
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ウェーブレット行列の
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SPIRE2012
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ウェーブレット行列の構築 (7/11)
この時点で前半に [0, 3]のデータが 後半に[4, 7]のデータが集まった
, , ,
, , ,
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ウェーブレット行列の構築 (10/11)
今度はデータが [0,1][2,3][4,5][6,7]の4つの範囲に分割された
,
,
,
,
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ウェーブレット行列の access(1/6)
access(0)の場合
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ウェーブレット行列の access(2/6)
access(0)の場合
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ウェーブレット行列の access(3/6)
access(0)の場合
これらを繋ぎ合わせると100(2進数)となる
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ウェーブレット行列の access(4/6)
access(5)の場合
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ウェーブレット行列の
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ウェーブレット行列の
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【個人研究】ウェーブレット行列 のrankを2倍高速化する(6/7)
なぜbeginは高々”文字種”の数の値しか取らないのか？
ウェーブレット行列の最終行は”2種類の値”ごとのブロック beginは最終的にこのブロックのうちのどれかの先頭に来る それぞれのブロックの先頭位置begin’に対して bv.rank(0, bv .rank(0, begin’), bv bv.rank(1, .rank(1, begin’)を持っておけば良い
rank(0, i) rank(1, i)
rank(4, i) rank(5, i)
rank(2, i) rank(3, i)
rank(6, i) rank(7, i)
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【個人研究】ウェーブレット行列 のrankを2倍高速化する(7/7)
で、実際性能はどうなの？
takeda25さんがwat-arrayとの比較をしてくださっています
データ長100,000,000、文字種1,000に対して ウェーブレット行列(高速版): 1.49 micro sec (53%) ウェーブレット木(wat-array): 2.51 micro sec (100%)
echizen_tm作のFM-Index (内部でウェーブレット木/行列を使用)での比較
データ長4,000,000、文字種256に対して ウェーブレット行列
