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基于狀態(tài)視圖的高效Hilbert編碼和解碼算法

賈連印 陳明鮮 李孟娟 游進(jìn)國(guó) 丁家滿

賈連印, 陳明鮮, 李孟娟, 游進(jìn)國(guó), 丁家滿. 基于狀態(tài)視圖的高效Hilbert編碼和解碼算法[J]. 電子與信息學(xué)報(bào), 2020, 42(6): 1494-1501. doi: 10.11999/JEIT190501
引用本文: 賈連印, 陳明鮮, 李孟娟, 游進(jìn)國(guó), 丁家滿. 基于狀態(tài)視圖的高效Hilbert編碼和解碼算法[J]. 電子與信息學(xué)報(bào), 2020, 42(6): 1494-1501. doi: 10.11999/JEIT190501
Lianyin JIA, Mingxian CHEN, Mengjuan LI, Jinguo YOU, Jiaman DING. State View Based Efficient Hilbert Encoding and Decoding Algorithms[J]. Journal of Electronics & Information Technology, 2020, 42(6): 1494-1501. doi: 10.11999/JEIT190501
Citation: Lianyin JIA, Mingxian CHEN, Mengjuan LI, Jinguo YOU, Jiaman DING. State View Based Efficient Hilbert Encoding and Decoding Algorithms[J]. Journal of Electronics & Information Technology, 2020, 42(6): 1494-1501. doi: 10.11999/JEIT190501

基于狀態(tài)視圖的高效Hilbert編碼和解碼算法

doi: 10.11999/JEIT190501
基金項(xiàng)目: 國(guó)家自然科學(xué)基金(61562054),國(guó)家留學(xué)基金委公派留學(xué)項(xiàng)目(201908530036)
詳細(xì)信息
    作者簡(jiǎn)介:

    賈連?。耗校?978年生,副教授,研究方向?yàn)閿?shù)據(jù)庫(kù)、信息檢索、并行計(jì)算

    陳明鮮:男,1994年生,碩士生,研究方向?yàn)閳D像處理、信息檢索和自然語(yǔ)言處理

    李孟娟:女,1983年生,館員,研究方向?yàn)椴⑿杏?jì)算和信息檢索

    游進(jìn)國(guó):男,1978年生,副教授,研究方向?yàn)閿?shù)據(jù)庫(kù)和數(shù)據(jù)倉(cāng)庫(kù)

    丁家滿:男,1974年生,副教授,研究方向?yàn)閿?shù)據(jù)庫(kù)和數(shù)據(jù)挖掘

    通訊作者:

    丁家滿 tjom2008@126.com

  • 1)對(duì)數(shù)據(jù)不向原點(diǎn)偏斜的情形,可通過(guò)適當(dāng)?shù)淖鴺?biāo)變換,如旋轉(zhuǎn)、平移等,使其盡可能地向原點(diǎn)偏斜。
  • 中圖分類號(hào): TN919.81

State View Based Efficient Hilbert Encoding and Decoding Algorithms

Funds: The National Natural Science Foundation of China (61562054), Fund of China Scholarship Council (201908530036)
  • 摘要:

    Hilbert曲線是高維降到1維的重要方法,具有較好的空間聚集和空間連續(xù)性,在地理信息系統(tǒng)、空間數(shù)據(jù)庫(kù)、信息檢索等方面有廣泛的應(yīng)用?,F(xiàn)有Hilbert編碼或解碼算法未考慮輸入數(shù)據(jù)對(duì)編碼或解碼效率的影響,因此將不同輸入數(shù)據(jù)同等對(duì)待。為此,該文通過(guò)設(shè)計(jì)高效的狀態(tài)視圖并結(jié)合快速置位檢測(cè)算法提出高效的免計(jì)前0的Hilbert編碼算法(FZF-HE)和免計(jì)前0的Hilbert解碼算法(FZF-HD),可快速識(shí)別輸入數(shù)據(jù)前部為0而無(wú)需迭代計(jì)算的部分,從而降低迭代查詢次數(shù)及算法復(fù)雜度,提高編解碼效率。實(shí)驗(yàn)結(jié)果表明,F(xiàn)ZF-HE算法和FZF-HD算法在數(shù)據(jù)均勻分布時(shí)效率稍高于現(xiàn)有算法,而在數(shù)據(jù)偏斜分布時(shí)效率遠(yuǎn)高于現(xiàn)有算法。

  • 圖  1  1階、2階和3階Hilbert曲線示意圖

    圖  2  1階Hilbert曲線對(duì)應(yīng)的4種狀態(tài)

    圖  3  均勻分布下編碼效率對(duì)比

    圖  4  $\beta $對(duì)編碼效率的影響

    圖  5  $\alpha $對(duì)編碼效率的影響

    圖  6  均勻分布下解碼效率對(duì)比

    圖  7  $\beta $對(duì)解碼效率的影響

    圖  8  $\alpha $對(duì)解碼效率的影響

    表  1  編碼狀態(tài)視圖

    狀態(tài)0000111122223333
    坐標(biāo)00011011000110110001101100011011
    編碼00011110001101101011010010011100
    下階狀態(tài)1030021121233302
    下載: 導(dǎo)出CSV

    表  2  解碼狀態(tài)視圖

    狀態(tài)0000111122223333
    編碼00011011000110110001101100011011
    坐標(biāo)00011110001011011110000111010010
    下階狀態(tài)1003011232212330
    下載: 導(dǎo)出CSV

    表  3  FZF-HE算法

     輸入:X,橫坐標(biāo)
        Y,縱坐標(biāo)
        n,階
     輸出:Hilbert編碼$Z$
     (1) Z←0
     (2) $p$←${\rm{msb}}(\max(X,Y))$//置位檢測(cè)
     (3) $t$←($n$-$p$-1)%2//計(jì)算第$n$-$p$階狀態(tài)
     (4) for $i$ from $n$-$p$ to $n$
     (5) $Z{\rm{ = }}Z{{ < < 2 | {\rm{Key}}[}}t{\rm{][}}{x_i}{\rm{][}}{y_i}{\rm{] }}$//查Key視圖
     (6) $t{\rm{ = Type[}}t{\rm{][}}{x_i}{\rm{][}}{y_i}{\rm{]}}$//查Type視圖
    下載: 導(dǎo)出CSV

    表  4  FZF-HD算法

     輸入:$Z$,Hilbert編碼
        n,階
     輸出:X,橫坐標(biāo)
        Y,縱坐標(biāo)
     (1) $X$, $Y$←0
     (2) $p$←${\rm{msb}}(Z)$//置位檢測(cè)
     (3) $t$←($n$-$p$/2-1)//計(jì)算第$n$-$p$/2階狀態(tài)
     (4) for $i$ from $n$-$p$/2 to $n$
     (5) ${\rm{coord}} = {\rm{InvKey}}[t][{z_{2i - 1}}{z_{2i}}]$ //查InvKey視圖
     (6) $ Y = Y < < 1 | {\rm{coord}} \& 0{\rm{x}}1 $
       $ X = X < < 1 | {\rm{coord}} > > 1\& 0{\rm{x}}1 $
     (7) $t = {\rm{InvType}}[t][{z_{2i - 1}}{z_{2i}}]$//查InvType視圖
    下載: 導(dǎo)出CSV
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  • 收稿日期:  2019-07-05
  • 修回日期:  2020-02-03
  • 網(wǎng)絡(luò)出版日期:  2020-02-27
  • 刊出日期:  2020-06-22

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