TW409216B - Rapid maintenance method for integrating binary tree and hash table - Google Patents

Rapid maintenance method for integrating binary tree and hash table Download PDF

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Publication number
TW409216B
TW409216B TW87106415A TW87106415A TW409216B TW 409216 B TW409216 B TW 409216B TW 87106415 A TW87106415 A TW 87106415A TW 87106415 A TW87106415 A TW 87106415A TW 409216 B TW409216 B TW 409216B
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Taiwan
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data
binary tree
scattered
maintenance method
tree
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TW87106415A
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Chinese (zh)
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Yu-Rung Liu
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Inst Information Industry
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Abstract

The invention relates to a rapid maintenance method for integrating binary tree and hash table, especially for solving the bad search efficiency of database with numerical and text data coexisted. For separating the numerical data and text data in the data field from each other, the ""binary tree"" is built according to the number keys, while the hash table is built according to the index key of text data, and the bi-direction associative pointer is built on said binary tree and hash table, for the two types of data to be regarded as one entity, therefore, rapid searching is achieved no matter the searching is through data or text, besides, one distributive data rapid maintenance method capable of improving searching effeciency by obtaining the respective data via said bi-direction associative pointer is achieved.

Description

409216 A7 B7 經 濟 部 中 央 標 準 局 員 工 消 费 合 作 社 印 製 五、發明説明(() 本發明係為一種整合二元樹與散置表之快速維護方法 ’為一種令互為分離的二元樹(binary tree)資料以及散 置表(hash table)組成之兩種型態的資料之間以指標相互 連結,使其無論由數值鍵進行搜尋或是以文字索引鍵進行 搜尋’均可達到相當良好的操作效率,據以解決兼具文字 及數值資料之搜尋效率欠佳的問題者。 按現今資料庫的搜尋方法中,依照資料型態即區分為 適用於數值型資料之二元樹”(binary tree)以及適用 於文子型態資料之散置表”(hash table),前述二元樹 的型態,概為如第五圖所示,主要為將數值型資料依照二 元樹演算法而有系統地將數值型資料排列成如圖面所示之 含有樹根、樹枝及樹葉的型態,以第五圖最左邊為例,以 數子7為樹根時,樹根右邊的節點為表示大於了的其他數 子樹根左邊的節點為表示小於7的其他數字,而依此向 下類推而形成樹狀的結構,此項型態最明顯的優點為在於 搜尋快速,在第五圖中,若欲尋找數字5時,即由樹根開 始,由於5比7小,故而再朝樹根的左下節點進行比較, 由於5大於4,因此再朝右下節點搜尋,直到尋及相同數 值為止,若無法尋得時,則回報搜尋失敗之訊息,此舉, 即為運用二分法的方式,達到對數值型資料高效率的搜尋 效果’而對於欲加入或刪除資料時,亦使(用相同的方法將 新的節點插入或將尋及之節點予以去除,另外,在插入新 的節點時,若樹根兩側呈不平衡時,則自動地透過高度平 衡(height Wd)演算法,對該二元樹進行旋轉^調 {請先閱讀背面之注意事項再填寫本頁) - ——訂 Α7Μ9216 Β7 經濟部中央標隼局負工消资合作杜印製 五、發明説明(V ) 整子樹樹根的位置,最终使得二元樹兩侧呈相同高度者, 以確保搜尋效率。 至於則述之散置表(hash table),主要為適用於文字 型資料的搜哥,如第六圖所示,散置表主要為依照欲搜尋 的文子糊位建立索引鍵(index)(鍵值),使得散置 表的其他攔位的内容為依照索引鍵值的前後順序排列,而 其實際作法上為將各鍵值轉換為記憶體儲存位址,透過散 置函式(hash function)將各項鍵值轉換成儲存位址,並 直接將相應鍵值的資料儲存在相應之位址中,如此,欲進 行文字鍵值之搜尋時,即可由前述函式計算得知資料的儲 存位址,進而快速地取得與該鍵值相應之資料者。 雖然前述二元樹以及散置表均可獲得極佳的搜尋效率 ,但因二元樹僅適用於數值型資料,而散置表僅適用於文 字型資料,而對於同時混合有數值型及文字型資料,且必 須經常性地加入或刪除資料的場合,僅透過二元樹的數值 型搜尋或僅以散置表的索引鍵搜尋之,即導致搜尋效率欠 佳*故而實應尋求適合的解決方案。 故本發明之主要目的在於提供一種整合二元樹與散置 表之快速維護方法,為一種無論是進行數值型搜尋或索引 鍵搜尋’均可獲得高效率者。 本發明之次一目的在於提供一種整合匕元樹與散置表 之快速維護方法,除了具有高效率的搜尋效果外,更為便 於資料的新增與刪除作業者α 本發明之另一目的在於提供一種整合二元樹與散置表 4 本紙張尺度適用中國國家標準(CNS ) Α4規格(210Χ297公釐 &lt;請先閲請背面之注意事項再填寫本頁) 士衣 -訂 ^ 4092x6 經濟部中央標準局員工消費合作社印製 五、發明说明(1 ) 之快速維護方法’主要為將欲儲存的資料分割成數值型資 料以及文字型資料兩部份’將數值型資料依照其數值建立 二元樹結構’而將文字型資料依照索引鍵建立散置表,而 在兩種資料型態的各筆資料中設置關聯指標,而使兩者整 合’因此’可對二元樹進行數值鍵之搜尋,並透過指標對 應取得位在散置表中之相應的文字資料,或對散置表進行 索引鍵之搜尋’而對應取得位在二元樹相應位置之數值資 料’使其無論是數值型或文字型搜尋均可達到高效率的要 求者。 本發明之再一目的在於提供一種整合二元樹與散置表 之快速維護方法,對於資料的增刪作業,則透過二元樹演 算法以及散置函式之計算,而使得數值資料及文字資料插 入至適當位置或由正確位置刪除,使兩項資料獲得一致性 〇 為使貴審查委員能夠進一步瞭解本發明之結構、特 徵及其他目的’茲附以圖式詳細說明后。 (一) 圖式部份: 第一圖:係本發明之分散式資料型態的示意圖。 第二圖:係本發明之二元樹節點之結構示意圖。 第三圖:係本發明之散置表項目之結構示意圖。 第四圖:係本發明之實施例圖。 t 第五圖:係習知二元樹結構之示意囷β 第六圖:係習知散置表結構之示意圖β (二) 圖號部份: _ 5 本紙張尺度適用中國國家標準(CNS ) Α4規ϋΐΟΧ297公ϋ 一 — (請先閱讀背面之注意事項再填寫本頁) 哝 409216 A7 B7 五、發明説明(次) (10)二元樹(12) (13 (2 〇)散置表 (2 2)資料襴 經濟部中央標準局員工消費合作社印装 (1 1 )數值鍵 節點指標(1 4)關聯指標 (2 1 )索引鍵 (2 3 )關聯指標 如第-圖所7F,本發明主要為將資料庫的結構予以分 割成兩個分散式之資料’其—為依據數值型資料進行如圖 面所不之一元樹(1 0),而針對文字型資料則依照索引 鍵建立散置表(2Q) ’另彳,在該二元樹(1())與散 置表(2 〇 )之各筆相應資料間更設置有關聯指標,而使 兩分散式資料之間呈雙向互通·。 可配合參看第二、三圖所示’為分別表示前述二元樹 (10)以及散置表(20)各筆資料的内部結構,在第 一圖之二元樹各節點的内容中,除了包括有數值鍵(1 1 )以及位在兩側之指向右子節點或左子節點之節點指標( 13) (12)之外,更包括有一供指向散置表(20) 相應項目之關聯指標(1 4),可在透過數值鍵進行二元 樹搜尋取得該節點内容後,即可直接依照該關聯指標(1 4)而取得散置表(2 0)對應處之各項文字資料,達到 相互連結的效果。 在第三圖之散置表各筆資料的内容中,除了包括有索 引鍵及相關的資料欄位之外,更設置有一可供指向前述二 元樹(1 0)相應節點之關聯指標(2 3 )’同理’若為 透過輸入索引鍵值進行查詢後,亦可透過該關聯指標(2 3 )而直接取得位在二元樹(1 0)相應處之數值型資料 本紙張尺度適用中國國家標準(CNS ) Α4規格(2丨〇&gt;&lt;297公t ) -----------_4-- (請先閱讀背面之注意事項再填寫本頁} 4β 气 ___ A7 B7 409216 五、發明説明($ ) 者,使兩分散式資料具有雙向互通的特性。 而對上述分散式資料進行資料新增(插入)的場合, 即依照欲寫入之資料的數值鍵找出其位在二元樹(1 〇 ) 中之正確位置’而將該新產生的數值節點入二元樹中,並 同時偵測其二元樹為在非平衡狀態(高度平衡)時,透過 高度平衡演算法調整二元樹之高度,在此同時,亦根據欲 寫入之資料的索引鍵及散置函式計算出文字型資料欲存放 的位址’而將索引鍵内容以及相關的文字資料儲存在散置 表相應的儲存位址處,然後,則為填入關聯指標於前述二 元樹(1 0 )以及散置表(2 0 )相應的位置中,使之建 立關聯性’同理,欲刪除某一資料,即為透過搜尋方式找 出相應於一元樹(1 〇)(或散置表(2〇))處之資料 ,將之刪除與透過前述關聯指標將對應於散置表(2 〇) (或二元樹(1 〇))處之資料,達到使兩種資料達到同 步增刪的效果。 故以前述說明可知,本發明為將欲儲存的資料分割成 兩部份,並在其間以關聯指標連結之下,令數值鍵得以二 π樹建立,而索引鍵以散置表建立,使得無論是透過數值 鍵或者是索引鍵進行查詢或搜尋作業下,均可獲得極佳的 搜尋效率,得以解決兼具數值及文字之資料型態之搜尋效 率欠佳的問題,而在經常性地增刪處理的場合,更可保持 兩分散式資料的一致性,確為一具新穎性及產業上利用者 ,而以現今在電腦網路(INTERNET)應用程式中,對於逾時 事件(time-out event)方面,例如送出訊息後等待回應, t紙張从適用中國國家梯準(&lt;:叫六4規格(2】(^:297公羞 (請先聞讀背面之注意事項再瑱寫本頁) 装 訂 經濟部央標準局員工消費合作社印製 409216 A7 B7 經濟部中央標準局員工消費合作社印製 五、發明説明(t) 等待回應中的訊息最重要的為何時逾時(time 〇ut)及送給 何者(用IP ADDRESS識別),而本發明之分散(複合) 式資料型態上,即可有效地進行管理,如帛四圖之示意圖 所示,將前述逾時時間作為“數值鍵”而建立二元樹 ◦)而令IP ADDRESS作為“索引鍵,,建立散置表(2 0 ),並透過如莉述的關聯指標,使得〖P仙與逾 時事件呈相互關聯,如此,即可使得逾時事件資料庫獲得 高效率的管理,當計時器(TIMER)發出中斷時,即透過對 二元樹(1〇)所存放的各項逾時時間資料進行快速搜尋 (比對),且只要處理逾時指標所指到的節點即可,亦可 根據IP ADDRESS迅速搜尋出逾時的事件,而對於新產生 之等待回應的訊息亦可迅速地加入至此逾時事件資料庫中 ’使传運用上獲致高效率的優點。 綜上所述,本發明之整合二元樹與散置表之快速維護 方法,可依據資料型態切割成數值性資料與文字型資料’ 運用不同的建置方法使之形成二元樹及散置表的型態,使 其不僅在進行數值或文字搜尋作業方面均有著高效率的優 點外,亦使得兩組資料之間呈同步與一致性,確為一可使 混合有文子及數值之資料獲得有效運用之分散式快速維護 方法’應符專利申請要件’爰依法提出申請。 本纸張尺度適用中國國家標準(CNS }A4現格(210X297公釐) 〔請先閲讀背面之注意事項再填寫本頁) —訂409216 A7 B7 Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs. 5. Description of the invention (() The invention is a fast maintenance method that integrates a binary tree and scattered tables. It is a binary tree that separates each other. tree) data and two types of data consisting of hash tables are linked to each other with indicators, making it possible to achieve a very good operation whether it is searched by numeric keys or by text index keys. Efficiency, so as to solve the problem of poor search efficiency with both text and numerical data. According to the current database search method, according to the data type, it is divided into binary trees suitable for numerical data "(binary tree) And a hash table suitable for text-type data ”, the type of the aforementioned binary tree is shown in the fifth figure, which is mainly used to systematically numerical data according to the binary tree algorithm. The numerical data are arranged as shown in the figure, which contains the root, branches and leaves. Take the leftmost part of the fifth figure as an example, and when the number 7 is the root, the node on the right side of the root In order to indicate that the nodes to the left of the roots of other numbers are greater than other numbers that are less than 7, and so on to form a tree-like structure, the most obvious advantage of this type is that it is fast to search. In the figure, if you want to find the number 5, it starts from the root of the tree. Since 5 is smaller than 7, compare it to the lower left node of the tree root. Since 5 is greater than 4, search for the lower right node until you find the same value. If you ca n’t find it, you will report a search failure message. This is to use the dichotomy method to achieve an efficient search effect on numerical data. And when you want to add or delete data, you also use (using In the same way, new nodes are inserted or removed. In addition, when inserting new nodes, if the two sides of the root of the tree are unbalanced, the height Wd algorithm is used to automatically The binary tree is rotated ^ tuned (please read the notes on the back before filling this page)--Order Α7Μ9216 Β7 Duplicated work and consumer capital cooperation of the Central Bureau of Standards of the Ministry of Economic Affairs. tree The position of the root of the tree ultimately makes the two sides of the binary tree have the same height to ensure the search efficiency. As for the hash table, it is mainly a search brother that is suitable for textual data, as shown in Figure 6. It is shown that the scattered table is mainly to create index keys (key values) according to the position of the text to be searched, so that the contents of the other stops of the scattered table are arranged in accordance with the order of the index key values. In order to convert each key value into a memory storage address, each key value is converted into a storage address through a hash function, and the data of the corresponding key value is directly stored in the corresponding address. When you want to search for a text key value, you can calculate the storage address of the data by the foregoing function calculation, and then quickly obtain the data corresponding to the key value. Although the aforementioned binary tree and scattered tables can obtain excellent search efficiency, because binary trees are only applicable to numerical data, scattered tables are only applicable to textual data, and for the combination of both numeric and text When you need to add or delete data frequently, you only need to search through the binary tree's numeric search or only use the index keys of the scattered tables, which results in poor search efficiency. Therefore, a suitable solution should be sought. Program. Therefore, the main object of the present invention is to provide a fast maintenance method that integrates a binary tree and a scattered table, which is a method that can obtain high efficiency whether it is a numerical search or an index key search. A second object of the present invention is to provide a fast maintenance method for integrating a dagger element tree and a scattered table. In addition to having a high-efficiency search effect, it is more convenient for operators to add and delete data. Another object of the present invention is to Provide an integrated binary tree and interspersed table 4 This paper size is applicable to Chinese National Standard (CNS) Α4 specifications (210 × 297 mm &lt; please read the notes on the back before filling this page) Shiyi-Order ^ 4092x6 Ministry of Economic Affairs Printed by the Consumer Standards Cooperative of the Central Standards Bureau V. Invention Description (1) The quick maintenance method 'mainly divides the data to be stored into numerical data and textual data' and establishes the binary data according to its value. "Tree structure" and the text data is created according to the index key to create a scattered table, and the two data types of each piece of data are set to associated indicators, so that the two are integrated, so the binary tree can be searched by numeric keys , And obtain the corresponding text data in the scattered table through the index correspondingly, or search the index key of the scattered table ', and correspondingly obtain the corresponding bit in the binary tree. The set of numerical data 'makes it possible to achieve high-efficiency requirements for both numerical and text search. Another object of the present invention is to provide a fast maintenance method for integrating binary trees and scattered tables. For the addition and deletion of data, binary data algorithms and calculation of scattered functions are used to make numerical data and text data. Inserted into the appropriate position or deleted from the correct position, so that the two materials are consistent. In order to allow your reviewers to further understand the structure, characteristics and other purposes of the present invention, a detailed description is attached with drawings. (I) Schematic part: The first figure: a schematic diagram of the distributed data type of the present invention. The second figure is a schematic structural diagram of a binary tree node of the present invention. The third figure is a schematic diagram of the structure of the scattered table item of the present invention. The fourth diagram is a diagram of an embodiment of the present invention. t The fifth figure: a schematic diagram of a conventional binary tree structure. β The sixth diagram: a schematic diagram of a conventional scattered table structure. β (II) Part of the drawing number: _ 5 This paper size applies to the Chinese National Standard (CNS). Α4ϋΐϋΐ〇 × 297 公 ϋ I— (Please read the notes on the back before filling this page) 哝 409216 A7 B7 V. Description of the invention (times) (10) Binary tree (12) (13 (2 〇) Interspersed table ( 2 2) Information: Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs (1 1) Numeric key node index (1 4) Correlation index (2 1) Index key (2 3) Correlation index is as shown in Figure 7-F, the invention It mainly divides the structure of the database into two decentralized data, which is to perform a meta-tree (1 0) as shown in the figure based on numerical data, and for the text-based data, the dispersion is established according to the index key. Table (2Q) 'In addition, there are more relevant indicators between the corresponding data of the binary tree (1 ()) and the scattered table (20), so that two decentralized data are two-way interlinked. Can be coordinated as shown in the second and third figures. 'Represents each of the aforementioned binary tree (10) and scattered tables (20). The internal structure of the node, in addition to the contents of each node of the binary tree in the first graph, includes a numeric key (1 1) and node indicators on either side that point to the right or left child node (13) (12) In addition, it also includes a related index (1 4) for pointing to the corresponding item in the scattered table (20). After the binary tree search is performed through the numeric key to obtain the node content, you can directly follow the related index (1 4 ) To obtain the text data corresponding to the scattered table (20), to achieve the effect of interconnection. In the content of each piece of data in the scattered table of the third figure, in addition to including the index key and related data fields In addition, a related indicator (2 3) is provided to point to the corresponding node of the binary tree (1 0) above. If the query is performed by entering the index key value, the related indicator (2 3 ) And directly obtain the numerical data at the corresponding position of the binary tree (1 0). This paper size applies the Chinese National Standard (CNS) A4 specification (2 丨 〇 &gt; &lt; 297mm t) ------- ----_ 4-- (Please read the precautions on the back before filling out this page} 4β Qi ___ A7 B7 409216 5. The invention description ($) makes the two decentralized data have the characteristic of two-way intercommunication. When adding (inserting) data to the above decentralized data, it is to find its position according to the numerical key of the data to be written. In the correct position of the binary tree (10), the newly generated numerical node is entered into the binary tree, and at the same time, when the binary tree is in an unbalanced state (highly balanced), a high balance calculation is performed. The height of the binary tree cannot be adjusted. At the same time, the content of the index data and related text data are also stored in the address of the text data according to the index key and the scatter function of the data to be written. The corresponding storage address of the interspersed table is then filled with the related indicators in the corresponding positions of the binary tree (1 0) and the interspersed table (2 0), so as to establish associations. Deleting a piece of data is to find the data corresponding to the unary tree (1 0) (or the interspersed table (2)) by searching. Deleting it and using the aforementioned related indicators will correspond to the interspersed table (2 〇) (or binary tree (1 〇)) To achieve the effect of synchronously adding and deleting two types of data. Therefore, according to the foregoing description, it is known that the present invention divides the data to be stored into two parts and links them with related indicators, so that the numeric keys can be established in a two-pi tree, and the index keys are established in a scattered table, so that regardless of When searching or searching through numeric keys or index keys, you can obtain excellent search efficiency, which can solve the problem of poor search efficiency with both numeric and text data types, and often add or delete In the occasion, the consistency of the two decentralized data can be maintained, and it is indeed a novelty and industrial user. Nowadays, in the Internet application, the time-out event In terms of, for example, waiting for a response after sending a message, t paper is applicable from China ’s national standard (<: called six 4 specifications (2) (^: 297 public shame (please read the precautions on the back before writing this page)) Order printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs 409216 A7 B7 Printed by the Consumer Cooperatives of the Central Standards Bureau of the Ministry of Economic Affairs V. Invention Description (t) The most important message waiting for a response is when it expires (ti me 〇ut) and to whom (identified by IP ADDRESS), and the decentralized (composite) data type of the present invention can be effectively managed, as shown in the diagram of Figure 24, the aforementioned timeout period Establish a binary tree as a "numerical key" and let IP ADDRESS as an "index key." Establish a scatter table (2 0), and use the related indicators as described in the above description to make "Psen and the timeout event appear mutually. Correlation, so that the timeout database can be managed efficiently. When the timer (TIMER) is interrupted, the timeout data stored in the binary tree (10) is quickly searched. (Comparison), and as long as the node indicated by the timeout indicator can be processed, the timeout event can be quickly searched according to IP ADDRESS, and the newly generated message waiting for a response can also be quickly added to this timeout event In the database, 'the advantage of high efficiency is achieved in the use of transmission. In summary, the rapid maintenance method of the integrated binary tree and scattered tables of the present invention can be cut into numerical data and text data according to the data type' Not used The method of building makes it form a binary tree and scattered tables, which not only has the advantage of high efficiency in performing numerical or text search operations, but also makes the two sets of data appear synchronous and consistent. It is indeed a decentralized rapid maintenance method that can effectively use data mixed with text and numerical values. It should be applied in accordance with the patent application requirements. This paper size applies the Chinese national standard (CNS} A4) (210X297) Li) [Please read the notes on the back before filling out this page) — Order

Claims (1)

409216 六、申請專利範圍 A8 B8 C8 D8 經濟部中央榇準局貝工消費合作社印製 . 種整合二元樹與散置表之快速維護方法.包括 70樹結構’為將資料中之數值型資料分離出,透過 對此數值型資料進行處理轉換為二元樹型態; 散置表’垚 ’马將資料中之文字型資料分離出,透過對此 文字型資料進行㈣鍵值處理; 關聯指軚’為設置在前述二元樹以及散置表之各筆相 應資料處; 藉x使其可進行數值鍵或索引鍵之快速搜尋與透過關 聯指標取得二元樹缝置表巾之資料者。 2如申請專利範圍第1項所述之整合二元樹與散置 表之决速維護方法,其中對於欲插入至二元樹中之新資料 或由二疋樹中刪除的資料,更視需要進行高度平衡運算’ 使二元樹的左右兩側呈相等高度與呈平衡狀態者。 3 ·如中請專利範圍第1項所述之整合二元樹與散置 表之快速維護方法,其中位在二元樹各筆資料中之關聯指 標,為供指向散置表中與之相應的項目内容者。 4 .如中請專利範圍第1項所述之整合二元樹與散置 表之快速維護方法,其令位在散置表各筆資料中之關聯指 標,為供指向二元樹中與之相應的數值鍵者。 本紙張尺度適用_囿國家梯準(〇阳)六4規格(2〗〇父297公釐) (請先閩讀背面之注意事項再填寫本頁) 衮. -1T . I d409216 VI. Application for patent scope A8 B8 C8 D8 Printed by the Central Laboratories of the Ministry of Economic Affairs of the Bayong Consumer Cooperative. A fast maintenance method that integrates binary trees and scattered tables. Includes 70 tree structures. It is separated and converted into a binary tree type by processing the numerical data; The scattered table '垚' horse separates the textual data in the data, and performs key-value processing on the textual data; Association refers to軚 'is set in the corresponding data of the binary tree and the scattered table; by x, it can be used for fast search of numeric keys or index keys and to obtain the data of the binary tree stitched table towel through related indicators. 2 The method for determining the speed of maintaining a binary tree and scattered tables as described in item 1 of the scope of the patent application, where new data to be inserted into the binary tree or data deleted from the binary tree are more needed Perform height balance operation 'Make the left and right sides of the binary tree equal height and balanced. 3 · The rapid maintenance method of the integrated binary tree and scattered tables as described in item 1 of the patent scope, in which the related indicators in the data of the binary tree are corresponding to the corresponding points in the scattered tables. Project content owner. 4. The rapid maintenance method of the integrated binary tree and the scattered table as described in item 1 of the patent scope, whose associated index in each piece of data in the scattered table is for direct reference to the binary tree. The corresponding numeric keyer. This paper is applicable to _ 囿 National Ladder Standard (〇 阳) 6 4 specifications (2〗 〇 Parent 297 mm) (Please read the precautions on the back before filling this page) 衮. -1T. I d
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Cited By (2)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE202015105540U1 (en) 2014-12-05 2015-10-29 Yuan-Hung WEN brake disc
DE202017103541U1 (en) 2016-08-30 2017-07-10 Yuan-Hung WEN brake disc

Cited By (4)

* Cited by examiner, † Cited by third party
Publication number Priority date Publication date Assignee Title
DE202015105540U1 (en) 2014-12-05 2015-10-29 Yuan-Hung WEN brake disc
DE102015117790A1 (en) 2014-12-05 2016-06-09 Yuan-Hung WEN brake disc
DE202017103541U1 (en) 2016-08-30 2017-07-10 Yuan-Hung WEN brake disc
DE102017113040A1 (en) 2016-08-30 2018-03-01 Yuan-Hung WEN brake disc

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