「找尋Top-K頻繁項目」（Top-K Frequent Items）是數據流分析中很熱門的議題，常被應用在許多領域，像是對網路流量的監控或是網頁廣告業者關心商品的點擊率等等。而在解決該問題時，基於硬體成本考量，我們將環境假設為記憶體空間不足，所以無法將每筆資料都儲存下來計算處理；取而代之，我們使用近似解法，只需使用有限的記憶體空間來計算無窮的數據流，但代價是計算的結果會有一個合理的誤差。Misra-Gries演算法就是一個解決Top-K問題的近似解法。

然而Misra-Gries演算法在處理資料偏度低的測試資料時正確率會很低。在我們實驗中，Misra-Gries演算法執行偏度為0.4，遵守Zipf規則產生的測資時，正確率只有32%。所以我們修改Misra-Gries演算法更新規則，加入「Sliding Window」概念，提高Top-K輸出結果的正確率，並將此Misra-Gries演算法改良版命名為「Sliding Window Misra-Gries演算法」，簡稱「WMG」。在環境假設記憶體空間不足的條件下，WMG演算法相較於Misra-Gries演算法只增加一個記憶體空間的使用，同樣地執行偏度為0.4的測資，正確率就提高到80%。此外我們以理論分析定義WMG的誤差界限，並以實驗佐證。

另一方面，為了使WMG可以應用在大數據環境處理串流資料，我們使用Apache Storm將WMG平行化實作，從實驗結果證實了WMG平行化版本是可以適用於大數據串流環境的，我們可以提高平行運算度，使得在相同時間內處理更多的資料量（Throughput），而且保證平行化後的Top-K正確率不會比Sequential版本差。

The problem of finding top-k frequent items over data streams is very popular and heavily studied in data streams analysis, and it is widely used in many applications, such as network traffic monitoring and identifying high-clicker commodity. However, exactly finding the top-k items is difficult, because the quantities of data in data streams are so large that it is costly to store all data and then process them. To deal with this problem, many algorithms are proposed to gain the approximate results with tolerable errors.

Misra-Gries algorithm is one of counter-based algorithms that are used to find frequent items and top-k items in data streams. However, when Misra-Gries algorithm process the test data whose distribution is low-skewed, the accuracy rate of top-k result is very low. In our experiment, Misra-Gries algorithm process the test data generated following the Zipfian distribution and the parameter skewness is set to 0.4, then the accuracy rate of top-k result is only 32%.

In order to improve the accuracy rate, we not only partially modify the update rule of Misra-Gries algorithm, but also add the concept of “sliding window” to the algorithm. Although the top-k result is approximate, the error is guaranteed not exceed an error bound. The algorithm we proposed is named to “sliding window Misra-Gries algorithm” that is abbreviated to “WMG”. WMG is very simple and use small memory space. WMG which just need one more memory space, compared to Misra-Gries algorithm, process the test date we mentioned above get the accuracy rate 80%.

In addition, we present a parallel version of WMG, so that it can process larger quantities of data in data streams. We explain how WMG algorithm is parallelized and implement the parallel version of WMG by Apache Storm. The experiment results show that our parallel design could achieve high throughput, and the accuracy rate of top-k result is not worse than the accuracy rate of the sequential version.

論文審定書 i
摘要 iii
Abstract iv
圖次 viii
表次 ix
第一章 序論 10
1.1 研究動機與目的 10
1.2 論文架構 12
第二章 問題定義 13
第三章 相關研究 15
第四章 研究背景 17
4.1 Misra-Gries Algorithm 17
4.2 Space Saving Algorithm 20
第五章 改良Misra-Gries演算法 22
5.1 Window定義 23
5.2 WMG演算法 24
5.3 誤差範圍分析 29
5.4 實驗設計與數據說明 31
5.4.1 測試資料 31
5.4.2 參數說明 32
5.4.3 實驗一 33
5.4.4 實驗二 36
5.4.5 實驗三 42
第六章 平行化處理 45
6.1 WMG平行化設計 45
6.2 使用工具 47
6.2.1 Storm特點 47
6.2.2 Storm集群組成 48
6.2.3 Storm基本概念 51
6.3 以Storm平行化實作 54
6.3.2 Input Spout 55
6.3.3 WMG Bolt 55
6.3.4 Merge Bolt 56
6.4 實驗環境 57
6.4.1 主機硬體資訊 57
6.4.2 軟體與函式庫版本 58
6.4.3 系統架設平台 58
6.5 實驗設計與數據說明 60
第七章 結論 64
參考文獻 65
附錄一：學位考試委員問題與回覆 69
附錄二：英文投稿論文 71

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