近年來， GPU 透過增加核心的方式，使得計算能力大幅提升。
GPU 之硬體設計概念著重於處理資料的平行運算，
因此若要妥善發揮其計算效能，使用上有一定的限制。
例如，若針對高度相依性的資料，其運算無法發揮 GPU 平行化的特性，以至於無法得到效能的提升。

現今諸多 GPU 相關的研究大多著重於探討 GPU 能增加的計算效益。
因此，藉由 GPU 與多核心 CPU 之間的比較，我們試圖研究 GPU 的成本效益分析。
在善加運用 GPU 與多核心 CPU 之兩個不同的硬體架構之下，我們分別實作幾個典型的演算法，並列出其實驗結果。
此外，我們更進一步的在本論文中，提出包含時間與花費之成本效益分析。

The GPU significantly improves the computing power by increasing the number of cores in recent years.
The design principle of GPU focuses on the parallism of data processing.
Therefore, there is some limitation of GPU application for the better computing power.
For example, the processing of highly dependent data could not be well-paralleled.
Consequently, it could not take the advantage of the computing power improved by GPU.

Most of researches in GPU have discussed the improvement of computing power.
Therefore, we try to study the cost effectiveness by the comparison between GPU and Multi-Core CPU.
By well-applying the different hardware architectures of GPU and Multi-Core CPU,
we implement some typical algorithms, respectively, and show the experimental result.
Furthermore, the analysis of cost effectiveness, including time and money spending, is also well discussed in this paper.

目錄
1 緒論 1
1.1 研究背景 .............................. 1
1.2 研究動機 .............................. 2
1.3 研究目的 .............................. 2
1.4 論文架構 .............................. 2
2 相關背景知識 3
2.1 CUDA .............................. 3
2.1.1 平行程式模型 ....................... 3
2.1.2 Kernel........................... 4
2.1.3 Device Memory ...................... 6
2.1.4 Shared Memory ...................... 9
2.1.5 時間測量 .......................... 10
2.1.6 Texture Memory ..................... 11
2.2 GPU 硬體架構 ........................... 13
2.2.1 GTX200 概觀 ....................... 13
2.2.2 Streaming Multiprocessor ................ 14
3 演算法的平行與實作 17
3.1 Bellman-Ford 演算法 ....................... 17
3.1.1 定義 ............................ 18
3.1.2 演算法 ........................... 18
3.1.3 平行化 Bellman-Ford 演算法 ............... 19
3.1.4 樹狀收斂 .......................... 20
3.1.5 GPU實作平行化 Bellman-Ford 演算法 ......... 21
3.2 Dijkstra’s 演算法 ......................... 27
3.2.1 定義 ............................ 27
3.2.2 演算法 ........................... 27
3.2.3 平行化 Dijkstra’s 演算法 ................. 28
3.2.4 平行化搜尋最小值 ..................... 29
3.2.5 GPU實作平行化 Dijkstra’s 演算法 ............ 30
3.3 Odd-Even Sorting 演算法 ..................... 40
3.3.1 定義 ............................ 40
3.3.2 演算法 ........................... 40
3.3.3 平行化 Odd-Even Sorting 演算法 ............. 41
3.3.4 GPU實作平行化 Odd-Even Sorting 演算法 ....... 43
4 實驗以及結果分析 46
4.1 實驗方式 .............................. 46
4.2 實驗環境設備 ........................... 47
4.3 程式效能增益 ........................... 48
4.3.1 CPU程式效能增益 .................... 48
4.3.2 GPU程式效能增益 .................... 48
4.4 平行化 Bellman-Ford 演算法實驗結果 .............. 49
4.5 平行化 Dijkstra’s 演算法實驗結果 ................. 51
4.6 平行化 Odd-Even Sorting 演算法實驗結果 ............ 53
4.7 結果分析 .............................. 55
5 結論以及未來展望 58

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