課程概述 |
這門課的目的在於學習演算法設計的六個基本策略,如下所示。
Greedy Method
Dynamic Programming (DP)
Prune-and-Search (P&S)
Branch-and-Bound (B&B)
Divide-and-Conquer (D&C)
Plane Sweep
這門課有二次程式考試。第一次考試要求同學設計一個能解決 the longest
common subsequence problem 的 DP 程式與一個能解決 2-d linear
programming problem 的 P&S 程式。第二次考試要求同學設計一個能解決
the 0/1 knapsack problem 的 B&B 程式與一個能解決 2-d closest pair
problem 的 D&C 程式。以上四個 problems 與其相對應的演算法在課堂上將
會詳細介紹。
這二次考試在期末有一次補考機會。若補考成績低於或等於原始成績,
則以原始成績作為最終成績。若補考成績高於原始成績,則以
"原始成績+(補考成績-原始成績)x90%" 作為最終成績。
同學必須閱讀以下四篇論文(DP、P&S、B&B、D&C 各一篇),並繳交書面
閱讀報告。
(DP) Wagner, "The string-to-string correction problem," Journal of the
ACM, vol.21, no.1, 1974, 168-173.
(P&S) Megiddo, "Linear-time algorithms for linear programming in R3
and related problems," SIAM Journal on Computing, vol.12, no.4,
1983, 759-776 (only Section 3 is required).
(B&B) A personal assignment problem solved by the branch-and-
bound strategy (in Section 5-6 of Lee, Tseng, Chang and Tsai's
book: Introduction to the Design and Analysis of Algorithms).
(D&C) Imai, Iri, and Murota, "Voronoi diagram in the Laguerre
geometry and its applications," SIAM Journal on Computing,
vol.14, no.1, 1985, 93-105.
每篇閱讀報告必須包含(但不限)以下內容,且必須用例子與圖表輔助說明。
問題定義
解法敘述(勿列出詳細程式碼)
讀後心得
閱讀報告請以中文書寫(可夾雜英文專有名詞),勿剪貼原始論文內容拼湊
而成,應忠實地將自己所理解的內容寫出。例子與圖表可援用原始論文或
自創,敘述方式不必遵循原著可自創。老師將親自批閱同學的閱讀報告,
評分依據如下。
態度(是否用心書寫?)
能力(是否看懂論文且掌握重點?是否敘述清楚且精簡扼要?是否使用合適
的例子與圖表輔助說明?)
此外,同學將分成八組研讀以下八篇論文(DP 三篇、P&S 一篇、B&B 與 D&C 各
二篇)並在課堂上報告。
(DP) Knuth, "Optimal binary search trees," Acta Informatica, vol.1, 1971,
14-25.
(DP) Hsu and Du, "New algorithms for the LCS problem," Journal of
Computer and System Sciences, vol.29, 1984, 133-152.
(DP) Wang, Chen, and Park, "On the set LCS and set-set LCS problems,"
Journal of Algorithms, vol.14, no.3, 1993, 466-477. (ignore Section 3:
The Set LCS Problem)
(P&S) Bhattacharya, Jadhav, Mukhopadhyay, and Robert, "Optimal
algorithms for some intersection radius problems," Computing, vol.52,
no.3, 1994, 269-279. (ignore Section 2: Intersection Radius Problem
for Hyperplanes)
(B&B) Wang and Lee, "An Efficient Channel Routing Algorithm to Yield
an Optimal Solution," IEEE Transactions on computers, vol.39, no.7,
1990, 957-962.
(B&B) Section 5-9 of Lee, Tseng, Chang and Tsai's book: Introduction to
the Design and Analysis of Algorithms.
(D&C) Guting, "Optimal divide-and-conquer to compute measure and
contour for a set of iso-rectangles," Acta Informatica, vol.21, 1984,
271-291.
(D&C) Lee, "An optimal time and minimal space algorithm for rectangle
intersection problems," International Journal of Computer and Information
Sciences, vol.15, no.1, 1984, 23-32.
所有論文皆有電子檔供下載。針對同學的報告,老師將會給予適當建議
(若有需要),相信對同學日後職場生涯有所助益。 |