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。第一次考試要求修課同學設計能解決
the longest common subsequence problem 的 DP 程式與能解決
two-dimensional linear programming problem 的 P&S 程式。
第二次考試要求修課同學設計能解決 the 0/1 knapsack problem
的 B&B 程式與能解決 two-dimensional closest pair problem 的
D&C 程式。每次考試都有一次補考的機會,補考後成績之計算
如下: max{原始成績, 原始成績 + (補考成績-原始成績) × 80%}。
修課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, pp. 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, pp.
759-776 (only Section 3 is required).
(B&B) A personal assignment problem solved by the branch-and-bound
strategy (Section 5-6 of Introduction to the Design and Analysis of Algorithms
by Lee, Tseng, Chang and Tsai)
(D&C) Imai, Iri, and Murota, "Voronoi diagram in the Laguerre geometry and
its applications," SIAM Journal on Computing, vol. 14, no. 1, 1985, pp. 93-105.
閱讀報告必須包含(但不限)以下內容。
問題定義
解法敘述 (勿列出詳細程式碼)
讀後心得
問題定義與解法敘述必須用例子與圖表輔助說明。閱讀報告請以中文書寫 (可夾雜
英文專有名詞),勿剪貼論文內容拼湊而成,應忠實地將自己所理解的部份寫出。
例子與圖表可直接取自論文或自創(自創較佳),敘述方式可自創不須遵循論文。
老師將會親自批閱同學的閱讀報告並給予建議。閱讀報告的評分依據如下。
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?)
修課同學將分成八組負責研讀以下八篇論文(DP 三篇、P&S 一篇、B&B 與
D&C 各二篇),並在課堂上作報告(presentation)。
(DP) Knuth, "Optimal binary search trees," Acta Informatica, vol.1, 1971, pp.14-25.
(DP) Hsu and Du, "New algorithms for the LCS problem," Journal of Computer and
System Sciences, vol.29, 1984, pp.133-152.
(DP) Wang, Chen, and Park, "On the set LCS and set-set LCS problems," Journal of
Algorithms, vol.14, no.3, 1993, pp.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, pp.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, pp.957-962.
(B&B) "A Job Scheduling Problem", Section 5-9 of Introduction to the Design
and Analysis of Algorithms by Lee, Tseng, Chang and Tsai.
(D&C) Guting, "Optimal divide-and-conquer to compute measure and contour for a
set of iso-rectangles," Acta Informatica, vol.21, 1984, pp.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, pp.23-32.
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