1. LeongHW, SoC, NUS (CS5234 -- Combinatorial and Graph Algorithms) Page 1 About CS5234: Course Overview CS5234: Combinatorial and Graph Algorithms  Level and Emphasis of Course o Advanced level, geared towards research o Learn to design more efficient algorithms o Learn advanced techniques for analysis of algorithms  Challenging Homeworks  Is this course suitable for you? o Course Pre-requisites o Mathematical Maturity o Programming Experience

2. LeongHW, SoC, NUS (CS5234 -- Combinatorial and Graph Algorithms) Page 2 CS5234: Comb and Graph Alg (Fall 2007)  Instructor: Leong Hon Wai, COM1 03-41 o http://www.comp.nus.edu.sg/~CS5234/2007-08/ http://www.comp.nus.edu.sg/~CS5234/2007-08/  Course Objectives: o covers advanced design and analysis of algorithms o emphasizes efficient algorithms and data structures o Algorithms for combinatorial optimisation o Use of algorithms in advanced software development  Target Students: o advanced undergraduate (4 th year) students o beginning graduate students o those doing research in algorithm design

3. LeongHW, SoC, NUS (CS5234 -- Combinatorial and Graph Algorithms) Page 3 CS5234: Overview…(2)  Prerequisite: o CS3230 Design and Analysis of Algorithms AND o C++ Programming Skills o Or Consent of Instructor  TextBook and Reference Material: o [CLRS01] Introduction to Algorithms, (2 nd edition) by Cormen, Leiserson, Rivest, Stein o (Material also comes from [Tarj83], [RND77], etc)

4. LeongHW, SoC, NUS (CS5234 -- Combinatorial and Graph Algorithms) Page 4 CS5234: Overview… (3)  Course Grading: o 30% Homeworks o 30%Programming Assignments o 40%Final Exam (OPEN BOOK)  Homework: (30%) o About 4-5 sets (about 1 every 2-3 weeks) o Very important part of the course  Project: (30%) o LEDA programming assignments o Programming project

5. LeongHW, SoC, NUS (CS5234 -- Combinatorial and Graph Algorithms) Page 5 CS5234: Topics (Tentative)  QUICK REVIEW: oAA, DS, DP, Greedy, Graph Alg  ADVANCED DATA STRUCTURES and ALGORITHMS oHeaps, Fast Graph Algorithms oAmortized Analysis and Binomial Heaps, Fibonacci Heaps oLEDA: Library of Efficient Data Structures and Algorithms  COMBINATORIAL Optimization oNetwork Flow Problems: Algorithms and Applications oMaximum Matching: Algorithms and Applications oCASE STUDY: Graph Partitioning and Berth Allocation Problem  NP-COMPLETENESS oNP-completeness: Cook's Theorem, Reduction oApproximation Algorithms oLocal Search Methods  SPECIAL TOPICS: oPresentations by Students

6. LeongHW, SoC, NUS (CS5234 -- Combinatorial and Graph Algorithms) Page 6 CS4534: References  Main Text: [CLRS01] Introduction to Algorithms, (2 nd edition) by Cormen, Leiserson, Rivest, Stein, MIT, (2001)  References: [Tar83]* Data Structures and Network Algorithms by Robert E. Tarjan, SIAM, 1983. [RND77] Combinatorial Algorithms: Theory & Practice by Reingold, Nievergelt & Deo, PH, (1977) [PS82] Combinatorial Optimization: Alg. & Complexity, by Papadimitriou & Steiglitz, PH, (1982)

7. LeongHW, SoC, NUS (CS5234 -- Combinatorial and Graph Algorithms) Page 7 About CS5234 Homeworks  RSA Problem o Routine Problems -- easy practice problems o Standard Problems -- to be submitted o Advanced Problems -- for challenge, fun

8. LeongHW, SoC, NUS (CS5234 -- Combinatorial and Graph Algorithms) Page 8 About CS5234 Homeworks – (2)  Academic Policy (on Plagiarism) o You do your work YOURSELF o If REALLY stuck, discuss ONLY general approaches u IF YOU DISCUSS, write names of collaborators o Do NOT copy/compare answers!  Your Homework Answers: o Concise & Precise Answers o Appropriate Level of Detail (see handouts)

9. LeongHW, SoC, NUS (CS5234 -- Combinatorial and Graph Algorithms) Page 9 CS5234: Is this the right Course for You?  I ASSUME knowledge of o Programming (CS1101); Data Structures (CS1102); o AND CS3230 Analysis of Algorithms;  If you have NOT done CS3230 or equiv.: o Take CS3230 instead! This is NOT a course to learn algorithms? o We assume that you ALREADY KNOW algorithms o TAKE CS3230 instead!

10. LeongHW, SoC, NUS (CS5234 -- Combinatorial and Graph Algorithms) Page 10 CS5234 Pre-Requisites…  CS3230 Analysis of Algorithms  Else, Background Knowledge Assumed oAlternatively, see that you have mastered the following Chapters from the text [CLRS01] (including the analysis of their running times): uChapters 3-5Mathematical Foundations uChapters 6-13Basic Data Structures uChapters 15-16DP and Greedy Algorithms uChapters 22-24Basic Graph Algorithms  Otherwise: oTalk to instructor (case-by-case)

11. LeongHW, SoC, NUS (CS5234 -- Combinatorial and Graph Algorithms) Page 11 Else, Background Knowledge Assumed ….  Data Structures: (with Analysis)  Stacks, Queues, Lists,  Binary search trees, balanced trees,  Heaps and priority queues  Algorithm Design Paradigms (with Analysis)  Standard sorting and searching algorithms  Graph algorithms: DFS, BFS,  Dijkstra's SP alg, MST Algorithms  Greedy Algorithms, Dynamic Prog, Divide-and-Conquer  Analysis of Algorithms  Expertise with Big-O notations  Competent with Algorithm Analysis: Quicksort, Heapsort, DFS, BFS, Divide-and-Conquer alg.

12. LeongHW, SoC, NUS (CS5234 -- Combinatorial and Graph Algorithms) Page 12 Q & A. --- The End ---

13. LeongHW, SoC, NUS (CS5234 -- Combinatorial and Graph Algorithms) Page 13 CS4234 Lecture 1 -- (14-Aug-07) “Quick Review”  Lecture Topics and Readings o Motivation o Asymptotics & Anal of Algs[CLRS]-C1-4 o Randomized Quicksort [CLRS]-C7 u 1.386 n lg n o Augmenting Data Structures [CLRS]-C14  Assignments (in/out): o Out: HW1 -- Due on 28-Aug-2007 Quickly get up to speed.

14. LeongHW, SoC, NUS (CS5234 -- Combinatorial and Graph Algorithms) Page 14 CS4234 Lecture 2 -- (21-Aug-07) “Quick Review”  Lecture Topics and Readings o Dynamic Programming Algs[CLRS]-C15 o Greedy Algorithms [CLRS]-C16 o Heaps (Priority Queues)[CLRS]-C6 o Graph Algorithms Assumed[CLRS]-C22-23 Quickly get up to speed.