All Computer Science is based on the concept of an efficient algorithm: a finite sequence of primitive instructions that, when executed according to their well-specified semantics, provably provide a mechanical solution to the infinitely many instances of a complex mathematical problem within a guaranteed number of steps of least asymptotic growth. We thus call these the 'virtues' of Theoretical Computer Science:

• full and unambiguous problem specification
• formal semantics of operational primitives
• algorithm design (as opposed to 'programming')
• and analysis (correctness, asymptotic cost)
• with proof of asymptotic optimality.

Building on undergraduate CS300 (Introduction to Algorithms), the graduate-level course CS500 discusses the design of advanced algorithms and analyzes their behaviour with respect to various notions of performance such as

• worst-case,
• average-case,
• expected, and
• amortized runtime;
• memory use,
• competitive ratio,
• approximation ratio etc.

Their practical impact is demonstrated in selected implementations.

Lecturer: Martin Ziegler

Classroom: Online

Schedule: Tuesdays and Thursdays, 9:00am to 10:30am
Lectures start from March 17th.

Language: English only

Teaching Assistants: 임동현 (klimdhn@kaist.ac.kr), Ivan Koswara (chaoticiak@kaist.ac.kr)

Homework: Handwritten individual solutions (English only) and programming assignments in ELICE.

Grading: In view of the recent switch to online teaching and cancelled midterm, the final grade is determined to 50% from homework and 50% from final exam.

Midterm: cancelled
Final exam: TBD

Prerequisites: CS204 (Discrete Mathematics), CS300 (Introduction to Algorithms)

• Cormen, Leiserson, Rivest, Stein: Introduction to Algorithms (3rd Edition), MIT Press (2009).
• Dasgupta, Papadimitriou, Vazirani: Algorithms, McGraw-Hill (2006).
• Kleinberg, Tardos: Algorithm Design, Pearson (2006).
• Vöcking, Alt, Dietzfelbinger, Reischuk, Scheideler, Vollmer, Wagner: Algorithms Unplugged, Springer (2011).
• Introduction to the Analysis of Algorithms (Robert Sedgewick and Philippe Flajolet)
• Online Computation and Competitive Analysis (Allan Borodin and Ran El-Yaniv)
• Probability and Computing: Randomized Algorithms and Probabilistic Analysis (Michael Mitzenmacher and Eli Upfal)
• M. Sipser: Introduction to the theory of computation, Boston (1997)
• E. Vigoda: Graduate Algorithms
• R. Sedgewick: Algorithms
• Coursera: Data Structures and Algorithms
• MIT OCW: Design and Analysis of Algorithms (2015)

0. Preliminaries (pdf,ppt,video)
1. Introduction (pdf,ppt,video)
2. Examples (pdf,ppt,video)
3. Tree Data Structures (pdf,ppt,video1,video2,video3,video4)
4. Amortized Analysis (pdf,ppt,video1,video2,video3,video4,video5,bonus)
5. Randomization (pdf,ppt,video1,video2,video3)
6. Online/Competitive (pdf,ppt,video1,video2,video3)
7. Complexity Theory (pdf,ppt,video1,video2)
8. Approximation (pdf,ppt,video1,video2,video3)
(9. Memory≈parallel Time)
10. Conclusion (pdf,ppt)

• KLMS
• ELICE