This course is a follow-up of "Algorithms and Data Structures". First techniques to compute the complexity of recursive algorithms will be presented, based on recurrences as they can be derived from the algorithms. In particular the Master Theorem will be discussed. Several applications are presented, in particular algorithms for huge matrices and geometric algorithms. The remaining main part of the course is about NP-completeness: investigating a wide range of algorithmic decision problems for which no polynomial algorithms are expected to exist. We give underlying theory and will prove NP-completeness for a wide range of problems, by which they are essentially equivalent. At the end some basics of the next complexity class are presented: PSPACE.
There is a 2hr written exam. Apart from that there will be 2 assignments you can hand in to get a "bonus".
The final grade is the minimum of 10 and f + a/10, where f is your written exam grade and a is your assignment grade.
There will be two moments in the course when homework exercises may be handed in. You are very strongly suggested to do so: these will be graded and commented. The average of your 2 homework grades, divided by 10 is your "bonus".
The course consists of 2 hours lecture (hoorcollege) Tuesday, 13:30--15:15, plus "self study" and an exercise class (werkcollege) on Friday, 8:30-10:15 .
An exception to this schedule is the "carnaval week" (week 9): Tuesday is lecture-free, so the lecture will be on Friday 28/2, 8:30-10:15 and there will be no exercise class.
Year-week | Order | Date and Location | Topics | Material | Exercises |
---|---|---|---|---|---|
6 | 1 | 4/2, LIN 1 | General techniques, Fibonacci, depth AVL trees, Divide and conquer, merge sort | slides lecture1, 19.4 (pp 523-525), first 6.5 pages of lecture notes | Ex. 4.3-3, 4.3-6 (page 87) and extra exercises, |
7 | 2 | 11/2, LIN 1 | Master Theorem, examples: merge sort, median | slides lecture2, pages 7-8 of lecture notes, Chapter until 4.5 (page 96), but not 4.2 + pp 220-222 | Ex. 4.4-1, 4.4-2, 4.4-3, 4.4-4 (pp 92-93), 4.5-1, 4.5-3 (pp 96-97) |
8 | 3 | 18/2, LIN 1 | Karatsuba multiplication, Strassen algorithm, proof sketch Master Theorem, smallest distance in set of points | slides lecture3, pages 9-10 of lecture notes, Remainder Chapter 4, Chapter 33.4 (pp 1039-1043) | Ex. 4-1, 4-3 (pp 107-108), 4.2-1, 4.2-7 (pp 82-83), 28.2-1 (pp 831), 33.4-3, 33.4-4, 33.4-6 (pp 1044). See also Assignment 1, which can be handed in by 28/2 |
9 | 4 | 28/2, HG00.307 | P and NP, SAT, NP-completeness | Chapter 34, also see lecture notes and Wikipedia on the Cook-Levin Theorem | Assignment 1 can be handed in on 28/2, in the delivery box of your TA in front of room M1.07A. Deadline: 11:00 AM. |
10 | 5 | 3/3, LIN 1 | Cook-Levin Theorem, NP-complete problems: CNF-SAT, <=3-SAT | Chapter 34 until page 1085 | Ex. 34.2-4, 34.2-5 (p 1066); 34.3-3, 34.3-6 (p 1077); 34.4-6 (p 1086) |
11 | 6 | 10/3, LIN 1 | NP-completeness: 3SAT, ILP, clique, vertex cover, 3-coloring | Rest Chapter 34, except pp 1092-1096 | Ex. 34.5-4, 34.5-5, problems 34-1 and 34-2 (pp 1101-1102) |
12 | 7 | 17/3, LIN 1 | Subset sum, the class PSPACE, course overview | see lecture notes | Assignment 2 can be handed in on 20/3 (It will appear on the webpage on 10/3) |