1. Design and Analysis of Algorithms (DAA) 3621511 (6 cp)
Pasi Fränti

2. DAA course at Autumn 2018 Web: http://cs.uef.fi/pages/franti/asa/
ETCS 6
Lectures (34h):
- Mon 14-17
- Tue 14-16
Exercises (16h):
- Fri 10-12
Exam dates:

3. Motivation Design Analysis
90% cases simple algorithms found from Bachelor level courses
Focus on the 10% tough ones
Analysis
Why not just measure processing time?
Time vs. space complexity analyses
Upper and lower limits

4. Key concepts Problem Algorithm Instance Can the problem be solved?
How difficult is the problem?
Real-life problems to algorithmic problems
Algorithm
How to find suitable algorithm?
How to make it efficient?
Instance
Upper and lower limits

5. Graph problems Coloring problem Shortest path Traveling salesman 117
216
110
246
Coloring problem
Shortest path
Traveling salesman
199
182
170
121
315
231
142 79
242
136
191
148 78
191
126
120
178
149 89
116
234
170 51
112 79
131
109 73
163 72 86 90
143 63 53
105 27 59 58
135
116

6. Clustering problem
Input
Output

7. What is algorithm?
We need a well-specified problem that tells what needs to be achieved
Algorithm solves the problem
It consists of a sequence of commands that takes an input and gives output
Algorithm
Input
Output

8. Non-solvable problems
Give list of all rational numbers in [0..1]
Longest sequence of  without the 0 digit
Stopping problem
Does algorithm A stop always?
Any algorithm
Solve
Stopping A B
TRUE
FALSE

9. Non-solvable problems
Give list of all rational numbers in [0..1]
Longest sequence of  without the 0 digit
Stopping problem
Algorithm C does
NOT stop always!
Any algorithm
Solve
Stopping
Algorithm “Vice Versa” A B
TRUE C
Eternal loop
FALSE
Stop

10. Algorithm principles Sequence Condition Loops One command at a time
Parallel and distributed computing
Condition IF
CASE
Loops
FOR
WHILE
REPEAT

11. Complexity Time complexity: How much time it takes to compute
Measured by a function T(N)
Space complexity:
How much memory it takes to compute
Measured by a function S(N)

12. Time complexity N = Size of the input T(N) = Time complexity function
Order of magnitude:
How rapidly T(N) grows when N grows
For example: O(N) O(logN) O(N²) O(2N)

13. Examples: Bubble sort (N²), Quicksort (N∙logN)
Asymptotic analysis
N3 --- cubic
N² --- quadratic
N logN
2N --- exponential
N --- linear
log N --- sub-linear
Examples: Bubble sort (N²), Quicksort (N∙logN)

14. Problem size vs. processing time
Processing power increases →
f(N)
T(N) = 1,000
T(N)=10,000
Growth rate
100N
N = 10
N=100
10 x
5N² 14 44
3.1 x
½N³ 12 27
2.3 x 2N 9 13
1.4 x
logN
21,000
210,000
Very high!!

15. Exponential time complexity1 2 4 8 16 32 64
128 1k 2k …
256
512 1M
Halfway…? 1G 1T 1P 1E
Large than Everest
264 = 18.4 ∙ 1018

16. Graph algorithms

17. Graph algorithms