DCS Lecture

1
DCS Lecture how to solve it
Patrick Prosser
2
Your Challenge
Put a different number in each circle (1 to 8)
such that adjacent circles cannot take
consecutive numbers
3
Thats illegal, okay?
5
6
Put a different number in each circle (1 to 8)
such that adjacent circles cannot take
consecutive numbers
4
Thats illegal, okay?
3
3
Put a different number in each circle (1 to 8)
such that adjacent circles cannot take
consecutive numbers
5
The Puzzle

• Place numbers 1 through 8 on nodes
• Each number appears exactly once

• No connected nodes have consecutive numbers

?
?
?
?
?
?
?
?
You have 4 minutes!
6
Bill Gates asks how do we solve it?
How do we solve it?
7
Heuristic Search
Which nodes are hardest to number?
?
?
?
?
?
?
?
?
Heuristic a rule of thumb
8
Heuristic Search
?
?
?
?
?
?
?
?
9
Heuristic Search
Which are the least constraining values to use?
?
?
?
?
?
?
?
?
10
Heuristic Search
Values 1 and 8
?
?
1
8
?
?
?
?
11
Heuristic Search
Values 1 and 8
?
?
1
8
?
?
?
?
Symmetry means we dont need to consider 8 1
12
Inference/propagation
We can now eliminate many values for other nodes
Inference/propagation reasoning
13
Inference/propagation
1,2,3,4,5,6,7,8
?
?
1
8
?
?
?
?
14
Inference/propagation
2,3,4,5,6,7
?
?
1
8
?
?
?
?
15
Inference/propagation
3,4,5,6
?
?
1
8
?
?
?
?
16
Inference/propagation
3,4,5,6
?
?
1
8
?
?
?
?
3,4,5,6
By symmetry
17
Inference/propagation
3,4,5,6
1,2,3,4,5,6,7,8
?
?
1
8
?
?
?
?
3,4,5,6
18
Inference/propagation
3,4,5,6
2,3,4,5,6,7
?
?
1
8
?
?
?
?
3,4,5,6
19
Inference/propagation
3,4,5,6
3,4,5,6
?
?
1
8
?
?
?
?
3,4,5,6
20
Inference/propagation
3,4,5,6
3,4,5,6
?
?
1
8
?
?
?
?
3,4,5,6
3,4,5,6
By symmetry
21
Inference/propagation
3,4,5,6
3,4,5,6
?
?
1
8
?
?
2,3,4,5,6
3,4,5,6,7
?
?
3,4,5,6
3,4,5,6
22
Inference/propagation
3,4,5,6
3,4,5,6
?
?
1
8
?
?
2,3,4,5,6
3,4,5,6,7
?
?
3,4,5,6
3,4,5,6
Value 2 and 7 are left in just one nodes domain
23
Inference/propagation
3,4,5,6
3,4,5,6
?
?
1
8
2
7
2,3,4,5,6
3,4,5,6,7
?
?
3,4,5,6
3,4,5,6
And propagate
24
Inference/propagation
3,4,5
3,4,5,6
?
?
1
8
2
7
2,3,4,5,6
3,4,5,6,7
?
?
3,4,5
3,4,5,6
And propagate
25
Inference/propagation
3,4,5
4,5,6
?
?
1
8
2
7
2,3,4,5,6
3,4,5,6,7
?
?
3,4,5
4,5,6
And propagate
26
Inference/propagation
3,4,5
4,5,6
?
?
1
8
2
7
?
?
3,4,5
4,5,6
Guess a value, but be prepared to backtrack
Backtrack?
27
Inference/propagation
3,4,5
4,5,6
3
?
1
8
2
7
?
?
3,4,5
4,5,6
Guess a value, but be prepared to backtrack
28
Inference/propagation
3,4,5
4,5,6
3
?
1
8
2
7
?
?
3,4,5
4,5,6
And propagate
29
Inference/propagation
5,6
3
?
1
8
2
7
?
?
4,5
4,5,6
And propagate
30
Inference/propagation
5,6
3
?
1
8
2
7
?
?
4,5
4,5,6
Guess another value
31
Inference/propagation
3
5
1
8
2
7
?
?
4,5
4,5,6
Guess another value
32
Inference/propagation
3
5
1
8
2
7
?
?
4,5
4,5,6
And propagate
33
Inference/propagation
3
5
1
8
2
7
?
?
4
4,6
And propagate
34
Inference/propagation
3
5
1
8
2
7
4
?
4
4,6
One node has only a single value left
35
Inference/propagation
3
5
1
8
2
7
4
6
6
36
Solution!
3
5
1
8
2
7
4
6
37
How does a computer solve it?
Bill Gates says how does a computer solve it?
38
A Constraint Satisfaction Problem

• Variable, vi for each node
• Domain of 1, , 8
• Constraints
• All values used
• Alldifferent(v1 v2 v3 v4 v5 v6 v7 v8)
• No consecutive numbers for adjoining nodes
• v1 - v2 gt 1
• v1 - v3 gt 1

39
How we might input the problem to a program
Viewing the problem as a graph with 8
vertices and 17 edges
40
(No Transcript)
41
Graph Theory?
42
(No Transcript)
43
(No Transcript)
44
(No Transcript)
45
Our Problem as a Graph
8 vertices, 17 edges
1
2
0
6
7
3
5
4
46
Computer scientists count from zero ?
By the way, Bill Gates says
47
A Java (Constraint) Program to solve our problem
48
Read in the name of the input file
49
Make a Problem and attach variables to it
Note variables represent our vertices
50
Constrain all variables take different values
51
Read in edges and constrain corresponding variable
s/vertices non-consecutive
52
Solve the problem!
Using constraint propagation and backtracking
search
53
Print out the number of solutions
54
Why have you read in the puzzle as a file?
Bill Gates wants to know
55
So that we can be more general
56
This technology is called constraint
programming
57
Constraint programming

• Model problem by specifying constraints on
  acceptable solutions
• define variables and domains
• post constraints on these variables
• Solve model
• choose algorithm
• incremental assignment / backtracking search
• complete assignments / stochastic search
• design heuristics

It is used for solving the following kinds of
problems
58
Some sample problems that use constraint
programming

• Crew scheduling (airlines)
• Railway timetabling
• Factory/production scheduling
• Vehicle routing problems
• Network design problems
• Design of locks and keys
• Spatial layout
• workforce management

59
BT workforce management
60
Constraints are everywhere!

• No meetings before 10am
• Network traffic lt 100 Gbytes/sec
• PCB width lt 21cm
• Salary gt 45k Euros

61
A Commercial Reality

• First-tier software vendors use CP technology

62
You know, were doing something on this!
Bill Gates is watching
63
(No Transcript)
64
(No Transcript)
65
So, how do YOU solve it?
66
Computing Science at Glasgow
Learn to program a computer, learn a bit of
discrete maths, algorithmics, learn about
hardware, security and data protection, computer
graphics, information management, project
management, interactive systems, computer
networks, operating systems, professional
issues, software engineering, machine learning,
bioinformatics, grid computing and of course
constraint
programming!
67
That was a 4th year lecture
Constraint Programming An Introduction by
example with help from Toby Walsh, Chris
Beck, Barbara Smith, Peter van Beek, Edward
Tsang, ...
68
Thats all for now folks