Constraint Satisfaction Problems

1
Tutorial

• Constraint Satisfaction Problems

2
CSP

• Exercise 1

3
Map Coloring

• Consider the following map. The task is to color
  the map using the three colors Red, Blue, and
  Green, such that no two adjacent regions take the
  same color.

4
Map Coloring

• Formulate the problem as a CSP. Clearly state the
  variables, domains, and constraints.
• Describe the topology of the constraint graph.
• What is the size of the search space?
• Color the map using
• Backtracking Search with MRV heuristic.
• Backtracking Search with MCV heuristic.
• Backtracking Search with LCV heuristic.
• Backtracking Search with Forward Checking
  heuristic.
• Note Variables and values are ordered as
  follows
• Variables WA, NT, Q, NSW, V, SA, T
• Values Red, Blue, and Green

5
CSP

• Exercise 2

6
3 colour me!
Use all heuristics including arc-propagation to
solve this problem.
7
CSP

• Exercise 3

8
CSP Examination Problem

• During an examination, an invigilator has to
  arrange six students in a way to make sure that
  the examination is properly conducted and no one
  cheats. 2 students have makeup in Artificial
  Intelligence, 1 student has makeup in Database, 2
  students have makeup in Mathematics, and 1
  student in Physics. As shown in figure below,
  there exist 6 desks arranged into two rows and
  three columns.

9
Examination Problem

• The problem for the invigilator is to arrange
  students so that students having the same makeup
  exam should not be neighbors (in the same column,
  in the same row or the same diagonal for example
  - neighbors of 5 are 1, 2, 3, 4 and 6, - and
  neighbors of 3 are 2 (same row), 5 (same
  diagonal) and 6 (same column)).
• Propose a formulation of the problem in term of
  CSP by specifying variables, domains and
  constraints
• Describe the topology of the constraint graph.
• Using Forward Checking with Backpropagation,
  propose a solution to help the invigilator.
  Variables and values should be selected according
  to alphabetical or ascending order.
• Using Backpropagation with MCV heuristic, propose
  a solution to help the invigilator. Variables and
  values are ordered according to alphabetical or
  ascending order.

10
CSP

• Exercise 4

11
Forward Checking

• Do it yourself
• Solve 6-queens