Problem Decomposition: Goal Trees, Rule Based Systems, Rule Based Expert Systems. Planning: STRIPS, Forward and Backward State Space Planning, Goal Stack Planning, Plan Space Planning, A Unified Framework For Planning. Constraint Satisfaction : N-Queens, Constraint Propagation, Scene Labeling, Higher order and Directional Consistencies, Backtracking and Look ahead Strategies.

1. Topic To Be Covered:
1.Example of CSP(MCP) 2.Varieties of csp
3.Backtracking in CSP
Jagdamba Education Society's
SND College of Engineering & Research Centre
Department of Computer Engineering
SUBJECT: Artificial Intelligence & Robotics
Lecture No-11(UNIT-02)
Prof.Dhakane Vikas N

2. Example of CSp : Map Coloring Problem
What is NEED of Constraint Satisfaction Approach???

3. Example of CSp : Map Coloring Problem
What is Map Coloring Problem?
 The MAP-COLORING problem is defined as follows: Given a map of
countries, and a fixed set of colors, assign a color to each region in the
map in such a way that no two adjacent regions have the same color.
 In this example variable are (WA,NT,Q,NSW,V,SA,T)
 Domain D={Red, Green, Blue)
 Constraints: Adjacent Region Must have different colors.e.g.(WA≠NT)

4. Example of CSp : Map Coloring Problem
What is Map Coloring
Problem?
 In this example variable are
(WA,NT,Q,NSW,V,SA,T)
 Domain D={Red, Green,
Blue)
 Constraints: Adjacent
Region Must have different
colors.e.g.(WA≠NT)
 Solution: Are Complete &
Consistent assignments:
e.g. WA=red, NT=green
Q=red , NSW=green
V=red , SA=blue,
T=green

5. Varieties of CSp
Based on Various Combination of different types of Variables &
Domains, we have varieties of CSP:
I. Discrete Variables & Finite Domains(Boolean CSP):
 It is CSP where the domain of value are Boolean e.g. true or False
 Any variable in CSP , you can set it to either True or False.
II. Discrete Variables & Infinite Domains:
 It is CSP where the domain of value are integers ,string etc.
 Any variable in CSP , you can set it to range of values.

6. Varieties of CSp
Varieties of Constraints
I. Unary Constraints
 It involves single variable
e.g., SA ≠green
II. Binary Constraints
 It involves pairs of Variable
e.g., SA ≠WA
III. Higher Order Constraints
 It involves 3 or More variables.

7. Backtracking In CSp
What is Backtracking??
Backtracking is a general algorithm for finding all (or some) solutions to
some computational problems, notably constraint satisfaction problems, that
incrementally builds candidates to the solutions, and abandons a candidate
("backtracks") as soon as it determines that the candidate cannot possibly be
completed to a valid solution.
1.Initial State
 The empty Assignment
2.Successor Function
 Assign a value to an unassigned variable that does not conflict with
current assignment; it fails when no legal assignment available.
3.Goal state(test)
 When the required assignment is complete.

8. Backtracking In CSp
Improving Backtracking Efficiency
Drawbacks of Backtracking
1. The other drawback of backtracking is having to perform redundant
work.
2. Finally, the basic backtracking algorithm still detects the conflict too late
as it is not able to detect the conflict before the conflict really occurs
 Drawbacks of backtracking technique can be reduced by reducing number
of backtracks.
 Following are the general purpose methods that can give huge gains in
speed by enforcing minimum number of backtracks.

12. Backtracking In CSp
Improving Backtracking Efficiency
 While Assigning Values to Particular Variable during Evaluation
Following Questions are Inevitable.
 By Answering These questions we can Design an Efficient strategy in
order to improve Efficiency of Backtracking Process.
I. Which Variable Should Be Assigned Next?
 The Answer to this question lead to two simple strategies to select the
next variable for assignment ,called as “Most Constrained Variable” & “
Most Constraining Variable”
II. In What order Should its Value Be tried?
 This question design a strategy called “Least Constraining Value”,
which helps us in choosing a value among all possible values from the
domain.

13. Backtracking In CSp
Improving Backtracking Efficiency
 While Assigning Values to Particular Variable during Evaluation
Following Questions are Inevitable.
 By Answering These questions we can Design an Efficient strategy in
order to improve Efficiency of Backtracking Process.
III. Can we detect Inevitable Failure Early?
 This is the key question which has impact on the speed of generating
solution.
 These are the strategies which can foresee the failure if the current
path of the assignment is followed.
 Thereby guide us whether we are on right track.
 There are two strategies related to this “Forward Checking”,
“Constraint Propagation”