AND-OR search graphs are used to represent problem solving and decomposition. The nodes represent states or goals, and successors are labeled as either AND or OR branches. AND branches indicate subgoals that must all be achieved, while OR branches represent alternative subgoals that could achieve the parent goal. AO* is an AND-OR graph algorithm that can find multiple solutions by combining AND and OR branches, but does not always find an optimal solution as it may not explore all possibilities once a solution is found. In contrast, A* is an OR graph algorithm that finds a single optimal solution by guaranteeing to explore all possibilities.

1. AND-OR search
With Example
15

2. AND-OR Search (AO*)
 AND/OR graph is a form of graph or tree
used in problem solving and problem
decomposition. The nodes of
the graph represent states or goals and their
successors are labeled as either AND or OR
branches.
 The AND successors are subgoals that must
all be achieved to satisfy the parent goal,
while OR branches indicate alternative
subgoals, any one of which could satisfy the
parent goal.
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Goal: Acquired Mobile
Goal:
Buy a
Mobile
Goal:
Earn
some
money
Goal:
Steal
Mobile

3. Subscribe
A
D
C
B
1
1
1
6 5
3
AND
OR
f(n)=g(n)+h(n)
f(n)=cost function
g(n)= Actual cost or edge value.
h(n)= heuristic value
Path-1 (AB) 1+6=7
Path-2 (ACD) 1+3+1+5=10
7 10
AB

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A
B D
C
F
E H
G J
I
1
1
1
1
1
1 1 1 1
15 8 7 1 6 3
10
13
20
f(n)=g(n)+h(n)
Path1: f(AB)=1+20=21
Path2: f(ACD)=1+13+1+10=25
f(BEF)= 1+15+1+8= 25
f(AB)=1+25=26 (revised)
f(DIJ)=1+6+1+3= 11
f(CGH)= 1+7+1+1=10
f(ACD)= 1+10+1+11=23 (revised)
25
min(26,23)=23
11
10
21 25
26 23

5. Difference between A* and AO*
A* algorithm
 A* algorithm is OR graph
algorithm.
 It just find only one solution.
 A* algorithm guarantees to give
an optimal solution.
AO* algorithm
 AO* is a AND-OR graph algorithm.
 It find more than one solution by
ANDing two or more branches.
 AO* algorithm does not always give
optimum solution. AO* doesn't
explore all other solutions once it got
a solution.
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6. Thanks For
Watching
Reference:
Artificial Intelligence
A Modern Approach Third Edition
Peter Norvig and Stuart J. Russell
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