Iterative Deepening A* (IDA*) is an extension of A* search that combines the benefits of depth-first and breadth-first search. It performs depth-first search with an iterative deepening limit on the cost function f(n), increasing the limit if the goal is not found. This allows IDA* to be optimal and complete like breadth-first search while having modest memory requirements like depth-first search. The algorithm starts with an initial f-limit of the start node's f-value, pruning any nodes where f exceeds the limit. If the goal is not found, the limit is increased to the minimum f among pruned nodes for the next iteration.

1. Iterative Deepening A*
Algorithm
(Extension of A*)
Lecture-17
Hema Kashyap
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2. Introduction
• Iterative deepening A* or IDA* is similar to
iterative-deepening depth-first, but with the
following modifications:
• The depth bound modified to be an f-limit
1. Start with limit = h(start)
2. Prune any node if f(node) > f-limit
3. Next f-limit=minimum cost of any node pruned
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3. Iterative Deepening Search
• Iterative Deepening is a kind of uniformed
search strategy
• Combines the benefits of depth-first and
breadth- first search
• Advantage-
– it is optimal and complete like breadth first search
– Modest memory requirement like depth-first
search
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4. IDA*(Iterative Deepening A*) Search
• Perform depth-first search LIMITED to some f-
bound.
• If goal found: ok.
• Else: increase de f-bound and restart.
• How to establish the f-bounds?
• - initially: f(S)
• generate all successors
• record the minimal f(succ) > f(S)
• Continue with minimal f(succ) instead of f(S)
f4
f3
f2
f1
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5. Example
S
f=100
A
f=120
B
f=130
C
f=120
D
f=140
G
f=125
E
f=140
F
f=125
f-new = 120f-limited, f-bound = 100
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6. Example
S
f=100
A
f=120
B
f=130
C
f=120
D
f=140
G
f=125
E
f=140
F
f=125
f-limited, f-bound = 120 f-new = 125
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7. Example
S
f=100
A
f=120
B
f=130
C
f=120
D
f=140
G
f=125
E
f=140
F
f=125
f-limited, f-bound = 125
SUCCESS
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8. IDA* Analysis
• IDA* is complete, optimal,
and optimally efficient
(assuming a consistent,
admissible heuristic), and
requires only a polynomial
amount of storage in the
worst case:
• IDA* is complete & optimal
Space usage is linear in the
depth of solution. Each
iteration is depth first
search, and thus it does not
require a priority queue.
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