General Computer Science 320201 GenCS I & II Lecture ... - Kwarc

c○: Michael Kohlhase 466
Iterative deepening search: Properties
Complete Yes
Time (d + 1)b 0 + db 1 + (d − 1)b 2 + . . . + b d ∈ O(b d+1 )
Space O(bd)
Optimal Yes (if step cost = 1)
(Depth-First) Iterative-Deepening Search often used in practice for search spaces of large,
infinite, or unknown depth.
Comparison:
Criterion
Breadthfirst
Uniformcost
Depthfirst
Iterative
deepening
Complete? Yes ∗ Yes ∗ No Yes
Time b d+1 ≈ b d b m b d
Space b d+1 ≈ b d bm bd
Optimal? Yes ∗ Yes No Yes
c○: Michael Kohlhase 467
Note: To find a solution (at depth d) we have to search the whole tree up to d. Of course since we
do not save the search state, we have to re-compute the upper part of the tree for the next level.
This seems like a great waste of resources at first, however, iterative deepening search tries to be
complete without the space penalties.
However, the space complexity is as good as depth-first search, since we are using depth-first
search along the way. Like in breadth-first search, the whole tree on level d (of optimal solution)
is explored, so optimality is inherited from there. Like breadth-first search, one can modify this
to incorporate uniform cost search.
As a consequence, variants of iterative deepening search are the method of choice if we do not
have additional information.
Comparison
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