Artificial Intelligence and Soft Computing: Behavioral ... - Arteimi.info

d=0
d=1
d=2
d=3
Fig. 12.16: A hierarchical plan with branching factor b=3, primitive steps
s = 3 in a plan and depth (d) of the tree=3.
On the other hand, if we try to solve it by a linear planner it has to generate as
many as
bs + (bs) 2 + (bs) 3 +…+ (bs) d-1
= O (bs) d .
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Further for linear ordering of these plans, we require a significant amount of
search among these plans. The total search complexity for linear ordering will
be O (bs) 2d . On the other hand, in a hierarchical plan, at each level, we select 1
out of b plans. So, the time required to eliminate inconsistent plans is O (b)
and the time required to find a linear ordering at each level is O (s). So, if
there are d levels, the ordering time of plans is O (s .d). Now, we can compare
the ordering time of a hierarchical planner with respect to a linear planner.
The factor of improvement of a hierarchical planner with respect to a linear
planner can be given by {(b s) 2d - (s d) / (s d) } =( b 2 d s 2 d –1 / d) –1.
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