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

the offspring of Q (fig. 4.8(b)) and the f’ at U through Q is compared less
to the f’ at U through R (this in fact is obvious, since g(U) via Q is 2, while
g(U) via R is 3). So, we prefer Q to R as a parent of U and, consequently,
we delink the arc from node R to node U (vide fig. 4.8(b) and (c)). It may be
noted that we would do the same de-linking operation, if U had offsprings
too.
RR T U
Fig. 4.8 (c): The modified tree after de-linking of the arc
from node R to node U in fig. 4.8 (b).
The third point to be discussed on the A* algorithm is to mark the arcs
with back-pointers, i.e., from child to parent nodes in the search space. This
helps in tracing the path from goal node to the root. Scrutinize fig. 4.8 (a)-(c)
for details.
The steps of the algorithm have already been illustrated. Now, the
properties of the algorithm will be presented in detail.
Properties of Heuristic Functions
The following notations will be required for understanding the properties of
the heuristic functions.
Notations Meaning
1. C (ni, nj) cost / expenses to traverse from node ni to node nj
2. K (ni, nj) cost on the cheapest path between ni and nj
3. γ a goal node
S
P Q
4. Γ the set of goals
5. Pn- γ the path from node n to γ