Necessary Expansions in Templateastar Where W>1 Is Wrong

[lior8]

we can see that in here that the loop goes over all nodes, not only closed ones, and compares g+h which is optimal, against f of the goal which can be bounded-suboptimal. This can lead to only generated nodes being counted as necessary.

[lior8]

A* here takes both W and a Phi function, and for weighted A* there are two equivalent functions: g/w+h and g+wh.
The latter gives us the behavior we want in terms of necessary expansions, but when it is the former, it no longer holds.
We can limit the correctness of necessary expansions in WA* to only optimal, or the g+wh case (i.e., the default phi function). Another option is to try and find some way to count the necessary expansions for every Phi.