Iterative Deepening A* Star Explanation

Question

Can somebody explain about Iterative Deepening A*? I still don't understand how it works. Iterative deepening search w/ Depth First Search, and If still not found the solution; increase the Depth++ until found solution.

If Iterative deepening using Depth, then Iterative Deepening A* use what to limit their search?

Here are a picture if you need to explain how it IDA* Works, i just don't understand how it works.

(1,2,4,9) and etc, is the step

0+2=2 is f(n)=g(n)+h(n)

Answer 1

If Iterative deepening using Depth, then Iterative Deepening A* use what to limit their search?

The naive implementation of IDA* would just have something like threshold++ at the end of every iteration, similar to your depth++ above. This is to keep IDA* admissible.

A better algorithm (that still keeps IDA* admissible) would be to increase the threshold by the next smallest g() cost that is available (from the closed set to the open set).

See: http://webdocs.cs.ualberta.ca/~jonathan/PREVIOUS/Courses/657/Notes/10.Single-agentSearch.pdf