This is a homework question, exactly as follows:
The heuristic path algorithm (Pohl, 1977) is a best-first search in which the evaluation function is f(n) = (2-w)g(n) + wh(n).
For what values of w is this complete?
Here's what I know:
w = 0: f(n)=2g(n) --> Uniform Cost Search, which is complete.
w = 1: f(n)=g(n) + h(n) --> A*, which is complete.
w = 2: f(n)=2h(n) --> greedy Best First Search, which is not complete.
What about all other values of w?
Please don't just give the answer, help me get to the solution.
Interesting thing about "all other values of w" for w>2: They all have the form f(n) = h(n) - g(n) with some constants in front of h and g. What impact, if any, does subtracting the cost have on completeness? Seems you should be able to generalize from there.