# Questions tagged [consistent-heuristic]

For questions related to consistent heuristics, which are heuristics whose estimate is always less than or equal to the estimated distance from any neighboring vertex to the goal, plus the cost of reaching that neighbor.

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### Given an admissible/consistent heuristic $h(n)$, would the tree and graph search versions of A* return the optimal path with $g(n)=2h(n)$?

I know that, if the heuristic function is admissible and consistent, then the A* algorithm always returns an optimal solution. But for the following situation, does A* search return optimal solution? ...
45 views

### Is $\min(h_1(s),\ h_2(s))$ consistent?

If $h_1(s)$ is a consistent heuristic and $h_2(s)$ is a admissible heuristic, is $\min(h_1(s),\ h_2(s))$ consistent?
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### If an heuristic is not admissible, can it be consistent?

I am solving a problem in which, according to the given values, the heuristic is not admissible. According to my calculation from other similar problems, it should be consistent, as well as keeping in ...
23 views

### Can an inadmissable heuristic be consistent? [duplicate]

If something is inadmissible, can we just assume it's also inconsistent? Also, I understand how to check if a heuristic is inadmissible, but I'm still a bit confused on checking consistency. If I have ...
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### If $h_i$ are consistent and admissible, are their sum, maximum, minimum and average also consistent and admissible?

Consider the following question: $n$ vehicles occupy squares $(1, 1)$ through $(n, 1)$ (i.e., the bottom row) of an $n \times n$ grid. The vehicles must be moved to the top row but in reverse order; ...
I understand that, in tree search, an admissible heuristic implies that $A*$ is optimal. The intuitive way I think about this is as follows: Let $P$ and $Q$ be two costs from any respective nodes $p$ ...