## Minimin Search

**Minimin search** determines individual single-agent moves in constant time per move. The minimin search algorithm searches forward from the current state to a fixed depth determined by the informational or computational resources available. At the search horizon, the A* evaluation function f(n) = g(n) + h(n) is applied to the frontier nodes. Since all the decisions are made by a single agent, the value of an interior node is the minimum of the frontier values in the sub tree below the node. A single move is then made to the neighbour of the current state with the minimum value.

Most heuristic functions obey the triangle inequality characteristic of distance measures. As a result, f(n) = g(n) + h(n) is guaranteed to be monotonically nondecreasing along a path. Moreover, since minimum search has a fixed depth limit, we can apply depth-first branch-and-bound to prune the search tree. The performance improvement due to branch-and-bound is quite dramatic in some cases extending the achievable seearch horizon by a factor of five relative to brute-force minimum search on sliding-title puzzles.

Minimin search with branch-and-bound is an algorithm for evaluating the immediate neighbours of the current node. As such, it is run until the best child is identified at which point the chosen move is executed in the real world. We can view the static evaluation function combined with lookahead search as simply a more accurate but computationally more expensive, heuristic function. In fact, it provides an entire spectrum of heuristic functions trading off accuracy for cast, depending on the search horizon.

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